Encoding method, decoding method, encoding device, and decoding device

Abstract

This encoding method for encoding coordinates of multiple vertices of a polygon included in a three-dimensional mesh comprises: deriving, by using coordinates of a first vertex among the multiple vertices and coordinates of a second vertex different from the first vertex among the multiple vertices, coordinates of a third vertex connected to the first vertex and the second vertex (S421), wherein the coordinates of the third vertex are located on a vector derived by using multiple normal vectors related to the three-dimensional mesh. For example, the vector may be a normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex.

Description

Encoding method, decoding method, encoding device, and decoding device

[0001] The present disclosure relates to encoding methods and the like.

[0002] In US Pat. No. 6,299,549 a method and apparatus for encoding and decoding three-dimensional mesh data is proposed.

[0003] Japanese Patent Application Laid-Open No. 2006-187015

[0004] Further improvements are desired in the process of encoding or decoding the coordinates of the vertices of a three-dimensional mesh.The present disclosure aims to improve the process of encoding or decoding the coordinates of the vertices of a three-dimensional mesh.

[0005] An encoding method according to one aspect of the present disclosure is an encoding method for encoding the coordinates of multiple vertices of a polygon contained in a three-dimensional mesh, which derives the coordinates of a first vertex among the multiple vertices and the coordinates of a second vertex among the multiple vertices that is different from the first vertex, and derives the coordinates of a third vertex connected to the first vertex and the second vertex, and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

[0006] A decoding method according to one aspect of the present disclosure is a decoding method for decoding the coordinates of multiple vertices of a polygon contained in a three-dimensional mesh, which uses the coordinates of a first vertex among the multiple vertices and the coordinates of a second vertex among the multiple vertices that is different from the first vertex to derive the coordinates of a third vertex connected to the first vertex and the second vertex, and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

[0007] These comprehensive or specific aspects may be realized as a system, an apparatus, an integrated circuit, a computer program, or a computer-readable recording medium such as a CD-ROM, or may be realized as any combination of a system, an apparatus, an integrated circuit, a computer program, and a recording medium.

[0008] The present disclosure may contribute to improvements in encoding processes related to the coordinates of vertices of a three-dimensional mesh.

[0009] 1 is a conceptual diagram showing a three-dimensional mesh according to an embodiment. FIG. 2 is a conceptual diagram showing basic elements of a three-dimensional mesh according to an embodiment. FIG. 3 is a conceptual diagram showing mapping according to an embodiment. FIG. 4 is a block diagram showing a configuration example of an encoding / decoding system according to an embodiment. FIG. 5 is a block diagram showing a configuration example of an encoding device according to an embodiment. FIG. 6 is a block diagram showing another configuration example of an encoding device according to an embodiment. FIG. 7 is a block diagram showing another configuration example of a decoding device according to an embodiment. FIG. 8 is a block diagram showing another configuration example of a decoding device according to an embodiment. FIG. 9 is a block diagram showing another configuration example of a decoding device according to an embodiment. FIG. 10 is a conceptual diagram showing another configuration example of a bit stream according to an embodiment. FIG. 11 is a conceptual diagram showing yet another configuration example of a bit stream according to an embodiment. FIG. 12 is a block diagram showing a specific example of an encoding / decoding system according to an embodiment. FIG. 13 is a conceptual diagram showing an example configuration of point cloud data according to an embodiment. FIG. 14 is a conceptual diagram showing an example data file of point cloud data according to an embodiment. FIG. 15 is a conceptual diagram showing an example configuration of mesh data according to an embodiment. FIG. 16 is a conceptual diagram showing an example data file of mesh data according to an embodiment. FIG. 17 is a conceptual diagram showing types of three-dimensional data according to an embodiment. FIG. 18 is a block diagram showing an example configuration of a three-dimensional data encoder according to an embodiment. FIG. 19 is a block diagram showing an example configuration of a three-dimensional data decoder according to an embodiment. FIG. 19 is a block diagram showing another configuration example of a three-dimensional data encoder according to an embodiment. FIG. 19 is a block diagram showing another configuration example of a three-dimensional data decoder according to an embodiment. FIG. 1 is a conceptual diagram showing a specific example of encoding processing according to an embodiment. FIG. 2 is a conceptual diagram showing a specific example of decoding processing according to an embodiment. FIG. 3 is a block diagram showing an implementation example of an encoding device according to an embodiment. FIG. 4 is a block diagram showing an implementation example of a decoding device according to an embodiment. FIG. 5 is a block diagram showing another configuration example of an encoding / decoding system according to an embodiment. FIG. 6 is a block diagram showing another configuration example of an encoding device according to an embodiment. FIG. 7 is a block diagram showing another configuration example of a decoding device according to an embodiment. FIG. 8 is a flow diagram showing processing by an encoding device according to an embodiment. FIG. 9 is an explanatory diagram conceptually showing encoding of a mesh frame according to an embodiment. FIG. 10 is a flow diagram showing processing by a decoding device according to an embodiment. FIG. 11 is an explanatory diagram conceptually showing decoding of a mesh frame according to an embodiment. FIG. 12 is a block diagram showing an example configuration of an encoding device according to an embodiment.1 is a block diagram showing an example of the configuration of a decoding device according to an embodiment. FIG. 2 is a diagram showing an example of a base mesh according to an embodiment. FIG. 3 is a diagram showing an example of a first mesh after a subdivision process has been performed once on the base mesh according to an embodiment. FIG. 4 is a diagram showing an example of a second mesh obtained by further performing a subdivision process once on the first mesh according to an embodiment. FIG. 5 is a diagram showing an example of a process for determining positions of subdivision points according to an embodiment. FIG. 6 is a diagram showing an example of a process for determining positions of subdivision points according to an embodiment. FIG. 7 is a diagram showing an example of a method for correcting vertices of a 3D mesh before subdivision according to an embodiment. FIG. 8 is a diagram showing an example of a 3D mesh according to an embodiment. FIG. 9 is a flowchart showing an example of a process procedure for subdivision process according to an embodiment. FIG. 10 is a diagram showing an example of a method for correcting subdivision points according to an embodiment. FIG. 11 is a flowchart showing an example of a process procedure for subdivision process according to an embodiment. FIG. 12 is a diagram showing an example of a process for determining positions of subdivision points according to an embodiment. FIG. 13 is a diagram showing an example of a decoded 3D mesh according to an embodiment. FIG. 14 is a diagram showing an example of a decoded 3D mesh when a constraint method according to an embodiment is applied. FIG. 15 is a diagram showing an example of a decoded 3D mesh when another constraint method according to an embodiment is applied. FIG. 16 is a flowchart showing an example of a process procedure for subdivision process according to an embodiment.

[0010] <Summary of the Disclosure> Three-dimensional (3D) meshes are used in computer graphics images, for example, which may be composed of multiple temporally distinct frames, each of which may be represented by a 3D mesh.

[0011] A 3D mesh is composed of vertex information indicating the positions of each of the vertices in 3D space, connectivity information indicating the connections between the vertices, and attribute information indicating the attributes of each vertex or face. Each face is constructed according to the connectivity between the vertices. Various computer graphics images can be expressed using such 3D meshes.

[0012] Furthermore, for transmission and storage of the 3D mesh, efficient encoding and decoding of the 3D mesh is expected. For efficient encoding and decoding of the 3D mesh, arithmetic coding and decoding may be used.

[0013] Further improvements are desired in the encoding or decoding process for three-dimensional data. The present disclosure aims to improve the encoding or decoding process for three-dimensional data.

[0014] Hereinafter, examples of inventions that can be obtained from the disclosure of this specification will be given, and the effects and the like that can be obtained from these inventions will be explained.

[0015] An encoding method according to one aspect of the present disclosure is an encoding method for encoding the coordinates of multiple vertices of a polygon contained in a three-dimensional mesh, which derives the coordinates of a first vertex among the multiple vertices and the coordinates of a second vertex among the multiple vertices that is different from the first vertex, and derives the coordinates of a third vertex connected to the first vertex and the second vertex, and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

[0016] According to this encoding method, the coordinates of the third vertex can be determined on a vector derived using multiple normal vectors. This may allow the coordinates of the third vertex to be closer to the coordinates of the vertices of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertices of the input three-dimensional mesh. Therefore, it is possible to improve encoding efficiency.

[0017] For example, the vector may be a normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex. This may allow the coordinates of the third vertex to be closer to the coordinates of the vertex of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data of information (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertex of the input three-dimensional mesh. This can improve coding efficiency.

[0018] For example, the plurality of normal vectors may include a normal vector of the first vertex and a normal vector of the second vertex, and the encoding method can appropriately derive a normal vector of a midpoint between the coordinates of the first vertex and the coordinates of the second vertex by using the normal vector of the first vertex and the normal vector of the second vertex.

[0019] For example, the plurality of normal vectors may include a plurality of normal vectors relating to a plane including the first vertex and the second vertex, and the encoding method can appropriately derive the normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex by using the plurality of normal vectors relating to the plane including the first vertex and the second vertex.

[0020] For example, the three-dimensional mesh may be a base mesh generated based on an input three-dimensional mesh, and the encoding method can improve encoding efficiency by appropriately deriving the coordinates of a third vertex to be added to the base mesh.

[0021] For example, the 3D mesh may be a sub-divided mesh obtained by sub-dividing a base mesh generated based on an input 3D mesh, whereby the encoding method can improve encoding efficiency by appropriately deriving the coordinates of a third vertex to be added to the sub-divided mesh.

[0022] For example, in deriving the coordinates of the third vertex, the coordinates of the third vertex before correction may be derived using the coordinates of the first vertex and the coordinates of the second vertex, and the coordinates of the third vertex before correction may be derived using the coordinates of the third vertex before correction and the vector. According to this, the encoding method can determine the third vertex by correcting the third vertex before correction that has been derived using a predetermined method, for example.

[0023] For example, in deriving the coordinates of the third vertex, if a first method is selected from among a plurality of methods for determining the coordinates of the sub-division points, the coordinates of the third vertex may be derived using the coordinates of the third vertex before the correction and the vector, and if a second method is selected from among the plurality of methods, the coordinates of the third vertex before the correction may be determined as the coordinates of the third vertex. This allows the encoding method to be switched between using the third vertex before the correction and using the third vertex after the correction, thereby improving encoding efficiency.

[0024] A decoding method according to one aspect of the present disclosure is a decoding method for decoding the coordinates of multiple vertices of a polygon contained in a three-dimensional mesh, which uses the coordinates of a first vertex among the multiple vertices and the coordinates of a second vertex among the multiple vertices that is different from the first vertex to derive the coordinates of a third vertex connected to the first vertex and the second vertex, and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

[0025] According to this decoding method, the coordinates of the third vertex can be determined on a vector derived using multiple normal vectors. This may allow the coordinates of the third vertex to approach the coordinates of the vertices of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data of information (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertices of the input three-dimensional mesh. Therefore, it is possible to improve coding efficiency.

[0026] For example, the vector may be a normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex. This may allow the coordinates of the third vertex to be closer to the coordinates of the vertex of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data of information (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertex of the input three-dimensional mesh. This can improve coding efficiency.

[0027] For example, the plurality of normal vectors may include a normal vector of the first vertex and a normal vector of the second vertex, and the decoding method can appropriately derive a normal vector of a midpoint between the coordinates of the first vertex and the coordinates of the second vertex by using the normal vector of the first vertex and the normal vector of the second vertex.

[0028] For example, the plurality of normal vectors may include a plurality of normal vectors relating to a plane including the first vertex and the second vertex, and the decoding method can appropriately derive the normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex by using the plurality of normal vectors relating to the plane including the first vertex and the second vertex.

[0029] For example, the 3D mesh may be a base mesh generated based on information decoded from a bitstream, whereby the decoding method can improve coding efficiency by appropriately deriving the coordinates of a third vertex added to the base mesh.

[0030] For example, the 3D mesh may be a sub-division mesh obtained by sub-dividing a base mesh generated based on information decoded from a bitstream, whereby the decoding method can improve coding efficiency by appropriately deriving the coordinates of a third vertex added to the sub-division mesh.

[0031] For example, in deriving the coordinates of the third vertex, the coordinates of the third vertex before correction may be derived using the coordinates of the first vertex and the coordinates of the second vertex, and the coordinates of the third vertex before correction may be derived using the coordinates of the third vertex before correction and the vector. According to this, the decoding method can determine the third vertex by correcting the third vertex before correction that has been derived using a predetermined method, for example.

[0032] For example, in deriving the coordinates of the third vertex, if a first method is selected from among a plurality of methods for determining the coordinates of the sub-division points, the coordinates of the third vertex may be derived using the coordinates of the third vertex before the correction and the vector, and if a second method is selected from among the plurality of methods, the coordinates of the third vertex before the correction may be determined as the coordinates of the third vertex. This allows the decoding method to switch between using the third vertex before the correction and using the third vertex after the correction, thereby improving coding efficiency.

[0033] An encoding device according to one aspect of the present disclosure is an encoding device that encodes the coordinates of multiple vertices of a polygon included in a three-dimensional mesh, and includes a memory and a circuit that can access the memory. In operation, the circuit uses the coordinates of a first vertex among the multiple vertices and the coordinates of a second vertex among the multiple vertices that is different from the first vertex to derive the coordinates of a third vertex connected to the first vertex and the second vertex, and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

[0034] This allows the encoding device to determine the coordinates of the third vertex on a vector derived using multiple normal vectors. This potentially allows the coordinates of the third vertex to be closer to the coordinates of the vertices of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertices of the input three-dimensional mesh. This improves encoding efficiency.

[0035] A decoding device according to one aspect of the present disclosure is a decoding device that decodes the coordinates of multiple vertices of a polygon included in a three-dimensional mesh, and includes a memory and a circuit that can access the memory. In operation, the circuit uses the coordinates of a first vertex among the multiple vertices and the coordinates of a second vertex among the multiple vertices that is different from the first vertex to derive the coordinates of a third vertex connected to the first vertex and the second vertex, and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

[0036] According to this, the decoding device can determine the coordinates of the third vertex on a vector derived using multiple normal vectors. As a result, it is possible to make the coordinates of the third vertex closer to the coordinates of the vertices of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data of information (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertices of the input three-dimensional mesh. Therefore, it is possible to improve coding efficiency.

[0037] These comprehensive or specific aspects may be realized as a system, an apparatus, an integrated circuit, a computer program, or a recording medium such as a computer-readable CD-ROM, or may be realized as any combination of a system, an apparatus, an integrated circuit, a computer program, or a recording medium.

[0038] Hereinafter, the embodiments will be specifically described with reference to the drawings.

[0039] The embodiments described below are all comprehensive or specific examples. The numerical values, shapes, materials, components, component placement and connection configurations, steps, and step order shown in the following embodiments are merely examples and are not intended to limit the present invention. Furthermore, among the components in the following embodiments, components that are not described in the independent claims that represent the highest concepts are described as optional components.

[0040] (Embodiment) In this embodiment, an encoding method, a decoding method, etc. will be described.

[0041] <Expressions and Terms> The following expressions and terms are used herein.

[0042] (1) Three-dimensional Mesh A three-dimensional mesh is a collection of multiple faces, and represents, for example, a three-dimensional object. A three-dimensional mesh is mainly composed of vertex information, connectivity information, and attribute information. A three-dimensional mesh may be expressed as a polygon mesh or a mesh. A three-dimensional mesh may also vary over time. A three-dimensional mesh may include metadata related to the vertex information, connectivity information, and attribute information, and may also include other additional information.

[0043] (2) Vertex Information Vertex information is information indicating a vertex. For example, the vertex information indicates the position of a vertex in a three-dimensional space. Furthermore, a vertex corresponds to a vertex of a face that constitutes a three-dimensional mesh. Vertex information may be expressed as "geometry." Furthermore, vertex information may be expressed as position information.

[0044] (3) Connection Information Connection information is information that indicates connections between vertices. For example, connection information indicates connections for forming faces or edges of a three-dimensional mesh. Connection information may be expressed as "Connectivity." Connection information may also be expressed as face information.

[0045] (4) Attribute Information Attribute information is information that indicates attributes of a vertex or a face. For example, attribute information indicates attributes such as a color, an image, and a normal vector associated with a vertex or a face. Attribute information may be expressed as "texture."

[0046] (5) Faces A face is an element that constitutes a three-dimensional mesh. Specifically, a face is a polygon on a plane in three-dimensional space. For example, a face can be defined as a triangle in three-dimensional space.

[0047] (6) Plane A plane is a two-dimensional plane in a three-dimensional space. For example, a polygon is formed on a plane, and multiple polygons are formed on multiple planes.

[0048] (7) Bitstream: A bitstream corresponds to coded information. A bitstream may also be referred to as a stream, a coded bitstream, a compressed bitstream, or a coded signal.

[0049] (8) Encoding and Decoding The term encoding may be substituted with terms such as storing, including, writing, describing, signaling, sending, notifying, saving, or compressing, and these terms may be interchangeable. For example, encoding information may mean including the information in a bitstream. Also, encoding information into a bitstream may mean encoding the information to generate a bitstream that includes the encoded information.

[0050] Additionally, the term "decode" may be replaced with terms such as "read," "decode," "read," "load," "derive," "obtain," "receive," "extract," "reconstruct," "reconstruct," "decompress," or "decompress," and these terms may be interchangeable. For example, decoding information may mean obtaining information from a bitstream. Decoding information from a bitstream may mean decoding the bitstream to obtain information contained in the bitstream.

[0051] (9) Ordinal Numbers In the description, ordinal numbers such as first and second may be assigned to components, etc. These ordinal numbers may be changed as appropriate. Furthermore, new ordinal numbers may be assigned to components, etc., or removed. Furthermore, these ordinal numbers may be assigned to elements in order to identify them, and may not correspond to a meaningful order.

[0052] <Three-dimensional mesh> Fig. 1 is a conceptual diagram showing a three-dimensional mesh according to this embodiment. A three-dimensional mesh is composed of multiple faces. For example, each face is a triangle. The vertices of these triangles are defined in three-dimensional space. The three-dimensional mesh then represents a three-dimensional object. Each face may have a color or an image.

[0053] FIG. 2 is a conceptual diagram showing the basic elements of a three-dimensional mesh according to this embodiment. A three-dimensional mesh is composed of vertex information, connection information, and attribute information. The vertex information indicates the positions of the vertices of a face in three-dimensional space. The connection information indicates the connections between the vertices. A face can be identified by the vertex information and connection information. In other words, a colorless three-dimensional object is formed in three-dimensional space by the vertex information and connection information.

[0054] The attribute information may be associated with a vertex or a face. The attribute information associated with a vertex may be expressed as "Attribute Per Point." The attribute information associated with a vertex may indicate an attribute of the vertex itself, or may indicate an attribute of a face connected to the vertex.

[0055] For example, a color may be associated with a vertex as attribute information. The color associated with a vertex may be the color of the vertex itself, or the color of a face connected to the vertex. The color of a face may be the average of multiple colors associated with multiple vertices of the face. Furthermore, a normal vector may be associated with a vertex or a face as attribute information. Such a normal vector can represent the front and back of a face.

[0056] A two-dimensional image may be associated with a surface as attribute information. The two-dimensional image associated with a surface is also expressed as a texture image or an "Attribute Map." Information indicating mapping between the surface and the two-dimensional image may be associated with the surface as attribute information. Information indicating such mapping may be expressed as mapping information, vertex information of a texture image, texture coordinates, or "Attribute UV Coordinate."

[0057] Furthermore, information such as color, image, and moving image used as attribute information may be expressed as "parametric space."

[0058] The attribute information allows texture to be reflected on the three-dimensional object. That is, a three-dimensional object having color is formed in three-dimensional space based on the vertex information, connection information, and attribute information.

[0059] In the above, the attribute information is associated with the vertices or faces, but it may also be associated with the edges.

[0060] 3 is a conceptual diagram illustrating mapping according to this embodiment. For example, a region of a two-dimensional image on a two-dimensional plane can be mapped onto a surface of a three-dimensional mesh in three-dimensional space. Specifically, coordinate information of the region in the two-dimensional image is associated with the surface of the three-dimensional mesh. As a result, an image of the mapped region in the two-dimensional image is reflected on the surface of the three-dimensional mesh.

[0061] By using the mapping, the 2D image used as attribute information can be separated from the 3D mesh. For example, in encoding the 3D mesh, the 2D image may be encoded by an image encoding method or a video encoding method.

[0062] <System Configuration> Fig. 4 is a block diagram showing an example of the configuration of a coding / decoding system according to this embodiment. In Fig. 4, the coding / decoding system includes a coding device 100 and a decoding device 200.

[0063] For example, the encoding device 100 obtains a three-dimensional mesh and encodes the three-dimensional mesh into a bitstream. Then, the encoding device 100 outputs the bitstream to the network 300. For example, the bitstream includes the encoded three-dimensional mesh and control information for decoding the encoded three-dimensional mesh. By encoding the three-dimensional mesh, information about the three-dimensional mesh is compressed.

[0064] The network 300 transmits a bitstream from the encoding device 100 to the decoding device 200. The network 300 may be the Internet, a wide area network (WAN), a local area network (LAN), or a combination of these. The network 300 is not necessarily limited to bidirectional communication, and may be a unidirectional communication network for terrestrial digital broadcasting, satellite broadcasting, or the like.

[0065] Furthermore, the network 300 can be replaced by a recording medium such as a DVD (Digital Versatile Disc) or a BD (Blu-Ray Disc (registered trademark)).

[0066] The decoding device 200 obtains a bitstream and decodes a three-dimensional mesh from the bitstream. By decoding the three-dimensional mesh, information about the three-dimensional mesh is expanded. For example, the decoding device 200 decodes the three-dimensional mesh according to a decoding method corresponding to the encoding method used by the encoding device 100 to encode the three-dimensional mesh. That is, the encoding device 100 and the decoding device 200 perform encoding and decoding according to encoding methods and decoding methods that correspond to each other.

[0067] The 3D mesh before encoding may also be referred to as an original 3D mesh, and the 3D mesh after decoding may also be referred to as a reconstructed 3D mesh.

[0068] 5 is a block diagram showing an example of the configuration of a coding device 100 according to this embodiment. For example, the coding device 100 includes a vertex information encoder 101, a connection information encoder 102, and an attribute information encoder 103.

[0069] The vertex information encoder 101 is an electrical circuit that encodes vertex information. For example, the vertex information encoder 101 encodes the vertex information into a bitstream according to a format defined for the vertex information.

[0070] The connection information encoder 102 is an electrical circuit that encodes the connection information, for example, the connection information encoder 102 encodes the connection information into a bitstream according to a format defined for the connection information.

[0071] The attribute information encoder 103 is an electric circuit that encodes the attribute information. For example, the attribute information encoder 103 encodes the attribute information into a bit stream in accordance with a format defined for the attribute information.

[0072] The vertex information, connectivity information, and attribute information may be coded using variable-length coding or fixed-length coding, such as Huffman coding or context-adaptive binary arithmetic coding (CABAC).

[0073] The vertex information encoder 101, the connection information encoder 102, and the attribute information encoder 103 may be integrated together, or each of the vertex information encoder 101, the connection information encoder 102, and the attribute information encoder 103 may be further subdivided into multiple components.

[0074] 6 is a block diagram showing another example of the configuration of the encoding device 100 according to this embodiment. For example, the encoding device 100 includes a pre-processor 104 and a post-processor 105 in addition to the configuration shown in FIG.

[0075] The preprocessor 104 is an electrical circuit that performs processing before encoding the vertex information, connectivity information, and attribute information. For example, the preprocessor 104 may perform a conversion process, a separation process, a multiplexing process, or the like on the 3D mesh before encoding. More specifically, for example, the preprocessor 104 may separate the vertex information, connectivity information, and attribute information from the 3D mesh before encoding.

[0076] The post-processor 105 is an electrical circuit that performs processing after the vertex information, connection information, and attribute information are encoded. For example, the post-processor 105 may perform conversion processing, separation processing, multiplexing processing, or the like on the encoded vertex information, connection information, and attribute information. More specifically, for example, the post-processor 105 may multiplex the encoded vertex information, connection information, and attribute information into a bitstream. Furthermore, for example, the post-processor 105 may further perform variable-length coding on the encoded vertex information, connection information, and attribute information.

[0077] 7 is a block diagram showing an example of the configuration of a decoding device 200 according to this embodiment. For example, the decoding device 200 includes a vertex information decoder 201, a connection information decoder 202, and an attribute information decoder 203.

[0078] The vertex information decoder 201 is an electrical circuit that decodes vertex information. For example, the vertex information decoder 201 decodes vertex information from a bitstream according to a format defined for the vertex information.

[0079] The connection information decoder 202 is an electrical circuit that decodes the connection information, for example, the connection information decoder 202 decodes the connection information from the bitstream according to a format defined for the connection information.

[0080] The attribute information decoder 203 is an electric circuit that decodes the attribute information. For example, the attribute information decoder 203 decodes the attribute information from the bitstream in accordance with a format defined for the attribute information.

[0081] The vertex information, connection information, and attribute information may be decoded using variable length decoding or fixed length decoding, which may correspond to Huffman coding, context-adaptive binary arithmetic coding (CABAC), or the like.

[0082] The vertex information decoder 201, the connection information decoder 202, and the attribute information decoder 203 may be integrated together, or each of the vertex information decoder 201, the connection information decoder 202, and the attribute information decoder 203 may be further subdivided into multiple components.

[0083] 8 is a block diagram showing another example of the configuration of the decoding device 200 according to this embodiment. For example, the decoding device 200 includes a pre-processor 204 and a post-processor 205 in addition to the configuration shown in FIG.

[0084] The preprocessor 204 is an electrical circuit that performs processing before decoding the vertex information, connection information, and attribute information. For example, the preprocessor 204 may perform conversion processing, separation processing, multiplexing processing, or the like on the bitstream before decoding the vertex information, connection information, and attribute information.

[0085] More specifically, for example, the preprocessor 204 may separate a sub-bitstream corresponding to vertex information, a sub-bitstream corresponding to connectivity information, and a sub-bitstream corresponding to attribute information from the bitstream. Also, for example, the preprocessor 204 may perform variable-length decoding on the bitstream in advance before decoding the vertex information, connectivity information, and attribute information.

[0086] The post-processor 205 is an electrical circuit that performs processing after the vertex information, connection information, and attribute information are decoded. For example, the post-processor 205 may perform conversion processing, separation processing, multiplexing processing, or the like on the decoded vertex information, connection information, and attribute information. More specifically, for example, the post-processor 205 may multiplex the decoded vertex information, connection information, and attribute information onto a three-dimensional mesh.

[0087] <Bitstream> Vertex information, connection information, and attribute information are coded and stored in a bitstream. The relationship between this information and the bitstream is shown below.

[0088] 9 is a conceptual diagram showing an example of the configuration of a bitstream according to this embodiment. In this example, connection information, vertex information, and attribute information are integrated in the bitstream. For example, the connection information, vertex information, and attribute information may be included in a single file.

[0089] Furthermore, multiple portions of this information may be stored sequentially, such as a first portion of connection information, a first portion of vertex information, a first portion of attribute information, a second portion of connection information, a second portion of vertex information, a second portion of attribute information, etc. These multiple portions may correspond to multiple portions that are different in time, multiple portions that are different in space, or multiple different faces.

[0090] Furthermore, the storage order of the connection information, vertex information, and attribute information is not limited to the above example, and a storage order different from the above example may be used.

[0091] 10 is a conceptual diagram showing another example of the configuration of a bitstream according to this embodiment. In this example, a plurality of files are included in the bitstream, and connection information, vertex information, and attribute information are stored in different files. Here, a file containing connection information, a file containing vertex information, and a file containing attribute information are shown, but the storage format is not limited to this example. For example, two types of information among the connection information, vertex information, and attribute information may be included in one file, and the remaining type of information may be included in another file.

[0092] Alternatively, the information may be split and stored in more files. For example, multiple pieces of connectivity information may be stored in multiple files, multiple pieces of vertex information may be stored in multiple files, or multiple pieces of attribute information may be stored in multiple files. These multiple pieces may correspond to multiple temporally different pieces, multiple spatially different pieces, or multiple different faces.

[0093] Furthermore, the storage order of the connection information, vertex information, and attribute information is not limited to the above example, and a storage order different from the above example may be used.

[0094] 11 is a conceptual diagram showing another example of the configuration of a bitstream according to this embodiment. In this example, the bitstream is composed of multiple separable sub-bitstreams, and connection information, vertex information, and attribute information are stored in different sub-bitstreams.

[0095] Here, a sub-bitstream containing connection information, a sub-bitstream containing vertex information, and a sub-bitstream containing attribute information are shown, but the storage format is not limited to this example.

[0096] For example, two types of information among the connection information, vertex information, and attribute information may be included in one sub-bitstream, and the remaining type of information may be included in another sub-bitstream. Specifically, attribute information of a two-dimensional image or the like may be stored in a sub-bitstream that complies with an image coding method, separate from the sub-bitstreams of the connection information and vertex information.

[0097] Also, each sub-bitstream may include multiple files, and multiple pieces of connectivity information may be stored in multiple files, multiple pieces of vertex information may be stored in multiple files, or multiple pieces of attribute information may be stored in multiple files.

[0098] 9, 10, and 11, and a storage order different from the above examples may be used. For example, the vertex information, connection information, and attribute information may be stored in the bitstream in this order. Alternatively, the connection information, connection information, and attribute information may be stored in the bitstream in any of the following orders: connection information, attribute information, and vertex information; vertex information, attribute information, and connection information; attribute information, connection information, and vertex information; or attribute information, vertex information, and connection information.

[0099] Furthermore, each of the connection information, vertex information, and attribute information may be divided into a plurality of data, and the plurality of data may be stored in a cyclical or random order within the bitstream.

[0100] 12 is a block diagram showing a specific example of an encoding / decoding system according to this embodiment. In FIG. 12, the encoding / decoding system includes a three-dimensional data encoding system 110, a three-dimensional data decoding system 210, and an external connector 310.

[0101] The three-dimensional data encoding system 110 includes a controller 111, an input / output processor 112, a three-dimensional data encoder 113, a three-dimensional data generator 115, and a system multiplexer 114. The three-dimensional data decoding system 210 includes a controller 211, an input / output processor 212, a three-dimensional data decoder 213, a system demultiplexer 214, a presenter 215, and a user interface 216.

[0102] In the three-dimensional data encoding system 110, sensor data is input from a sensor terminal to a three-dimensional data generator 115. The three-dimensional data generator 115 generates three-dimensional data, such as point cloud data or mesh data, from the sensor data and inputs it to a three-dimensional data encoder 113.

[0103] For example, the three-dimensional data generator 115 generates vertex information, and generates connection information and attribute information corresponding to the vertex information. The three-dimensional data generator 115 may process the vertex information when generating the connection information and attribute information. For example, the three-dimensional data generator 115 may reduce the amount of data by deleting duplicate vertices, or may transform the vertex information (such as by shifting its position, rotating it, or normalizing it). The three-dimensional data generator 115 may also render the attribute information.

[0104] Furthermore, although the three-dimensional data generator 115 is a component of the three-dimensional data encoding system 110 in FIG. 12, it may be arranged externally and independently of the three-dimensional data encoding system 110.

[0105] The sensor terminal that provides the sensor data for generating the three-dimensional data may be, for example, a moving body such as an automobile, a flying object such as an airplane, a mobile terminal, a camera, etc. Furthermore, a distance sensor such as a LIDAR, a millimeter wave radar, an infrared sensor, or a range finder, a stereo camera, or a combination of multiple monocular cameras may also be used as the sensor terminal.

[0106] The sensor data may be the distance (position) of the object, monocular camera images, stereo camera images, color, reflectance, sensor attitude, orientation, gyro, sensing position (GPS information or altitude), speed, acceleration, sensing time, temperature, air pressure, humidity, or magnetism.

[0107] The three-dimensional data encoder 113 corresponds to the encoding device 100 shown in FIG. 5 and other figures. For example, the three-dimensional data encoder 113 encodes three-dimensional data to generate encoded data. The three-dimensional data encoder 113 also generates control information when encoding the three-dimensional data. The three-dimensional data encoder 113 then inputs the encoded data together with the control information to the system multiplexer 114.

[0108] The encoding method for the three-dimensional data may be an encoding method using geometry or an encoding method using a video codec. Here, the encoding method using geometry may also be referred to as a geometry-based encoding method. The encoding method using a video codec may also be referred to as a video-based encoding method.

[0109] The system multiplexer 114 multiplexes the encoded data and control information input from the 3D data encoder 113 to generate multiplexed data using a specified multiplexing method. The system multiplexer 114 may multiplex other media such as video, audio, subtitles, application data, or document files, or reference time information, along with the encoded data and control information of the 3D data. Furthermore, the system multiplexer 114 may multiplex attribute information related to the sensor data or the 3D data.

[0110] For example, the multiplexed data may have a file format for storage or a packet format for transmission. As these formats, ISOBMFF or a format based on ISOBMFF may be used. Also, MPEG-DASH, MMT, MPEG-2 TS Systems, RTP, or the like may be used.

[0111] The multiplexed data is then output as a transmission signal to the external connector 310 by the input / output processor 112. The multiplexed data may be transmitted as a transmission signal by wire or wirelessly. Alternatively, the multiplexed data is stored in an internal memory or a storage device. The multiplexed data may be transmitted to a cloud server via the Internet or may be stored in an external storage device.

[0112] For example, the transmission or storage of the multiplexed data is performed by a method according to the medium for transmission or storage, such as broadcasting or communication. The communication protocol may be http, ftp, TCP, UDP, IP, or a combination thereof. Furthermore, a pull-type communication method or a push-type communication method may be used.

[0113] For wired transmission, Ethernet (registered trademark), USB, RS-232C, HDMI (registered trademark), coaxial cable, etc. may be used. For wireless transmission, 3GPP (registered trademark), 3G / 4G / 5G defined by IEEE, wireless LAN, Wi-Fi, Bluetooth, or millimeter wave may be used. For broadcasting, for example, DVB-T2, DVB-S2, DVB-C2, ATSC3.0, or ISDB-S3 may be used.

[0114] The sensor data may be input to the three-dimensional data generator 115 or the system multiplexer 114. The three-dimensional data or encoded data may be output as a transmission signal directly to the external connector 310 via the input / output processor 112. The transmission signal output from the three-dimensional data encoding system 110 is input to the three-dimensional data decoding system 210 via the external connector 310.

[0115] Furthermore, each operation of the three-dimensional data encoding system 110 may be controlled by a controller 111 that executes an application program.

[0116] In the three-dimensional data decoding system 210, a transmission signal is input to an input / output processor 212. The input / output processor 212 decodes multiplexed data having a file format or a packet format from the transmission signal and inputs the multiplexed data to a system demultiplexer 214. The system demultiplexer 214 obtains coded data and control information from the multiplexed data and inputs them to a three-dimensional data decoder 213. The system demultiplexer 214 may extract other media or reference time information from the multiplexed data.

[0117] The three-dimensional data decoder 213 corresponds to the decoding device 200 shown in Fig. 7 etc. For example, the three-dimensional data decoder 213 decodes three-dimensional data from the encoded data based on a predefined encoding method. The three-dimensional data is then presented to the user by the presenter 215.

[0118] Additionally, additional information such as sensor data may be input to the presenter 215. The presenter 215 may present three-dimensional data based on the additional information. Additionally, a user instruction may be input from a user terminal to the user interface 216. Then, the presenter 215 may present three-dimensional data based on the input instruction.

[0119] The input / output processor 212 may acquire the three-dimensional data and the encoded data from the external connector 310 .

[0120] Furthermore, each operation of the three-dimensional data decoding system 210 may be controlled by a controller 211 that executes an application program.

[0121] 13 is a conceptual diagram showing an example of the configuration of point cloud data according to this embodiment. The point cloud data is data of a group of points representing a three-dimensional object.

[0122] Specifically, a point cloud is made up of a plurality of points, and has position information indicating the three-dimensional coordinate position of each point and attribute information indicating the attribute of each point. The position information is also expressed as geometry.

[0123] The type of attribute information may be, for example, color, reflectance, etc. One point may be associated with attribute information of one type, one point may be associated with attribute information of multiple different types, or one point may be associated with attribute information having multiple values ​​for the same type.

[0124] 14 is a conceptual diagram showing an example of a data file of point cloud data according to this embodiment. This example shows a case where there is a one-to-one correspondence between position information items and attribute information items, and shows position information and attribute information for N points that make up the point cloud data. In this example, the position information is information indicating a three-dimensional coordinate position using three axes, x, y, and z, and the attribute information is information indicating a color using RGB. A PLY file or the like can be used as a representative data file for point cloud data.

[0125] 15 is a conceptual diagram showing an example of the configuration of mesh data according to this embodiment. Mesh data is data used in CG (Computer Graphics) and the like, and is three-dimensional mesh data that shows the three-dimensional shape of an object using multiple surfaces. Each surface is also expressed as a polygon, and has a polygonal shape such as a triangle or a rectangle.

[0126] Specifically, a 3D mesh is composed of a plurality of points constituting a point cloud, as well as a plurality of edges and a plurality of faces. Each point is also expressed as a vertex or a position. Each edge corresponds to a line segment connected by two vertices. Each face corresponds to an area surrounded by three or more edges.

[0127] Furthermore, a three-dimensional mesh has position information indicating the three-dimensional coordinate positions of vertices. The position information is also expressed as vertex information or geometry. A three-dimensional mesh also has connection information indicating the relationship between multiple vertices that make up an edge or a face. The connection information is also expressed as connectivity. A three-dimensional mesh also has attribute information indicating the attributes of the vertices, edges, or faces. The attribute information in a three-dimensional mesh is also expressed as texture.

[0128] For example, the attribute information may indicate the color, reflectance, or normal vector for a vertex, edge, or face. The direction of the normal vector may represent the front and back of the face.

[0129] The mesh data may be stored in a data file format such as an object file.

[0130] 16 is a conceptual diagram showing an example of a data file of mesh data according to this embodiment. In this example, the data file includes position information G(1) to G(N) of N vertices that make up the three-dimensional mesh, and attribute information A1(1) to A1(N) of the N vertices. Also, in this example, M pieces of attribute information A2(1) to A2(M) are included. The attribute information items do not need to correspond one-to-one to vertices or faces. Furthermore, attribute information need not exist.

[0131] The connection information is represented by a combination of vertex indices. n[1, 3, 4] indicates a triangular face formed by three vertices, n=1, n=3, and n=4. Also, m[2, 4, 6] indicates that the attribute information of m=2, m=4, and m=6 corresponds to the three vertices, respectively.

[0132] Furthermore, the actual contents of the attribute information may be written in a separate file. A pointer to that content may be associated with a vertex, a face, or the like. For example, attribute information indicating an image for a face may be stored in a two-dimensional attribute map file. The file name of the attribute map and two-dimensional coordinate values ​​in the attribute map may be written in attribute information A2(1) to A2(M). The method of specifying attribute information for a face is not limited to these methods, and any method may be used.

[0133] 17 is a conceptual diagram showing types of three-dimensional data according to this embodiment. Point cloud data and mesh data may represent static objects or dynamic objects. A static object is an object that does not change over time, and a dynamic object is an object that changes over time. A static object may correspond to three-dimensional data for any point in time.

[0134] For example, point cloud data for a given point in time may be referred to as a PCC frame, mesh data for a given point in time may be referred to as a mesh frame, and PCC frames and mesh frames may be simply referred to as frames.

[0135] The area of ​​the object may be limited to a certain range, as in normal video data, or may not be limited, as in map data. The density of points or surfaces may be determined in various ways. Sparse point cloud data or sparse mesh data may be used, or dense point cloud data or dense mesh data may be used.

[0136] Next, encoding and decoding of a point cloud or a three-dimensional mesh will be described. The device, process, or syntax for encoding and decoding vertex information of a three-dimensional mesh in the present disclosure may be applied to encoding and decoding of a point cloud. The device, process, or syntax for encoding and decoding of a point cloud in the present disclosure may be applied to encoding and decoding vertex information of a three-dimensional mesh.

[0137] Furthermore, a device, process, or syntax for encoding and decoding attribute information of a point cloud in the present disclosure may be applied to encoding and decoding connectivity information or attribute information of a three-dimensional mesh.Furthermore, a device, process, or syntax for encoding and decoding connectivity information or attribute information of a three-dimensional mesh in the present disclosure may be applied to encoding and decoding attribute information of a point cloud.

[0138] Furthermore, at least some of the processing may be shared between the encoding and decoding of point cloud data and the encoding and decoding of mesh data, thereby reducing the scale of the circuit and software program.

[0139] 18 is a block diagram showing an example configuration of a three-dimensional data encoder 113 according to this embodiment. In this example, the three-dimensional data encoder 113 includes a vertex information encoder 121, an attribute information encoder 122, a metadata encoder 123, and a multiplexer 124. The vertex information encoder 121, the attribute information encoder 122, and the multiplexer 124 may correspond to the vertex information encoder 101, the attribute information encoder 103, the post-processor 105, etc. in FIG.

[0140] In this example, the three-dimensional data encoder 113 encodes the three-dimensional data according to a geometry-based encoding method, which takes into account the three-dimensional structure. In addition, in the geometry-based encoding method, attribute information is encoded using configuration information obtained in encoding the vertex information.

[0141] Specifically, first, vertex information, attribute information, and metadata included in three-dimensional data generated from sensor data are input to a vertex information encoder 121, an attribute information encoder 122, and a metadata encoder 123, respectively. Here, connectivity information included in the three-dimensional data may be treated in the same way as attribute information. In addition, in the case of point cloud data, position information may be treated as vertex information.

[0142] The vertex information encoder 121 encodes the vertex information into compressed vertex information and outputs the compressed vertex information as encoded data to the multiplexer 124. The vertex information encoder 121 also generates metadata for the compressed vertex information and outputs it to the multiplexer 124. The vertex information encoder 121 also generates configuration information and outputs it to the attribute information encoder 122.

[0143] The attribute information encoder 122 uses the configuration information generated by the vertex information encoder 121 to encode the attribute information into compressed attribute information and outputs the compressed attribute information as encoded data to the multiplexer 124. The attribute information encoder 122 also generates metadata of the compressed attribute information and outputs it to the multiplexer 124.

[0144] The metadata encoder 123 encodes compressible metadata into compressed metadata and outputs the compressed metadata as encoded data to the multiplexer 124. The metadata encoded by the metadata encoder 123 may be used to encode vertex information and attribute information.

[0145] The multiplexer 124 multiplexes the compressed vertex information, the compressed vertex information metadata, the compressed attribute information, the compressed attribute information metadata, and the compressed metadata into a bitstream, and then inputs the bitstream to the system layer.

[0146] 19 is a block diagram showing an example configuration of a three-dimensional data decoder 213 according to this embodiment. In this example, the three-dimensional data decoder 213 includes a vertex information decoder 221, an attribute information decoder 222, a metadata decoder 223, and a demultiplexer 224. The vertex information decoder 221, the attribute information decoder 222, and the demultiplexer 224 may correspond to the vertex information decoder 201, the attribute information decoder 203, the preprocessor 204, and the like in FIG.

[0147] In this example, the three-dimensional data decoder 213 decodes three-dimensional data according to a geometry-based encoding method. The three-dimensional structure is taken into consideration in the decoding according to the geometry-based encoding method. Furthermore, in the decoding according to the geometry-based encoding method, attribute information is decoded using configuration information obtained in decoding vertex information.

[0148] Specifically, first, a bitstream is input from the system layer to a demultiplexer 224. The demultiplexer 224 separates compressed vertex information, compressed vertex information metadata, compressed attribute information, compressed attribute information metadata, and compressed metadata from the bitstream. The compressed vertex information and compressed vertex information metadata are input to a vertex information decoder 221. The compressed attribute information and compressed attribute information metadata are input to an attribute information decoder 222. The metadata is input to a metadata decoder 223.

[0149] The vertex information decoder 221 decodes vertex information from the compressed vertex information using metadata of the compressed vertex information. The vertex information decoder 221 also generates configuration information and outputs it to the attribute information decoder 222. The attribute information decoder 222 decodes attribute information from the compressed attribute information using the configuration information generated by the vertex information decoder 221 and the metadata of the compressed attribute information. The metadata decoder 223 decodes metadata from the compressed metadata. The metadata decoded by the metadata decoder 223 may be used to decode the vertex information and the attribute information.

[0150] Thereafter, the vertex information, attribute information, and metadata are output as three-dimensional data from the three-dimensional data decoder 213. Note that, for example, this metadata is metadata of the vertex information and attribute information, and can be used in an application program.

[0151] 20 is a block diagram showing another example configuration of the three-dimensional data encoder 113 according to the present embodiment. In this example, the three-dimensional data encoder 113 includes a vertex image generator 131, an attribute image generator 132, a metadata generator 133, a video encoder 134, a metadata encoder 123, and a multiplexer 124. The vertex image generator 131, the attribute image generator 132, and the video encoder 134 may correspond to the vertex information encoder 101 and the attribute information encoder 103 in FIG. 6 , etc.

[0152] In this example, the 3D data encoder 113 encodes the 3D data according to a video-based encoding method. In encoding according to the video-based encoding method, multiple 2D images are generated from the 3D data, and the multiple 2D images are encoded according to a video encoding method. Here, the video encoding method may be High Efficiency Video Coding (HEVC), Versatile Video Coding (VVC), or the like.

[0153] Specifically, first, vertex information and attribute information included in three-dimensional data generated from sensor data are input to a metadata generator 133. The vertex information and attribute information are then input to a vertex image generator 131 and an attribute image generator 132, respectively. The metadata included in the three-dimensional data is then input to a metadata encoder 123. Here, connectivity information included in the three-dimensional data may be treated in the same way as attribute information. In the case of point cloud data, position information may be treated as vertex information.

[0154] The metadata generator 133 generates map information of a plurality of two-dimensional images from the vertex information and attribute information, and inputs the map information to the vertex image generator 131, the attribute image generator 132, and the metadata encoder 123.

[0155] The vertex image generator 131 generates a vertex image based on the vertex information and map information, and inputs the generated image to the video encoder 134. The attribute image generator 132 generates an attribute image based on the attribute information and map information, and inputs the generated image to the video encoder 134.

[0156] The video encoder 134 encodes the vertex images and attribute images into compressed vertex information and compressed attribute information, respectively, in accordance with a video encoding method, and outputs the compressed vertex information and compressed attribute information as encoded data to the multiplexer 124. The video encoder 134 also generates metadata for the compressed vertex information and metadata for the compressed attribute information, and outputs them to the multiplexer 124.

[0157] The metadata encoder 123 encodes the compressible metadata into compressed metadata and outputs the compressed metadata as encoded data to the multiplexer 124. The compressible metadata includes map information. The metadata encoded by the metadata encoder 123 may also be used to encode vertex information and attribute information.

[0158] The multiplexer 124 multiplexes the compressed vertex information, the compressed vertex information metadata, the compressed attribute information, the compressed attribute information metadata, and the compressed metadata into a bitstream, and then inputs the bitstream to the system layer.

[0159] 21 is a block diagram showing another example configuration of the 3D data decoder 213 according to this embodiment. In this example, the 3D data decoder 213 includes a vertex information generator 231, an attribute information generator 232, a video decoder 234, a metadata decoder 223, and a demultiplexer 224. The vertex information generator 231, the attribute information generator 232, and the video decoder 234 may correspond to the vertex information decoder 201 and the attribute information decoder 203 in FIG. 8, etc.

[0160] In this example, the 3D data decoder 213 decodes the 3D data according to a video-based coding method. In the decoding according to the video-based coding method, a plurality of 2D images are decoded according to a video coding method, and 3D data is generated from the plurality of 2D images. Here, the video coding method may be High Efficiency Video Coding (HEVC), Versatile Video Coding (VVC), or the like.

[0161] Specifically, first, a bitstream is input from the system layer to the demultiplexer 224. The demultiplexer 224 separates compressed vertex information, compressed vertex information metadata, compressed attribute information, compressed attribute information metadata, and compressed metadata from the bitstream. The compressed vertex information, compressed vertex information metadata, compressed attribute information, and compressed attribute information metadata are input to the video decoder 234. The compressed metadata is input to the metadata decoder 223.

[0162] The video decoder 234 decodes the vertex images in accordance with the video encoding method. At this time, the video decoder 234 decodes the vertex images from the compressed vertex information using the metadata of the compressed vertex information. Then, the video decoder 234 inputs the vertex images to the vertex information generator 231. The video decoder 234 also decodes the attribute images in accordance with the video encoding method. At this time, the video decoder 234 decodes the attribute images from the compressed attribute information using the metadata of the compressed attribute information. Then, the video decoder 234 inputs the attribute images to the attribute information generator 232.

[0163] The metadata decoder 223 decodes metadata from the compressed metadata. The metadata decoded by the metadata decoder 223 includes map information used to generate vertex information and attribute information. The metadata decoded by the metadata decoder 223 may also be used to decode vertex images and attribute images.

[0164] The vertex information generator 231 reproduces vertex information from the vertex image in accordance with the map information included in the metadata decoded by the metadata decoder 223. The attribute information generator 232 reproduces attribute information from the attribute image in accordance with the map information included in the metadata decoded by the metadata decoder 223.

[0165] Thereafter, the vertex information, attribute information, and metadata are output as three-dimensional data from the three-dimensional data decoder 213. Note that, for example, this metadata is metadata of the vertex information and attribute information, and can be used in an application program.

[0166] Fig. 22 is a conceptual diagram showing a specific example of encoding processing according to this embodiment. Fig. 22 shows a three-dimensional data encoder 113 and a description encoder 148. In this example, the three-dimensional data encoder 113 includes a two-dimensional data encoder 141 and a mesh data encoder 142. The two-dimensional data encoder 141 includes a texture encoder 143. The mesh data encoder 142 includes a vertex information encoder 144 and a connection information encoder 145.

[0167] The vertex information encoder 144, the connection information encoder 145, and the texture encoder 143 may correspond to the vertex information encoder 101, the connection information encoder 102, and the attribute information encoder 103 in FIG.

[0168] For example, the two-dimensional data encoder 141 operates as a texture encoder 143 and generates a texture file by encoding the texture corresponding to the attribute information as two-dimensional data according to an image encoding method or a video encoding method.

[0169] The mesh data encoder 142 also operates as a vertex information encoder 144 and a connectivity information encoder 145, and generates a mesh file by encoding the vertex information and connectivity information. The mesh data encoder 142 may further encode mapping information for textures. The encoded mapping information may then be included in the mesh file.

[0170] The description encoder 148 also generates a description file by encoding a description corresponding to metadata such as text data. The description encoder 148 may encode the description at the system layer. For example, the description encoder 148 may be included in the system multiplexer 114 of FIG. 12 .

[0171] The above operations generate a bitstream containing texture files, mesh files, and description files, which may be multiplexed into the bitstream in file formats such as glTF (Graphics Language Transmission Format) or USD (Universal Scene Description).

[0172] The three-dimensional data encoder 113 may include two mesh data encoders as the mesh data encoder 142. For example, one mesh data encoder encodes vertex information and connectivity information of a static three-dimensional mesh, and the other mesh data encoder encodes vertex information and connectivity information of a dynamic three-dimensional mesh.

[0173] Correspondingly, two mesh files may then be included in the bitstream: for example, one mesh file corresponding to a static 3D mesh and another mesh file corresponding to a dynamic 3D mesh.

[0174] Furthermore, the static three-dimensional mesh may be a three-dimensional mesh of an intraframe coded using intraprediction, and the dynamic three-dimensional mesh may be a three-dimensional mesh of an interframe coded using interprediction. Furthermore, information on the dynamic three-dimensional mesh may be differential information between vertex information or connectivity information of the three-dimensional mesh of an intraframe and vertex information or connectivity information of the three-dimensional mesh of an interframe.

[0175] Fig. 23 is a conceptual diagram showing a specific example of the decoding process according to this embodiment. Fig. 23 shows a three-dimensional data decoder 213, a description decoder 248, and a renderer 247. In this example, the three-dimensional data decoder 213 includes a two-dimensional data decoder 241, a mesh data decoder 242, and a mesh reconstructor 246. The two-dimensional data decoder 241 includes a texture decoder 243. The mesh data decoder 242 includes a vertex information decoder 244 and a connectivity information decoder 245.

[0176] The vertex information decoder 244, the connection information decoder 245, the texture decoder 243, and the mesh reconstructor 246 may correspond to the vertex information decoder 201, the connection information decoder 202, the attribute information decoder 203, and the post-processor 205 in Fig. 8. The presenter 247 may correspond to the presenter 215 in Fig. 12.

[0177] For example, the two-dimensional data decoder 241 operates as a texture decoder 243, and decodes the texture corresponding to the attribute information from the texture file as two-dimensional data in accordance with an image coding method or a video coding method.

[0178] The mesh data decoder 242 also operates as a vertex information decoder 244 and a connectivity information decoder 245 to decode vertex information and connectivity information from the mesh file. The mesh data decoder 242 may further decode mapping information for textures from the mesh file.

[0179] The description decoder 248 also decodes descriptions corresponding to metadata such as text data from the description file. The description decoder 248 may decode the descriptions at the system layer. For example, the description decoder 248 may be included in the system demultiplexer 214 of FIG. 12 .

[0180] The mesh reconstructor 246 reconstructs a 3D mesh from the vertex information, connectivity information, and textures according to the description. The renderer 247 renders and outputs the 3D mesh according to the description.

[0181] Through the above operations, a 3D mesh is reconstructed and output from a bitstream containing a texture file, a mesh file, and a description file.

[0182] The three-dimensional data decoder 213 may include two mesh data decoders as the mesh data decoder 242. For example, one mesh data decoder decodes vertex information and connectivity information of a static three-dimensional mesh, and the other mesh data decoder decodes vertex information and connectivity information of a dynamic three-dimensional mesh.

[0183] Correspondingly, two mesh files may then be included in the bitstream: for example, one mesh file corresponding to a static 3D mesh and another mesh file corresponding to a dynamic 3D mesh.

[0184] Furthermore, the static three-dimensional mesh may be a three-dimensional mesh of an intraframe coded using intraprediction, and the dynamic three-dimensional mesh may be a three-dimensional mesh of an interframe coded using interprediction. Furthermore, information on the dynamic three-dimensional mesh may be differential information between vertex information or connectivity information of the three-dimensional mesh of an intraframe and vertex information or connectivity information of the three-dimensional mesh of an interframe.

[0185] A dynamic 3D mesh coding method is sometimes called DMC (Dynamic Mesh Coding), and a video-based dynamic 3D mesh coding method is sometimes called V-DMC (Video-based Dynamic Mesh Coding).

[0186] The point cloud encoding method is sometimes called PCC (Point Cloud Compression). The point cloud video-based encoding method is sometimes called V-PCC (Video-based Point Cloud Compression). The point cloud geometry-based encoding method is sometimes called G-PCC (Geometry-based Point Cloud Compression).

[0187] <Implementation Example> Fig. 24 is a block diagram showing an implementation example of the encoding device 100 according to this embodiment. The encoding device 100 includes a circuit 151 and a memory 152. For example, multiple components of the encoding device 100 shown in Fig. 5 etc. are implemented by the circuit 151 and memory 152 shown in Fig. 24.

[0188] The circuit 151 is a circuit that performs information processing and is a circuit that can access the memory 152. For example, the circuit 151 is a dedicated or general-purpose electric circuit that encodes a three-dimensional mesh. The circuit 151 may be a processor such as a CPU. Alternatively, the circuit 151 may be a collection of multiple electric circuits.

[0189] The memory 152 is a dedicated or general-purpose memory that stores information used by the circuit 151 to encode the three-dimensional mesh. The memory 152 may be an electric circuit and may be connected to the circuit 151. The memory 152 may also be included in the circuit 151. The memory 152 may also be a collection of multiple electric circuits. The memory 152 may also be a magnetic disk, an optical disk, or the like, and may also be expressed as a storage, a recording medium, or the like. The memory 152 may also be a non-volatile memory or a volatile memory.

[0190] For example, the memory 152 may store a three-dimensional mesh or a bitstream, or may store a program for the circuit 151 to encode the three-dimensional mesh.

[0191] Note that the encoding device 100 does not necessarily have to implement all of the components shown in Figure 5 and the like, and does not necessarily have to perform all of the processes shown here. Some of the components shown in Figure 5 and the like may be included in another device, and some of the processes shown here may be executed by another device. Furthermore, the encoding device 100 may implement any combination of the components of the present disclosure, and may perform any combination of the processes of the present disclosure.

[0192] Fig. 25 is a block diagram showing an example implementation of a decoding device 200 according to this embodiment. The decoding device 200 includes a circuit 251 and a memory 252. For example, multiple components of the decoding device 200 shown in Fig. 7 and other figures are implemented by the circuit 251 and memory 252 shown in Fig. 25.

[0193] The circuit 251 is a circuit that performs information processing and is a circuit that can access the memory 252. For example, the circuit 251 is a dedicated or general-purpose electric circuit that decodes a three-dimensional mesh. The circuit 251 may be a processor such as a CPU. Alternatively, the circuit 251 may be a collection of multiple electric circuits.

[0194] The memory 252 is a dedicated or general-purpose memory that stores information for the circuit 251 to decode the 3D mesh. The memory 252 may be an electric circuit and may be connected to the circuit 251. The memory 252 may also be included in the circuit 251. The memory 252 may also be a collection of multiple electric circuits. The memory 252 may also be a magnetic disk, an optical disk, or the like, and may also be expressed as a storage, a recording medium, or the like. The memory 252 may also be a non-volatile memory or a volatile memory.

[0195] For example, the memory 252 may store a three-dimensional mesh or a bitstream, or may store a program for the circuit 251 to decode the three-dimensional mesh.

[0196] Note that the decoding device 200 does not necessarily have to implement all of the components shown in Figure 7 and the like, and does not necessarily have to perform all of the processes shown here. Some of the components shown in Figure 7 and the like may be included in another device, and some of the processes shown here may be executed by another device. Furthermore, the decoding device 200 may implement any combination of the components of the present disclosure, and may perform any combination of the processes of the present disclosure.

[0197] The encoding method and the decoding method including the steps performed by each component of the encoding device 100 and the decoding device 200 of the present disclosure may be executed by any device or system. For example, part or all of the encoding method and the decoding method may be executed by a computer including a processor, a memory, an input / output circuit, etc. In this case, the encoding method and the decoding method may be executed by the computer executing a program for causing the computer to execute the encoding method and the decoding method.

[0198] Alternatively, the program or the bitstream may be recorded on a non-transitory computer-readable recording medium such as a CD-ROM.

[0199] An example of a program may be a bitstream. For example, a bitstream including an encoded three-dimensional mesh includes syntax elements for causing the decoding device 200 to decode the three-dimensional mesh. The bitstream then causes the decoding device 200 to decode the three-dimensional mesh according to the syntax elements included in the bitstream. Thus, the bitstream may play a role similar to that of a program.

[0200] The bitstream may be an encoded bitstream containing the encoded 3D mesh, or may be a multiplexed bitstream containing the encoded 3D mesh and other information.

[0201] Furthermore, each component of the encoding device 100 and the decoding device 200 may be configured with dedicated hardware, general-purpose hardware that executes the above-mentioned programs, or a combination of these. The general-purpose hardware may be configured with a memory in which the programs are recorded and a general-purpose processor that reads and executes the programs from the memory. Here, the memory may be a semiconductor memory or a hard disk, and the general-purpose processor may be a CPU.

[0202] Furthermore, the dedicated hardware may be configured with a memory, a dedicated processor, etc. For example, the dedicated processor may execute the encoding method and the decoding method by referring to a memory for recording data.

[0203] Furthermore, as described above, each component of the encoding device 100 and the decoding device 200 may be an electric circuit. These electric circuits may form a single electric circuit as a whole, or each may be a separate electric circuit. Furthermore, these electric circuits may correspond to dedicated hardware, or may correspond to general-purpose hardware that executes the above-mentioned programs, etc. Furthermore, the encoding device 100 and the decoding device 200 may be implemented as an integrated circuit.

[0204] Furthermore, the encoding device 100 may be a transmitting device that transmits the three-dimensional mesh, and the decoding device 200 may be a receiving device that receives the three-dimensional mesh.

[0205] Displacement Encoding and Decoding The following terminology is used here by way of example:

[0206] (1) Image An image is a data unit made up of a set of pixels, and includes a picture or a block smaller than a picture. Images include both moving images and still images.

[0207] (2) Picture A picture is a unit of image processing that is made up of a set of pixels, and is also called a frame or field.

[0208] (3) Block A block is a processing unit consisting of a specific number of pixels. The term "block" shown in the following example is also used. The shape of a block is not particularly limited. A block may be, for example, a rectangular shape of M x N pixels or a square shape of M x M pixels. A block may also be a triangular shape, a circular shape, or another shape. Examples of blocks are as follows:

[0209] Slice, tile, or brick CTU, superblock, or basic division unit VPDU, processing division unit for hardware CU, processing block unit, prediction block unit (PU), or orthogonal transform block unit (TU) Sub-block

[0210] (4) Pixel or Sample A pixel or sample is the smallest point of an image, in other words, the smallest unit. Pixels or samples include not only pixels at integer positions, but also pixels at sub-pixel positions generated based on pixels at integer positions.

[0211] (5) Pixel Value or Sample Value: A pixel value or sample value is a unique value of a pixel. The pixel value or sample value may include a luma value, a chroma value, or an RGB gradation level, and may also include a depth value or a binary value of 0 or 1.

[0212] (6) Flags A flag indicates one or more bits. A flag is, for example, a parameter or index represented by two or more bits. A flag may indicate not only a value represented by a binary number, but also a value represented by a number other than a binary number.

[0213] (7) Signal: A signal is something that is symbolized or coded to transmit information. A signal includes a discrete digital signal or a continuous analog signal.

[0214] (8) Stream or Bit Stream A stream or bit stream is a digital data sequence that indicates the flow of digital data. A stream or bit stream may be a single stream, or may be configured to include multiple streams with multiple layers. A stream or bit stream may be transmitted by serial communication using a single transmission path, or may be transmitted by packet communication using multiple transmission paths.

[0215] (9) Difference: For scalar quantities, difference can include simple difference (x - y) and difference calculations, such as absolute difference (|x - y|), squared difference (x^2 - y^2), square root difference (√(x - y)), weighted difference (ax - b, where a and b are constants), or offset difference (x - y + a, where a is an offset).

[0216] (10) Sum. For scalar quantities, sums can include simple sum (x + y) and addition operations. Sum can also include absolute sum (|x + y|), sum of squares (x^2 + y^2), square root of sum (√(x + y)), weighted sum (ax + by, where a and b are constants), or offset sum (x + y + a, where a is an offset).

[0217] (11) "Based on" The expression "based on something" means that something other than that "something" may be taken into consideration. Also, "based on" can be used both when a direct result is obtained and when a result is obtained through an intermediate result.

[0218] (12) "Used" or "Using" The phrases "something was used" or "used something" mean that something other than the "something" may be taken into consideration. The phrases "used" or "used" may be used both in cases where a direct result is obtained and in cases where a result is obtained via an intermediate result.

[0219] (13) Prohibition "Prohibit" can be rephrased as "not permitted." Also, "not prohibited / prohibited" or "permitted / permitted" does not necessarily mean "obligation."

[0220] (14) "Restriction" or "Limitation" "Restriction" or "Limitation" can be rephrased as "not permitted / not allowed" or "not permitted / permitted." Furthermore, "prohibited / not prohibited" or "not permitted / permitted" does not necessarily mean "obligation." Furthermore, what is prohibited quantitatively or qualitatively may be either partial or total.

[0221] (15) Chroma The term chroma is an adjective, represented by the symbols Cb or Cr, that indicates that a sample array or a single sample represents one of the two color-difference signals associated with a primary color. The term chroma is sometimes used instead of the term chrominance.

[0222] (16) Luma The term luma is an adjective, represented by the symbols or subscripts Y or L, that indicates that a sample array or a single sample represents a monochrome signal for a primary color. The term luma is sometimes used instead of the term luminance.

[0223] The encoding / decoding system of this embodiment will be described below.

[0224] A typical three-dimensional model (also called a 3D model) digitally represents an object so that a user can explore the model using zoom, pan, and rotation in all three dimensions while it is rendered over time. One way to construct such a representation is to build a 3D mesh using triangles. The model stores the positions of the triangle vertices, their connectivity to each other, and their associated attributes (such as normals or UV patches).

[0225] Storing all this information in uncompressed form requires a very large storage space and therefore a very large bandwidth for transmission. The triangles that form the mesh often have repeating patterns and similar properties, especially in temporal and spatial neighborhoods. These repetitions can be exploited to develop efficient encoding and decoding methods for storage and transmission. One such encoding and decoding method is Video-based Dynamic Mesh Coding (V-DMC).

[0226] 26 is a block diagram showing another example of the configuration of the encoding / decoding system according to this embodiment. As shown in FIG. 26, the encoding / decoding system includes an encoding device 100 and a decoding device 200.

[0227] The encoding / decoding system accepts input three-dimensional meshes (also called 3D meshes) in the form of three-dimensional coordinates of vertices (vertex information), connectivity (connection information) and associated attributes (attribute information), which may include texture maps as well as geometry.

[0228] The encoding device 100 takes an input 3D mesh (also referred to as an input 3D mesh or input mesh) in the form of three-dimensional coordinates of vertices, connectivity, and associated attributes. The encoding device 100 encodes all associated information into a stream. The stream may consist of a single bitstream or multiple bitstreams.

[0229] The network 300 transmits the stream generated by the encoding device to the decoding device 200. The network 300 may be the Internet, a wide area network (WAN), a local area network (LAN), or any combination thereof. Furthermore, the network 300 is not necessarily limited to a two-way communication network, but may also be a one-way communication network that transmits broadcast waves such as terrestrial digital broadcasting or satellite broadcasting. Instead of the network 300, a recording medium such as a digital versatile disc (DVD) or a blue-ray disc (BD) on which a stream is recorded may be used.

[0230] The stream is transmitted to a decoding device 200 via a network 300. The decoding device 200 decodes the bitstream and generates a 3D mesh using the 3D coordinates, connectivity, and associated attributes of the decoded vertices. The decoding device 200 outputs the generated 3D mesh (also referred to as an output 3D mesh or output mesh).

[0231] FIG. 27 is a diagram showing another example of the configuration of the encoding device 100.

[0232] As shown in FIG. 27, the encoding device 100 includes a preprocessor 1102 and a compressor 1107 .

[0233] The encoding device 100 reads an input mesh 1101 and passes it to a preprocessor 1102. The preprocessor 1102 processes the input mesh 1101 to extract a base mesh 1103, displacement data 1104, texture data 1105, and an attribute map 1106. The encoding device 100 passes the extracted base mesh 1103, displacement data 1104, texture data 1105, and attribute map 1106 to a compressor 1107.

[0234] The compressor 1107 can compress the base mesh 1103 , the displacement data 1104 , the texture data 1105 and the attribute map 1106 to generate a bitstream 1108 that can be sent to the decoding device 200 .

[0235] FIG. 28 is a diagram showing another example of the configuration of the decoding device 200.

[0236] As shown in FIG. 28, the decoding device 200 includes a decompressor 2102 and a post-processor 2107 .

[0237] The decoding device 200 reads a bitstream 2101 and passes it to a decompressor 2102. The decompressor 2102 decompresses a base mesh 2103, displacement data 2104, texture data 2105, and an attribute map 2106 from the bitstream 2101, and passes them to a post-processor 2107. An example of the displacement data 2104 is a displacement vector.

[0238] The post-processor 2107 processes the base mesh 2103 according to the displacement data 2104 and the attribute map 2106 to generate an output mesh 2108. The post-processor 2107 may further use information from the texture data 2105 to generate the output mesh 2108.

[0239] The encoding process performed by the encoding device 100 will be described in detail below.

[0240] Fig. 29 is a flow diagram showing the processing of the encoding device 100. Fig. 30 is an explanatory diagram conceptually showing the encoding of mesh frames. The processing of the encoding device 100 will be described with reference to Figs. 29 and 30.

[0241] In step S101, the encoding device 100 reads a three-dimensional mesh frame that is an input mesh frame. The input mesh frame is a mesh frame that is input to the encoding device 100. An example of a three-dimensional mesh frame that is an input mesh frame is shown as mesh frame 1301 (see FIG. 30 ).

[0242] In step S102, the encoding device 100 performs a decimation process on the input mesh frame read in step S101 to generate a base mesh frame having fewer vertices than the input mesh frame. The base mesh frame generated by decimating the mesh frame 1301 is shown as a base mesh frame 1302 (see FIG. 30 ). Note that the vertices of the base mesh frame 1302 may be located at positions different from those of the mesh frame 1301. Note that the base mesh frame 1302 may be subdivided by adding new vertices between existing vertices.

[0243] In step S103, the encoding device 100 calculates displacement information that the decoding device 200 uses to reconstruct a mesh frame. The displacement information corresponds to a displacement vector directed from a vertex of the base mesh frame generated in step S102 to a vertex of the input mesh frame. One method for calculating the displacement information is to subtract the coordinates of the vertex of the base mesh frame from the coordinates of the vertex of the input mesh frame. The displacement information calculated from the mesh frame 1301 and the base mesh frame 1302 is shown as displacement information 1303 (see FIG. 30 ). The displacement information 1303 is in vector format, in other words, expressed as a displacement vector. Note that the displacement information is converted into wavelet coefficients by wavelet transform, and then the wavelet coefficients can be assigned to planes of a video frame and encoded using a video codec.

[0244] In step S104, the encoding device 100 encodes the base mesh frame generated in step S102, the displacement information generated in step S103, the attribute map, and the texture data into a bitstream (corresponding to a compressed bitstream). An example of the bitstream is shown as bitstream 1304 (see FIG. 30).

[0245] Specifically, the bitstream 1304 includes vertex coordinates and connectivity information for vertices A, C, E, and F, displacement information, a video bitstream including texture data, and a compressed attribute map (see FIG. 30). The displacement information includes displacement information for displacing vertices based on vertex coordinates obtained from the subdivided base mesh frame. The compressed attribute map is texture coordinates for applying texture data to a mesh frame reconstructed using the base mesh frame and the displacement information.

[0246] The decoding process performed by the decoding device 200 will be described in detail below.

[0247] Fig. 31 is a flow diagram showing the processing of the decoding device 200. Fig. 32 is an explanatory diagram conceptually showing the decoding of a three-dimensional mesh. The processing of the decoding device 200 will be described with reference to Figs. 31 and 32.

[0248] In step S201, the decoding device 200 decodes a base mesh frame from a bitstream (corresponding to a compressed bitstream). An example of the decoded base mesh frame (corresponding to a decoded base mesh frame) is shown as a decoded base mesh frame 2301 (see FIG. 32).

[0249] In step S202, the decoding device 200 generates new vertices between existing vertices by subdivision of the base mesh frame decoded in step S201. An example of a mesh frame including the subdivided vertices is shown as mesh frame 2302 (see FIG. 32). At this point, the mesh frame 2302 includes all the vertices and connectivity relationships of the original mesh frame. Note that the positions of the vertices included in the mesh frame 2302 may differ from the corresponding vertices included in the input mesh frame.

[0250] In step S203, the decoding device 200 decodes the disparity information from the bitstream (corresponding to the compressed bitstream). An example of the decoded disparity information is shown as disparity information 2303 (see FIG. 32). The disparity information 2303 is in vector format, in other words, expressed as a disparity vector. At this time, the decoding device 200 decodes the wavelet coefficients using a video decoder and performs an inverse wavelet transform to restore the disparity vector.

[0251] In step S204, the decoding device 200 reconstructs the shape of the mesh frame by moving the vertices of the base mesh frame, including the subdivided vertices, to new positions using the displacement information. The decoding device 200 further reconstructs the decoded 3D mesh by applying texture data to the faces generated by the vertices and connectivity information of the mesh frame. An example of a reconstructed mesh frame is shown as mesh frame 2304 (see FIG. 32).

[0252] <Configuration Example of Encoding Device> Next, a configuration example of an encoding device will be described. Fig. 33 is a block diagram showing a configuration example of an encoding device 600. An input three-dimensional mesh, which is a three-dimensional mesh made up of a plurality of faces (e.g., polygons such as triangles or quadrangles) that represent the three-dimensional shape of an object, and an input texture map, which is a texture map that represents a pattern on the surface of the object, are input to the encoding device 600. The encoding device 600 generates a bitstream by compression-encoding the input three-dimensional mesh and the input texture map.

[0253] This encoding device 600 includes a thinning unit 601, a texture coordinate determination unit 602, a base mesh encoding unit 603, a base mesh decoding unit 604, a subdivision unit 605, a displacement vector calculation unit 606, a displacement vector encoding unit 607, a displacement vector decoding unit 608, a three-dimensional mesh reconstruction unit 609, a texture conversion unit 610, a texture encoding unit 611, and a multiplexing unit 612.

[0254] The thinning unit 601 performs thinning processing on the input three-dimensional mesh. Specifically, the thinning unit 601 generates a three-dimensional mesh by thinning out one or more vertices from the input three-dimensional mesh.

[0255] The texture coordinate determination unit 602 determines texture coordinates corresponding to the vertices of each face included in the 3D mesh whose vertices have been thinned out. Here, the 3D mesh whose vertices have been thinned out and its corresponding texture coordinates are collectively referred to as a base mesh.

[0256] The base mesh encoding unit 603 encodes the base mesh to generate a base mesh bitstream. The base mesh decoding unit 604 decodes the base mesh bitstream to generate a decoded base mesh. The subdivision unit 605 subdivides the decoded base mesh to generate a subdivided decoded base mesh with finer faces.

[0257] The displacement vector calculation unit 606 calculates a displacement vector for each vertex of each face included in the subdivision decoded base mesh. This displacement vector is used to deform the subdivision decoded base mesh to match the input 3D mesh. Specifically, a displacement vector is generated for each of multiple vertices included in the subdivision decoded base mesh. For example, the displacement vector may be the difference between the positions of corresponding vertices included in the subdivision decoded base mesh and the input 3D mesh. More specifically, the displacement vector may be a vector extending from a first vertex included in the subdivision decoded base mesh frame to a second vertex included in the input 3D mesh that corresponds to the first vertex. Alternatively, the displacement vector may be a vector extending from a vertex of the subdivision decoded base mesh to a face included in the input 3D mesh.

[0258] The disparity vector encoding unit 607 encodes a plurality of disparity vectors to generate a disparity vector bit stream, and the disparity vector decoding unit 608 decodes the disparity vector bit stream to generate a plurality of decoded disparity vectors.

[0259] The disparity vector encoding unit 607 encodes a plurality of disparity vectors to generate a disparity vector bit stream, and the disparity vector decoding unit 608 decodes the disparity vector bit stream to generate a plurality of decoded disparity vectors.

[0260] The three-dimensional mesh reconstruction unit 609 reconstructs a decoded three-dimensional mesh using the plurality of decoded displacement vectors and the sub-divided decoded base mesh. Specifically, the three-dimensional mesh reconstruction unit 609 generates a decoded three-dimensional mesh by transforming the sub-divided decoded base mesh using the plurality of decoded displacement vectors.

[0261] The texture conversion unit 610 converts the input texture map into a layout that corresponds to the decoded 3D mesh based on the input 3D mesh and the decoded 3D mesh, thereby generating a converted texture map. Specifically, the texture conversion unit 610 changes the texture coordinates of each first vertex of the input texture map to the texture coordinates of a second vertex that corresponds to the first vertex and is included in the decoded 3D mesh.

[0262] The texture encoding unit 611 generates a texture bitstream by encoding the transformed texture map. The multiplexing unit 612 generates a bitstream by multiplexing the base mesh video stream, the displacement vector video stream, and the texture bitstream. That is, the bitstream includes the encoded base mesh, the encoded displacement vector, and the encoded transformed texture map.

[0263] <Configuration Example of Decoding Device> Next, a configuration example of a decoding device will be described. FIG. 34 is a block diagram showing a configuration example of a decoding device 700. The decoding device 700 generates a decoded 3D mesh and a decoded texture map by decoding a bitstream. The bitstream is generated by encoding a 3D mesh composed of multiple faces (e.g., polygons such as triangles or quadrangles) representing the 3D shape of an object, and a texture map representing a pattern on the surface of the object. For example, this bitstream is encoded by the encoding device 600 shown in FIG. 33.

[0264] The decoding device 700 includes a separating unit 701 , a base mesh decoding unit 702 , a subdivision unit 703 , a displacement vector decoding unit 704 , a 3D mesh reconstruction unit 705 , and a texture decoding unit 706 .

[0265] The separation unit 701 separates a base mesh stream, a displacement vector bit stream, and a texture bit stream from the bit stream. The base mesh decoding unit 702 decodes the base mesh stream to generate a decoded base mesh including a 3D mesh and texture coordinates corresponding to the 3D mesh. This decoded base mesh corresponds to the decoded base mesh output from the base mesh decoding unit 604 shown in Figure 33.

[0266] The subdivision unit 703 generates a subdivided decoded base mesh with finer faces by subdividing the decoded base mesh, in the same manner as the subdivision unit 605 shown in FIG.

[0267] The displacement vector decoding unit 704 generates a decoded displacement vector by decoding the displacement vector bitstream. The 3D mesh reconstruction unit 705 reconstructs a decoded 3D mesh using the decoded displacement vector and the subdivision decoded base mesh. These processes are similar to the processes of the displacement vector decoding unit 608 and the 3D mesh reconstruction unit 609 shown in Figure 33. The texture decoding unit 706 generates a decoded texture map by decoding the texture bitstream.

[0268] <Subdivision Processing> Next, the subdivision processing performed in the subdivision unit 605 will be described. Note that the processing performed in the subdivision unit 703 is similar to the processing performed in the subdivision unit 605, and the processing of the subdivision unit 605 will be described below as a representative example. Fig. 35 is a diagram showing an example of a base mesh. The base mesh shown in Fig. 35 includes vertices A, B, and C, and edges AB, BC, and CA connecting the vertices A, B, and C.

[0269] Figure 36 is a diagram showing an example of a first mesh after a single subdivision process has been performed on the base mesh shown in Figure 35. In the first mesh shown in Figure 36, vertices D, E, and F are inserted into the base mesh shown in Figure 35. Edges AB, BC, and CA are also divided into edges AD and DB, edges BE and EC, and edges CF and FA, respectively. Edges DE, EF, and FD are also added.

[0270] Figure 37 is a diagram showing an example of a second mesh obtained by further performing a subdivision process once on the first mesh shown in Figure 36. In the second mesh shown in Figure 37, vertices G, H, I, J, K, L, M, N, and O are inserted into the first mesh shown in Figure 36. Furthermore, each edge is divided and new edges are added. By repeating this division process a predetermined number of times, the base mesh is subdivided and the faces are refined.

[0271] <Sub-division point insertion process> Next, a method for determining the positions of vertices (hereinafter also referred to as sub-division points) to be inserted when dividing an edge in the sub-division process will be described. Figures 38 and 39 are diagrams showing an example of the process for determining the positions of these sub-division points.

[0272] 38, the subdivision unit 605 determines a subdivision point for dividing the edge v0v1 by using a weighted average of the coordinates of multiple vertices. For example, the subdivision unit 605 may determine the midpoint X of the edge v0v1 as the subdivision point for the edge v0v1.

[0273] Alternatively, the subdivision unit 605 may determine a subdivision point Y for dividing the edge v0 / v1 using the vertices v0 and v1 as well as multiple vertices connected to these vertices v0 and v1. For example, the coordinate of the subdivision point Y may be a weighted average of the coordinates of the eight vertices v0, v1, v2, v3, v4, v5, v6, and v7.

[0274] In the example shown in FIG. 39 , the subdivision unit 605 determines a subdivision point Y for dividing edge v0 / v1 using the normal vector n0 of vertex v0 and the normal vector n1 of vertex v1. For example, the subdivision unit 605 derives a vector d0 based on the normal vector n0 of vertex v0, a plane a that is perpendicular to the normal vector n0 and includes vertex v0, and the midpoint X of edge v0 / v1. Vector d0 is a vector whose starting point is X, whose ending point is a point on plane a, and which is perpendicular to plane a. Similarly, the subdivision unit 605 derives a vector d1 based on the normal vector n1 of vertex v1, a plane b that is perpendicular to vector n1 and includes vertex v1, and the midpoint X of edge v0 / v1. Vector d1 is a vector whose starting point is X, whose ending point is a point on plane b, and which is perpendicular to plane b.

[0275] The normal vector of a vertex is calculated from the multiple normal vectors of the multiple faces to which the vertex belongs. For example, the normal vector of a vertex is calculated by taking a weighted average of the multiple normal vectors of the multiple faces to which the vertex belongs. The weights are set, for example, according to the areas of the multiple faces. The normal vector of a face is also calculated from the coordinates of the multiple vertices that make up the face.

[0276] Next, the subdivision unit 605 determines the coordinate of the subdivision point Y at which the edge v0v1 is divided by Y = X + w × (d0 + d1). In this formula, X is the coordinate of the midpoint X, Y is the coordinate of the subdivision point Y, (d0 + d1) is the resultant vector of vectors d0 and d1, and w is a scaling value for scaling the resultant vector (d0 + d1). w may be set according to the number of subdivisions. For example, w may be set to 1 / 16 the first time, 1 / 8 the second time, and 1 / 4 the third time.

[0277] 38, by determining the subdivision points for dividing the edge v0v1 using the multiple vertices connected to the edge v0v1, it may be possible to set the subdivision points at positions close to the surface of the input 3D mesh. This may reduce the amount of code for the displacement vector while maintaining the accuracy of the decoded 3D mesh.

[0278] 39, by determining the subdivision points using the normal vectors of vertices v0 and v1, it may be possible to set the subdivision points at positions close to the surface of the input 3D mesh. This may enable the amount of code for the displacement vector to be reduced while maintaining the accuracy of the decoded 3D mesh.

[0279] Note that the method for determining the sub-division points for dividing the edge v0v1 is not limited to these, and any other method may be used as long as it uniquely determines the positions of the sub-division points.

[0280] <Vertex Coordinate Correction Process> The following describes a method for correcting vertex coordinates in the subdivision process. As described in the subdivision point insertion process above, the subdivision points inserted to divide an edge can be set at positions close to the surface of the input 3D mesh but not on the edge. Meanwhile, the vertices of the base mesh are maintained as they are in the decoded base mesh. Depending on the thinning method used by the thinning unit 601, the vertices of the base mesh may be set at positions away from the input 3D mesh. For example, if the base mesh is determined to reduce the average error with respect to the input 3D mesh, the vertices of the base mesh are determined to reduce the error in the surface portion of the face. Therefore, there is a high possibility that the vertices of the base mesh will be far from the surface of the input 3D mesh. As a result, there is a possibility that the amount of code for the displacement vectors corresponding to the vertices of the base mesh may not be sufficiently reduced.

[0281] In this embodiment, a method for correcting vertices of a 3D mesh before subdivision will be described. For example, the subdivision unit 605 corrects the vertices of the base mesh after adding subdivision points in the first subdivision. Note that the subdivision unit 605 is not limited to correcting the vertices of the base mesh in the first subdivision, but may also correct the vertices of the mesh before subdivision in the Mth (M is an integer equal to or greater than 2)th subdivision (i.e., the mesh that has been subdivision M−1 times).

[0282] 40 is a diagram showing an example of a method for correcting vertices of a 3D mesh before subdivision. The subdivision unit 605 determines a correction vector dn for correcting the vertex v0 using the normal vector n0 of the vertex v0 and the midpoint Xn of the edge v0vn connected to the vertex v0. For example, the subdivision unit 605 derives the correction vector dn based on the normal vector n0 of the vertex v0, a plane cn that is perpendicular to the normal vector n0 and includes the midpoint Xn of the edge v0vn, and the vertex v0. The correction vector dn is a vector whose start point is v0 and whose end point is a point on the plane cn, and is perpendicular to the plane cn.

[0283] Next, the subdivision unit 605 determines the coordinate v0' of the corrected vertex v0 by v0' = v0 + wn × dn. In this formula, v0 is the coordinate of the vertex v0, v0' is the coordinate of the vertex v0', and wn is a scaling value for scaling the vector dn. wn may be set depending on the subdivision in which the vertex to be corrected was inserted. For example, wn may be set to a value such as 1 / 32 for the 0th time (i.e., the base mesh), 1 / 16 for the first time, 1 / 8 for the second time, and 1 / 4 for the third time.

[0284] The subdivision unit 605 determines the vector dn by, for example, dn = {(Xn-v0)*n0}*n0, where Xn is the coordinate of the midpoint Xn, v0 is the coordinate of the vertex v0, and (Xn-v0)*n0 is the dot product of the vector (Xn-v0) and the normal vector n0.

[0285] In addition, when the vertices to divide the edge v0vn are determined using the method shown in Figure 39, the subdivision unit 605 may determine the vector dn to be a vector obtained by inverting the direction of the vector corresponding to the vector d0 shown in Figure 39.

[0286] By correcting the vertex v0 using the correction vector derived in this way, the vertex of the base mesh can be brought closer to the surface of the input 3D mesh, which may reduce the amount of code for the displacement vector corresponding to the vertex of the base mesh.

[0287] FIG. 41 is a diagram showing an example of a three-dimensional mesh. FIG. 41 shows vertices v0 to v6 and their midpoints X1 to X6. As shown in FIG. 41, vertex v0 is usually connected to multiple vertices. Therefore, while the example shown in FIG. 40 shows an example in which the position of vertex v0 is corrected by one correction vector dn, the position of vertex v0 may also be corrected using multiple correction vectors.

[0288] For example, the subdivision unit 605 determines the corrected coordinate v0' of vertex v0 by using N correction vectors, as follows: v0' = v0 + (w1 × d1 + ... + wN × dN) / N. Here, N is an integer equal to or less than the number of vertices connected to v0. That is, to correct vertex v0, correction vectors of all vertices v0 to v6 connected to vertex v0 may be used, or correction vectors of some of the vertices v0 to v6 may be used. Furthermore, whether correction vectors of all vertices v0 to v6 are used or correction vectors of some of the vertices v0 to v6 may be switched depending on predetermined conditions, etc.

[0289] In the formula, v0 is the coordinate of vertex v0, v0' is the coordinate of vertex v0', vector dn (n = 1, ..., N) is a correction vector derived using the normal vector of vertex v0 and the midpoint Xn of edge v0vn connected to vertex v0, and wn (n = 1, ..., N) is a scaling value for scaling vector dn. wn may be set depending on the subdivision in which the vertex to be corrected was inserted. For example, wn may be set to a value such as 1 / 32 for the 0th time (i.e., base mesh), 1 / 16 for the first time, 1 / 8 for the second time, and 1 / 4 for the third time.

[0290] Alternatively, wn may be a value weighted according to the length of edge v0vn. For example, wn may be weighted more as the length of edge v0vn becomes shorter. Furthermore, this weighting may be performed on a value set according to the number of subdivisions in which the point was inserted.

[0291] If wn has the same value w regardless of n, the subdivision unit 605 may determine the coordinate v0' of the corrected vertex v0 by v0'=v0+w×(d1+ . . . +dN) / N.

[0292] By correcting the vertex v0 using multiple correction vectors in this way, the accuracy of the correction can be improved, and the vertices of the base mesh can be brought closer to the surface of the input 3D mesh with higher accuracy. This may result in further reduction in the amount of code required for the displacement vectors corresponding to the vertices of the base mesh.

[0293] 42 is a flowchart showing an example of the processing procedure for the subdivision process performed by the subdivision unit 605. In this example, the subdivision unit 605 repeatedly executes steps S301 to S310 for each subdivision layer. As a result, subdivision points are determined for each subdivision layer, the mesh connectivity information is updated, and the vertices included in the mesh before subdivision are corrected.

[0294] In the processing of each subdivision layer, steps S302 to S305 are repeated for each edge of the mesh before subdivision, and steps S306 to S308 are repeated for each vertex before subdivision.

[0295] In the processing of each edge of the mesh before subdivision in steps S302 to S305, the subdivision unit 605 first derives correction vectors for correcting edge endpoints corresponding to vertices before subdivision. That is, the subdivision unit 605 derives correction vectors for each of the two edge endpoints (S303). The subdivision unit 605 then stores the derived correction vectors in a memory or the like.

[0296] For example, in step S303, the subdivision unit 605 derives a correction vector using the method described with reference to FIG. 40 . For example, if the vertex for which a correction vector is to be derived is vertex v0 and the vertex located at the endpoint opposite v0 on the edge being processed is vertex vn, the subdivision unit 605 derives a correction vector d0 based on the normal vector n0 of vertex v0, a plane cn that is perpendicular to the normal vector n0 and includes the midpoint Xn of edge v0vn, and the vertex v0. The correction vector d0 is a vector whose starting point is v0 and whose ending point is a point on plane cn, and is perpendicular to plane cn. Similarly, a correction vector dn for vertex vn is derived.

[0297] Next, the subdivision unit 605 determines subdivision points for subdividing the edge (S304). For example, the subdivision unit 605 determines the subdivision points using the subdivision method shown in FIG.

[0298] In the processing of each vertex before subdivision in steps S306 to S308, the subdivision unit 605 corrects the vertices included in the mesh before subdivision using the integrated value of the correction vector corresponding to the vertex being processed (S307). Here, the integrated value of the correction vector is calculated for each vertex. The integrated value of the correction vector for the target vertex is generated by multiplying the correction vectors of the corresponding vertex and one or more vertices related to the target vertex. For example, the one or more vertices related to the target vertex are one or more vertices connected to the corresponding vertex. For example, in the example shown in FIG. 41 , the vertices related to vertex v0 are vertices v1 to v6, and the integrated value of the correction vector for vertex v0 is generated by multiplying the correction vector for vertex v0 by the multiple correction vectors for the multiple vertices v1 to v6. Similarly, in the example shown in FIG. 41 , the vertices related to vertex v1 are vertices v0, v2, and v6, and the integrated value of the correction vector for vertex v1 is generated by multiplying the correction vector for vertex v1 by the multiple correction vectors for the multiple vertices v0, v2, and v6.

[0299] For example, the subdivision unit 605 uses the integrated value (d1+ ... +dN) of the correction vector corresponding to the vertex v0 being processed (N is the number of vertices connected to the vertex being processed) to determine the coordinate v0' of the corrected vertex v0 using v0' = v0 + w × (d1 + ... +dN) / N. In this formula, v0 is the coordinate of the vertex v0, v0' is the coordinate of the vertex v0', and w is a scaling value for scaling the correction vector. w may be set depending on the number of subdivisions in which the vertex to be corrected was inserted. For example, w may be set to a value such as 1 / 32 for the 0th time (i.e., the base mesh), 1 / 16 for the first time, 1 / 8 for the second time, and 1 / 4 for the third time.

[0300] After the process of step S307 has been performed on all vertices, the subdivision unit 605 updates the mesh connection information (S309), thereby incorporating multiple subdivision points into the mesh as new vertices.

[0301] Note that FIG. 42 illustrates an example in which step S303 and steps S306 to S308 are performed on all sub-division hierarchical layers to perform the correction process, thereby correcting the vertices included in the mesh before sub-division. However, it is not necessary to perform the correction process on all sub-division hierarchical layers; whether or not to perform step S303 and steps S306 to S308 may be switched depending on the sub-division hierarchical layer to be processed. In other words, the correction process may be performed on only some of the sub-division hierarchical layers among multiple sub-division hierarchical layers. For example, the correction process (steps S303 and steps S306 to S308) may be performed on only the first sub-division hierarchical layer (i.e., the first sub-division) to correct the vertices of the mesh before sub-division (i.e., the base mesh).

[0302] In the above description, the processing of the subdivision unit 605 included in the encoding device 600 has been mainly described, but the processing of the subdivision unit 703 included in the decoding device 700 is similar.

[0303] <Sub-division point correction method 1> Below, a method for correcting the position (coordinates) of a sub-division point determined by the sub-division method described above or the like will be described. Fig. 43 is a diagram showing an example of a sub-division point correction method. For example, the sub-division unit 605 corrects the sub-division point Y that divides the edge v0v1, determined by the method shown in Fig. 39, to the sub-division point Y1 using a straight line passing through the midpoint X of the edge v0v1 (for example, the normal to the midpoint X).

[0304] Specifically, the subdivision unit 605 determines the point Y1 as the intersection of a plane d that includes the subdivision point Y and is perpendicular to the normal vector nX of the midpoint X, and a line that includes the normal vector nX. For example, the normal vector nX is a vector obtained by normalizing the average vector of the normal vectors of the face that includes the edge v0v1. Alternatively, the normal vector nX may be a vector obtained by normalizing the average vector of the normal vector n0 of the vertex v0 and the normal vector n1 of the vertex v1.

[0305] The subdivision unit 605 may determine the coordinate of the corrected subdivision point Y1 by Y1=X+{(Y-X)*nX}*nX. In this formula, X is the coordinate of point X, Y is the coordinate of point Y, and Y1 is the coordinate of point Y1. (Y-X)*nX represents the dot product of the vector (Y-X) and the normal vector nX.

[0306] In this way, by setting the subdivision points on the normals or on lines approximating the normals that pass through the midpoints of the edges, it is possible to prevent unevenness in the shapes or sizes of faces formed within the faces of the base mesh by the subdivision process, which may prevent uneven distribution of distortions in the decoded 3D mesh and the decoded texture map.

[0307] 44 is a flowchart showing an example of the processing procedure for the subdivision process performed by the subdivision unit 605. In this example, the subdivision unit 605 repeatedly executes steps S401 to S407 for each subdivision layer. As a result, the subdivision points determined for each subdivision layer are corrected, and the mesh connectivity information is updated.

[0308] In the processing of each subdivision layer, the processing of steps S402 to S405 is repeated for each edge of the mesh before subdivision. In the processing of each edge of the mesh before subdivision in steps S402 to S405, the subdivision unit 605 first determines subdivision points for subdividing the edge (S403). For example, the subdivision unit 605 determines the subdivision points using the subdivision method shown in FIG.

[0309] Next, the subdivision unit 605 corrects the determined subdivision points (S404). For example, the subdivision unit 605 corrects the subdivision points using the method described with reference to FIG. 43. For example, if the edge to be processed is edge v0v1, the subdivision point Y that divides edge v0v1 determined in step S403 is corrected using a straight line passing through the midpoint X of edge v0v1 (for example, a normal to midpoint X), thereby determining a corrected subdivision point Y1.

[0310] Note that when determining the sub-division points in step S403, the sub-division unit 605 may select one from a plurality of methods for determining sub-division points and determine the sub-division points using the selected method. In this case, the sub-division unit 605 may omit the processing of step S404 if the sub-division points determined by the selected method are always included in a straight line passing through the midpoint X of edge v0 / v1 (e.g., a normal to midpoint X). In other words, the sub-division unit 605 may perform step S404 when a first method included in the plurality of methods for determining sub-division points is selected, but may not perform step S404 (step S404 may be omitted) when a second method included in the plurality of methods and different from the first method is selected.

[0311] After steps S402 to S405 have been performed on all edges, the subdivision unit 605 updates the mesh connectivity information (S406), thereby incorporating multiple subdivision points into the mesh as new vertices.

[0312] 44, the sub-division points are determined (S403) and then corrected (S404), but these two processes may be performed together. For example, the corrected sub-division points may be determined by a single calculation combining these processes.

[0313] <Sub-division point correction method 2> Another example of the sub-division point correction method will be described below. First, the sub-division point determination method shown in Fig. 39 will be described in detail. Fig. 45 is a diagram showing an example of processing for determining the positions of sub-division points. In this example, sub-division points q that divide an edge vp in a mesh that is the target of the sub-division processing are set. １ In this case, the coordinates of the vertex v and the vertex p and the normal vector n of the vertex v are determined. ｖ and the normal vector n of vertex p ｐ Using the above, the subdivision point q is calculated using the following (Equation 1), (Equation 2), and (Equation 3). １ In addition, in (Equation 1), the coordinates of the normal vector n ｖ and n ｐ Coefficient value d for ｖ and d ｐ is the dot product of the edge direction and the normal vector, as shown in (Equation 2) and (Equation 3). ｉ is a scaling value. w may be set according to the number of subdivisions. For example, w ｉ may be set to a value such as 1 / 16 the first time, 1 / 8 the second time, and 1 / 4 the third time.

[0314]

[0315] Here, for example, for a vertex v on an edge vp, the edge vp and the normal vector n ｖ When the direction of the edge vp is nearly perpendicular to the direction of the input 3D mesh, the original shape (shape of the input 3D mesh) in the vicinity of the edge vp is flat. In this case, in (Equation 1), the coefficient value d ｖ The value of becomes smaller, and the subdivision point q １ Normal vector n of vertex v with respect to the coordinates of ｖ The contribution of vector qq １ The length of vp is shortened, and the subdivision point q is located near the edge vp. １ is generated.

[0316] On the other hand, the edge vp and the normal vector n ｖ If the direction of the edge vp is close, it means that the original shape near the edge vp is rounded. In this case, in (Equation 1), the coefficient value d ｖ The value of becomes larger, and the subdivision point q １ Normal vector component n of vertex v with respect to the coordinates of ｖ The contribution of vector qq １ The length of the edge vp becomes large, and the subdivision point q １ is generated.

[0317] This method of generating subdivision points using normal vectors, i.e., normal-based subdivision, allows for the generation of subdivision points at positions close to the original shape of the decoded 3D mesh based solely on the mesh information of the target mesh for the subdivision process, potentially reducing the amount of coding required for the displacement vectors while maintaining the accuracy of the decoded 3D mesh.

[0318] On the other hand, depending on the combination with the encoding method, the following problem may arise: Fig. 46 is a diagram for explaining this problem, showing an example of a decoded 3D mesh.

[0319] One encoding method is a one-dimensional transmission method for displacement vectors. Generally, transmitting all three-dimensional components of the displacement vector for each vertex position increases the reconstruction accuracy in the decoding device, but increases the amount of code. Furthermore, the normal direction component of a displacement vector is generally the largest, and the normal direction component is dominant in the displacement. Therefore, in the one-dimensional transmission method, to reduce the amount of code for this displacement vector, a one-dimensional displacement vector containing only one-dimensional displacement amounts (e.g., the normal direction component of each vertex) is transmitted. In this case, the decoding device applies displacement of only the normal direction component to the sub-divided vertex positions to perform coordinate correction (reconstruction).

[0320] Fig. 46 shows an example in which this one-dimensional transmission method of displacement vectors is combined with the normal-based subdivision method shown in Fig. 45. In Fig. 46, F represents the original shape (shape of the input 3D mesh), and vertex q ｏ is the subdivision point q １are the vertices included in the input 3D mesh corresponding to the vertex q. ｒ is the subdivision point q １ The reconstructed vertices are obtained by applying the one-dimensional displacement method to the subdivision point q. １ vertex q ｏ However, as shown in FIG. 46, the normal vector n ｖ and the normal vector n of vertex p ｐ When the direction is different from that of the normal-based subdivision method, if a one-dimensional transmission method is used, the subdivision point q １ is generated at a position shifted from the midpoint q of the edge vp in the direction of the vertex v or in the direction of the vertex p.

[0321] In the example shown in FIG. 46, the subdivision point q １ is generated at a position shifted in the direction of the vertex v. Therefore, this subdivision point q １ Normal vector n ｑ１ Even if a one-dimensional displacement vector along the direction of ｒ is vertex q ｏ I get separated from them.

[0322] This vertex q ｏ and vertex q ｒ The difference in the position of causes distortion of the decoded mesh when the normal subdivision method and the one-dimensional transmission method are used, and causes a loss of restoration accuracy of the decoded mesh.

[0323] In order to solve this problem, in this embodiment, the subdivision point q is set so that the position of the subdivision point does not move to the edge end side by the subdivision process. １ Constrain the position of .

[0324] One of these constraint methods is the method shown in Fig. 43. Below, we will explain the case where the method shown in Fig. 43 is applied to the example shown in Fig. 46. Fig. 47 is a diagram showing an example of a decoded 3D mesh when this constraint method is applied.

[0325] In this method, the subdivision unit 605 determines the subdivision point q １ After finding the vector qq１ the normal vector n of vertex v ｖ and the normal vector n of vertex p ｐ and the mean vector n ａｖｅ The projected point is projected onto the corrected subdivision point q ２ This is expressed by the following equations (Equation 4) and (Equation 5). １ The coordinates of are calculated using the above (Equation 1) to (Equation 3).

[0326]

[0327] This constraint allows the position of the subdivision point to be corrected to a position close to the original shape while maintaining the position near the center of the edge. ２ From vertex q ｏ At the displacement to the subdivision point q ２ This makes it possible to suppress the degradation of restoration accuracy when using a one-dimensional transmission method.

[0328] Next, another constraint method will be described. FIG. 48 is a diagram for explaining another constraint method, showing an example of a decoded 3D mesh. In this method, the subdivision unit 605 determines a bisecting plane R of the edge to be subjected to the subdivision process, and calculates the subdivision point q obtained using the normal-based subdivision method. １ By projecting onto the bisection plane R, the corrected subdivision point q ３ This is expressed by the following equations (6) and (7). １ The coordinates of are calculated using the above (Equation 1) to (Equation 3).

[0329]

[0330] In addition, the vector vp shown in (Equation 6) ｎｏｒｍ is a vector in the direction of the edge vp connecting the vertex v and the vertex p. The bisecting plane R is, for example, a perpendicular bisecting plane between the vertex v and the vertex p.

[0331] By projecting this onto the bisection plane R, the subdivision point q ３ is located directly above the midpoint q of the edge vp. ３ By this, vertex q on the original shape Fｏ The position of the subdivision point q can be restored with high accuracy. ３ The direction of the normal vector of vertex q ｏ Therefore, the normal-based subdivision method and the one-dimensional transmission method can be combined to improve coding efficiency by using this constraint method.

[0332] The subdivision unit 605 may switch between the constraint method shown in Fig. 47 and the constraint method shown in Fig. 48 for each subdivision point. For example, the subdivision unit 605 may switch which constraint method to use by using information on surrounding edges or vertices, or information additionally transmitted to the decoding device.

[0333] Fig. 49 is a flowchart showing an example of the processing procedure for the subdivision processing shown in Fig. 48, which is performed by the subdivision unit 605. In this example, the subdivision unit 605 repeatedly executes steps S411 to S417 for each subdivision layer. As a result, the subdivision points determined for each subdivision layer are corrected, and the mesh connectivity information is updated.

[0334] In the processing of each subdivision layer, the processing of steps S412 to S415 is repeated for each edge of the mesh before subdivision. In the processing of each edge of the mesh before subdivision in steps S412 to S415, the subdivision unit 605 first determines subdivision points for subdividing the edge (S413). For example, the subdivision unit 605 determines the subdivision points using the subdivision method shown in FIG.

[0335] Next, the sub-division unit 605 corrects the determined sub-division points (S414). For example, the sub-division unit 605 corrects the sub-division points using the method described with reference to FIG.

[0336] After steps S412 to S415 have been performed on all edges, the subdivision unit 605 updates the mesh connectivity information (S416), thereby incorporating multiple subdivision points into the mesh as new vertices.

[0337] 49, the sub-division points are determined (S413) and then corrected (S414), but these two processes may be performed together. For example, the corrected sub-division points may be determined by a single calculation combining these processes.

[0338] In the above description, the processing of the subdivision unit 605 included in the encoding device 600 has been mainly described, but the processing of the subdivision unit 703 included in the decoding device 700 is similar.

[0339] <Summary> As described above, the encoding device (three-dimensional data encoding device) according to this embodiment performs the processing shown in Fig. 50. Fig. 50 is a flowchart of the encoding processing performed by the encoding device.

[0340] The encoding device encodes the coordinates of multiple vertices of a polygon included in a three-dimensional mesh. The encoding device derives the coordinates of a third vertex (e.g., subdivision point Y1) connected to the first and second vertices using the coordinates of a first vertex (e.g., vertex v0) among the multiple vertices and the coordinates of a second vertex (e.g., vertex v1) different from the first vertex (S421), and the coordinates of the third vertex are located on a vector (e.g., vector nX) derived using multiple normal vectors (e.g., normal vectors n0 and n1) related to the three-dimensional mesh. For example, the coordinates of the third vertex are located at a position other than on a line (e.g., edge v0-v1) connecting the first vertex and the second vertex.

[0341] This allows the encoding device to determine the coordinates of the third vertex on a vector derived using multiple normal vectors. This potentially allows the coordinates of the third vertex to be closer to the coordinates of the vertices of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertices of the input three-dimensional mesh. This improves encoding efficiency.

[0342] For example, the vector is a normal vector (e.g., normal vector nX) of the midpoint (e.g., midpoint X) between the coordinates of the first vertex and the coordinates of the second vertex. This may allow the coordinates of the third vertex to be closer to the coordinates of the vertex of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data of information (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertex of the input three-dimensional mesh. This can improve coding efficiency.

[0343] For example, the multiple normal vectors include a normal vector of a first vertex (e.g., normal vector n0) and a normal vector of a second vertex (e.g., normal vector n1). This allows the encoding device to appropriately derive the normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex by using the normal vector of the first vertex and the normal vector of the second vertex.

[0344] For example, the plurality of normal vectors may include a plurality of normal vectors relating to a plane including the first vertex and the second vertex, allowing the encoding device to appropriately derive the normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex by using the plurality of normal vectors relating to the plane including the first vertex and the second vertex.

[0345] For example, the three-dimensional mesh is a base mesh generated based on the input three-dimensional mesh, and the encoding device can improve encoding efficiency by appropriately deriving the coordinates of the third vertex to be added to the base mesh.

[0346] For example, the 3D mesh is a sub-divided mesh obtained by sub-dividing a base mesh generated based on the input 3D mesh, and the encoding device can improve encoding efficiency by appropriately deriving the coordinates of the third vertex to be added to the sub-divided mesh.

[0347] For example, in deriving the coordinates of the third vertex (S421), the encoding device derives the coordinates of the third vertex (e.g., point Y) before correction using the coordinates of the first vertex and the coordinates of the second vertex, and derives the coordinates of the third vertex using the coordinates of the third vertex before correction and a vector. In this way, the encoding device can determine the third vertex by correcting the third vertex before correction that was derived using a predetermined method, for example.

[0348] For example, in deriving the coordinates of the third vertex (S421), if a first method is selected from among a plurality of methods for determining the coordinates of the sub-division points, the encoding device derives the coordinates of the third vertex using the coordinates of the third vertex before correction and a vector, and if a second method is selected from among the plurality of methods, the encoding device determines the coordinates of the third vertex before correction as the coordinates of the third vertex. This allows the encoding device to switch between using the third vertex before correction and the third vertex after correction, thereby improving encoding efficiency.

[0349] For example, as shown in FIG. 24, the encoding device includes a memory 152 and a circuit 151 that can access the memory 152, and the circuit 151 performs the above processing in operation.

[0350] Moreover, the decoding device (three-dimensional data decoding device) according to the embodiment performs the processing shown in Fig. 51. Fig. 51 is a flowchart of the decoding processing by the decoding device.

[0351] A decoding device decodes coordinates of multiple vertices of a polygon included in a three-dimensional mesh. The decoding device derives coordinates of a third vertex (e.g., subdivision point Y1) connected to the first and second vertices (e.g., subdivision point Y1) using coordinates of a first vertex (e.g., vertex v0) among the multiple vertices and coordinates of a second vertex (e.g., vertex v1) among the multiple vertices that is different from the first vertex (S431), and the coordinates of the third vertex are located on a vector (e.g., vector nX) derived using multiple normal vectors (e.g., normal vectors n0 and n1) related to the three-dimensional mesh. For example, the coordinates of the third vertex are located at a position other than on a line (e.g., edge v0v1) connecting the first vertex and the second vertex.

[0352] According to this, the decoding device can determine the coordinates of the third vertex on a vector derived using multiple normal vectors. As a result, it is possible to make the coordinates of the third vertex closer to the coordinates of the vertices of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data of information (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertices of the input three-dimensional mesh. Therefore, it is possible to improve coding efficiency.

[0353] For example, the vector is a normal vector (e.g., normal vector nX) of the midpoint (e.g., midpoint X) between the coordinates of the first vertex and the coordinates of the second vertex. This may allow the coordinates of the third vertex to be closer to the coordinates of the vertex of the input three-dimensional mesh. Therefore, for example, it is possible to reduce the amount of data of information (e.g., a displacement vector) indicating the difference (displacement) between the coordinates of the third vertex and the coordinates of the vertex of the input three-dimensional mesh. This can improve coding efficiency.

[0354] For example, the multiple normal vectors include a normal vector of a first vertex (e.g., normal vector n0) and a normal vector of a second vertex (e.g., normal vector n1). This allows the decoding device to appropriately derive the normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex, using the normal vector of the first vertex and the normal vector of the second vertex.

[0355] For example, the plurality of normal vectors may include a plurality of normal vectors relating to a plane including the first vertex and the second vertex, and the decoding device may use the plurality of normal vectors relating to the plane including the first vertex and the second vertex to appropriately derive the normal vector of the midpoint between the coordinates of the first vertex and the coordinates of the second vertex.

[0356] For example, the 3D mesh is a base mesh generated based on the input 3D mesh, and the decoding device can improve coding efficiency by appropriately deriving the coordinates of the third vertex to be added to the base mesh.

[0357] For example, the 3D mesh is a sub-divided mesh obtained by sub-dividing a base mesh generated based on the input 3D mesh, and the decoding device can improve coding efficiency by appropriately deriving the coordinates of the third vertex to be added to the sub-divided mesh.

[0358] For example, in deriving the coordinates of the third vertex (S431), the decoding device derives the coordinates of the third vertex (e.g., point Y) before correction using the coordinates of the first vertex and the coordinates of the second vertex, and derives the coordinates of the third vertex using the coordinates of the third vertex before correction and a vector. In this way, the decoding device can determine the third vertex by correcting the third vertex before correction that has been derived using a predetermined method, for example.

[0359] For example, in deriving the coordinates of the third vertex (S431), if a first method is selected from among a plurality of methods for determining the coordinates of the sub-division points, the decoding device derives the coordinates of the third vertex using the coordinates of the third vertex before correction and a vector, and if a second method is selected from among the plurality of methods, the decoding device determines the coordinates of the third vertex before correction as the coordinates of the third vertex. This allows the decoding device to switch between using the third vertex before correction and the third vertex after correction, thereby improving coding efficiency.

[0360] For example, as shown in FIG. 25, the decoding device includes a memory 252 and a circuit 251 that can access the memory 252, and the circuit 251 performs the above processing in operation.

[0361] For example, as shown in FIG. 48 , the encoding method is an encoding method for encoding coordinates of a plurality of vertices of a polygon included in a three-dimensional mesh, and encodes a third vertex (for example, subdivision point q) connected to the first vertex and the second vertex by using the coordinates of a first vertex (for example, vertex v) among the plurality of vertices and the coordinates of a second vertex (for example, vertex p) different from the first vertex among the plurality of vertices. ３ The coordinates of the third vertex are located on a plane (for example, a bisecting plane R) that is perpendicular to the edge connecting the first vertex and the second vertex.

[0362] For example, in deriving the coordinates of the third vertex, the coordinates of the first vertex and the coordinates of the second vertex are used to derive the third vertex before correction (for example, the subdivision point q １ ) and derive the coordinates of the third vertex before the correction and the vector in the direction of the edge connecting the first vertex and the second vertex (for example, vector vp ｎｏｒｍ ) to find the third vertex (e.g., subdivision point q ３ ) coordinates are derived.

[0363] For example, the plane is a perpendicular bisecting plane between the first vertex and the second vertex, and the coordinates of the third vertex are the coordinates of the point where the third vertex before correction is projected onto the perpendicular bisecting plane.

[0364] For example, the three-dimensional mesh may be a base mesh generated based on an input three-dimensional mesh, or may be a sub-divided mesh obtained by sub-dividing the base mesh generated based on the input three-dimensional mesh.

[0365] For example, in deriving the coordinates of the third vertex, if a first method is selected from among a plurality of methods for determining the coordinates of the subdivision points, the third vertex before correction (e.g., subdivision point q １ ) and the vector (e.g., vector vp ｎｏｒｍ ) to find the third vertex (e.g., subdivision point q ３ ) is derived, and if the second method is selected from the plurality of methods, the coordinates of the third vertex before the correction are determined as the coordinates of the third vertex.

[0366] For example, the encoding method further includes: generating a corrected third vertex (e.g., vertex q) using the coordinates of the third vertex and the displacement vector. ｒ ) and encode the displacement vector into a bitstream. For example, the displacement vector is a one-dimensional displacement vector including only a one-dimensional displacement amount.

[0367] For example, as shown in FIG. 24, the encoding device includes a memory 152 and a circuit 151 that can access the memory 152, and the circuit 151 performs the above processing in operation.

[0368] For example, the decoding method is a decoding method for decoding coordinates of a plurality of vertices of a polygon included in a three-dimensional mesh, and the decoding method uses the coordinates of a first vertex (e.g., vertex v) among the plurality of vertices and the coordinates of a second vertex (e.g., vertex p) different from the first vertex among the plurality of vertices to decode a third vertex (e.g., subdivision point q) connected to the first vertex and the second vertex. ３ The coordinates of the third vertex are located on a plane (for example, a bisecting plane R) that is perpendicular to the edge connecting the first vertex and the second vertex.

[0369] For example, in deriving the coordinates of the third vertex, the coordinates of the first vertex and the coordinates of the second vertex are used to derive the third vertex before correction (for example, the subdivision point q １ ) and derive the coordinates of the third vertex before the correction and the vector in the direction of the edge connecting the first vertex and the second vertex (for example, vector vp ｎｏｒｍ ) to find the third vertex (e.g., subdivision point q ３ ) coordinates are derived.

[0370] For example, the plane is a perpendicular bisecting plane between the first vertex and the second vertex, and the coordinates of the third vertex are the coordinates of the point where the third vertex before correction is projected onto the perpendicular bisecting plane.

[0371] For example, the three-dimensional mesh may be a base mesh generated based on an input three-dimensional mesh, or may be a sub-divided mesh obtained by sub-dividing the base mesh generated based on the input three-dimensional mesh.

[0372] For example, in deriving the coordinates of the third vertex, if a first method is selected from among a plurality of methods for determining the coordinates of the subdivision points, the third vertex before correction (e.g., subdivision point q １ ) and the vector (e.g., vector vp ｎｏｒｍ ) to find the third vertex (e.g., subdivision point q ３) is derived, and if the second method is selected from the plurality of methods, the coordinates of the third vertex before the correction are determined as the coordinates of the third vertex.

[0373] For example, the decoding method further includes decoding a displacement vector from the bitstream, and using the coordinates of the third vertex and the displacement vector to determine a corrected third vertex (e.g., vertex q ｒ The displacement vector is a one-dimensional displacement vector including only a one-dimensional displacement amount.

[0374] For example, as shown in FIG. 25, the decoding device includes a memory 252 and a circuit 251 that can access the memory 252, and the circuit 251 performs the above processing in operation.

[0375] <Other Examples> Although the aspects of the encoding device and the decoding device have been described above according to the embodiments, the aspects of the encoding device and the decoding device are not limited to the embodiments. Modifications that a person skilled in the art can conceive of may be applied to the embodiments, and multiple components in the embodiments may be combined in any manner.

[0376] For example, a process performed by a specific component in the embodiment may be performed by another component instead of the specific component. Also, the order of multiple processes may be changed, or multiple processes may be performed in parallel.

[0377] Furthermore, as described above, at least some of the configurations of the present disclosure may be implemented as an integrated circuit. At least some of the processes of the present disclosure may be used as an encoding method or a decoding method. A program for causing a computer to execute the encoding method or the decoding method may be used. A non-transitory computer-readable recording medium on which the program is recorded may be used. A bitstream for causing a decoding device to perform a decoding process may be used.

[0378] Furthermore, at least some of the configurations and processes of the present disclosure may be used as a transmitting device, a receiving device, a transmitting method, or a receiving method. A program for causing a computer to execute the transmitting method or the receiving method may be used. Furthermore, a non-transitory computer-readable recording medium on which the program is recorded may be used.

[0379] In the above-described embodiments, each component may be configured with dedicated hardware, or may be realized by executing a software program suitable for each component. Each component may also be realized by a program execution unit such as a CPU or processor reading and executing a software program recorded on a recording medium such as a hard disk or semiconductor memory.

[0380] The present disclosure is useful, for example, in encoding devices, decoding devices, transmitting devices, receiving devices, etc. related to three-dimensional meshes, and is applicable to computer graphics systems, three-dimensional data display systems, etc.

[0381] 100 Encoding device 101, 121, 144 Vertex information encoder 102, 145 Connection information encoder 103, 122 Attribute information encoder 104, 204, 1102 Preprocessor 105, 205, 2107 Postprocessor 110 Three-dimensional data encoding system 111, 211 Controller 112, 212 Input / output processor 113 Three-dimensional data encoder 114 System multiplexer 115 Three-dimensional data generator 123 Metadata encoder 124 Multiplexer 131 Vertex image generator 132 Attribute image generator 133 Metadata generator 134 Video encoder 141 Two-dimensional data encoder 142 Mesh data encoder 143 Texture encoder 148 Description encoder 151, 251 Circuit 152, 252 Memory 200 Decoding device 201, 221, 244 Vertex information decoder 202, 245 Connection information decoder 203, 222 Attribute information decoder 210 Three-dimensional data decoding system 213 Three-dimensional data decoder 214 System demultiplexer 215, 247 Presentation device 216 User interface 223 Metadata decoder 224 Demultiplexer 231 Vertex information generator 232 Attribute information generator 234 Video decoder 241 Two-dimensional data decoder 242 Mesh data decoder 243 Texture decoder 246 Mesh reconstructor 248 Description decoder 300 Network 310 External connection device 600 Encoding device 601 Decimation unit 602 Texture coordinate determination unit 603 Base mesh encoding unit 604, 702 Base mesh decoding unit 605, 703 Subdivision unit 606 Displacement vector calculation unit 607 Displacement vector coding unit 608, 704 Displacement vector decoding unit 609, 705 3D mesh reconstruction unit 610 Texture conversion unit 611 Texture coding unit 612 Multiplexing unit 700 Decoding device 701 Separation unit 706 Texture decoding unit 1101 Input mesh 1103, 2103 Base mesh1104, 2104 Displacement data 1105, 2105 Texture data 1106, 2106 Attribute map 1107 Compressor 1108, 2101, 1304 Bitstream 1301, 2302, 2304 Mesh frame 1302, 2301 Base mesh frame 1303, 2303 Displacement information 2102 Decompressor 2108 Output mesh

Claims

1. An encoding method for encoding the coordinates of multiple vertices of a polygon included in a three-dimensional mesh, comprising: deriving the coordinates of a third vertex connected to the first vertex and the second vertex using the coordinates of a first vertex of the multiple vertices and the coordinates of a second vertex of the multiple vertices that is different from the first vertex; and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

2. The encoding method according to claim 1, wherein the vector is a normal vector of a midpoint between the coordinates of the first vertex and the coordinates of the second vertex.

3. The encoding method according to claim 2, wherein the plurality of normal vectors include a normal vector of the first vertex and a normal vector of the second vertex.

4. The encoding method according to claim 2, wherein the plurality of normal vectors include a plurality of normal vectors relating to a plane including the first vertex and the second vertex.

5. The encoding method according to claim 1, wherein the three-dimensional mesh is a base mesh generated based on an input three-dimensional mesh.

6. The encoding method according to claim 1, wherein the three-dimensional mesh is a sub-divided mesh obtained by sub-dividing a base mesh generated based on an input three-dimensional mesh.

7. The encoding method according to claim 1, wherein in deriving the coordinates of the third vertex, the coordinates of the third vertex before correction are derived using the coordinates of the first vertex and the coordinates of the second vertex, and the coordinates of the third vertex before correction are derived using the coordinates of the third vertex before correction and the vector.

8. The encoding method of claim 7, wherein, in deriving the coordinates of the third vertex, if a first method is selected from among a plurality of methods for determining the coordinates of subdivision points, the coordinates of the third vertex are derived using the coordinates of the third vertex before the correction and the vector, and if a second method is selected from among the plurality of methods, the coordinates of the third vertex before the correction are determined to be the coordinates of the third vertex.

9. A decoding method for decoding the coordinates of multiple vertices of a polygon included in a three-dimensional mesh, comprising: deriving the coordinates of a third vertex connected to the first vertex and the second vertex using the coordinates of a first vertex of the multiple vertices and the coordinates of a second vertex of the multiple vertices that is different from the first vertex; and the coordinates of the third vertex are located on a vector derived using multiple normal vectors related to the three-dimensional mesh.

10. The decoding method according to claim 9, wherein the vector is a normal vector of a midpoint between the coordinates of the first vertex and the coordinates of the second vertex.

11. The decoding method according to claim 10, wherein the plurality of normal vectors include a normal vector of the first vertex and a normal vector of the second vertex.

12. The decoding method according to claim 10, wherein the plurality of normal vectors include a plurality of normal vectors relating to a plane including the first vertex and the second vertex.

13. The decoding method of claim 9, wherein the three-dimensional mesh is a base mesh generated based on information decoded from a bitstream.

14. The decoding method according to claim 9, wherein the three-dimensional mesh is a sub-divided mesh obtained by sub-dividing a base mesh generated based on information decoded from a bitstream.

15. The decoding method of claim 9, wherein in deriving the coordinates of the third vertex, the coordinates of the third vertex before correction are derived using the coordinates of the first vertex and the coordinates of the second vertex, and the coordinates of the third vertex before correction are derived using the coordinates of the third vertex before correction and the vector.

16. The decoding method of claim 15, wherein in deriving the coordinates of the third vertex, if a first method is selected from among a plurality of methods for determining the coordinates of subdivision points, the coordinates of the third vertex are derived using the coordinates of the third vertex before the correction and the vector, and if a second method is selected from among the plurality of methods, the coordinates of the third vertex before the correction are determined to be the coordinates of the third vertex.

17. An encoding device for encoding coordinates of multiple vertices of a polygon included in a three-dimensional mesh, comprising: a memory; and a circuit capable of accessing the memory, wherein the circuit operates to: use the coordinates of a first vertex of the multiple vertices and the coordinates of a second vertex of the multiple vertices that is different from the first vertex to derive coordinates of a third vertex connected to the first vertex and the second vertex; and the coordinates of the third vertex lie on a vector derived using multiple normal vectors related to the three-dimensional mesh.

18. A decoding device for decoding coordinates of multiple vertices of a polygon included in a three-dimensional mesh, comprising: a memory; and a circuit capable of accessing the memory, wherein the circuit operates to: use the coordinates of a first vertex of the multiple vertices and the coordinates of a second vertex of the multiple vertices that is different from the first vertex to derive the coordinates of a third vertex connected to the first vertex and the second vertex; and the coordinates of the third vertex lie on a vector derived using multiple normal vectors related to the three-dimensional mesh.

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