Coding dynamic mesh vertex displacements

Abstract

A method and apparatus for deriving a curve of a mesh sequence from frames of a video bitstream, the curve including a plurality of vertices, subdividing the curve by adding a plurality of subdivided vertices, calculating one or more displacement vectors between each of the plurality of vertices on the curve and each of the plurality of subdivided vertices on the subdivided curve, transforming the one or more displacement vectors, outputting one or more original coefficients, tracking a current frame with a previous frame, obtaining a one-to-one correspondence between the plurality of vertices of the current frame and the plurality of vertices of the previous frame, predicting one or more coefficients of each of the plurality of vertices in the current frame based on the one-to-one correspondence, performing entropy coding on the one or more prediction residuals, and encoding the one or more prediction residuals.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 63 / 358,084, filed July 1, 2022, and U.S. Patent Application No. 18 / 315,020, filed May 10, 2023, the disclosures of which are incorporated herein by reference in their entireties.

[0002] This disclosure is directed to a set of advanced video coding techniques, and more specifically, to compression techniques for encoding vertex displacements of dynamic subdivided meshes. [Background technology]

[0003] Advances in 3D capture, modeling, and rendering are facilitating the ubiquitous presence of 3D content across several platforms and devices. Today, it is possible to film a baby's first steps on one continent, while the baby's grandparents on another continent watch (and even interact with) this, enjoying a fully immersive experience with the child. Nevertheless, to achieve this sense of realism, models are becoming ever more sophisticated, and a significant amount of data is tied to the creation and consumption of these models. 3D meshes are widely used to represent such immersive content.

[0004] Dynamic mesh sequences can consist of a significant amount of information that changes over time and therefore require a large amount of data. Therefore, efficient compression techniques are needed to store and transmit such content. Mesh compression standards IC, MESHGRID, and FAMC were previously developed by MPEG to address dynamic meshes with constant connectivity and time-varying geometry and vertex attributes. However, these standards do not take time-varying attribute maps and connectivity information into account. Digital content creation (DCC) tools typically generate such dynamic meshes. Correspondingly, it is difficult for volume acquisition techniques to generate constant connectivity dynamic meshes, especially under real-time constraints. This type of content is not supported by existing standards. Therefore, a new mesh compression standard is needed to directly handle dynamic meshes with time-varying connectivity information and, optionally, time-varying attribute maps. Such a standard targets lossy and lossless compression for various applications, such as real-time communication, storage, free-viewpoint video, AR, and VR. Features such as random access and scalable / progressive coding are also considered. Summary of the Invention [Problem to be solved by the invention]

[0005] The following presents a simplified summary of one or more embodiments of the present disclosure in order to provide a basic understanding of such embodiments. This summary is not an extensive overview of all contemplated embodiments, and is not intended to identify key or critical elements of all embodiments or to delineate the scope of any or all embodiments. Its sole purpose is to present some concepts of one or more embodiments of the present disclosure in a simplified form as a prelude to the more detailed description that is presented later.

[0006] This disclosure provides a compression technique for encoding vertex displacements of dynamic refinement meshes. [Means for solving the problem]

[0007] According to some embodiments, there is provided a method implemented by at least one processor that may include the steps of: deriving a curve of a mesh sequence from a frame of a video bitstream, the curve including a plurality of vertices; subdividing the curve by adding a plurality of subdivided vertices; calculating one or more displacement vectors between each of the plurality of vertices on the curve and each of the plurality of subdivided vertices on the subdivided curve; transforming the one or more displacement vectors and outputting one or more original coefficients; and determining whether a current frame is coded using inter-picture information or intra-picture information. In response to determining that the current frame is coded using inter-picture information, the method may include steps of tracking the current frame with a previous frame to obtain a one-to-one correspondence between a plurality of vertices of the current frame and a plurality of vertices of the previous frame; predicting one or more coefficients of each of the plurality of vertices in the current frame based on the one-to-one correspondence; performing entropy coding on the one or more prediction residuals; and encoding the one or more prediction residuals based on the one or more predicted coefficients, and in response to determining that the current frame is coded using intra-picture information, the method may include steps of encoding the one or more coefficients using arithmetic coding.

[0008] According to other aspects of one or more embodiments, an apparatus and a non-transitory computer-readable medium consistent with the method are also provided.

[0009] Additional embodiments will be set forth in the description that follows, and in part will be obvious from the description, and / or may be learned by practice of presented embodiments of the present disclosure.

[0010] Further features, nature and various advantages of the disclosed subject matter will become more apparent from the following detailed description and accompanying drawings. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a schematic diagram of a simplified block diagram of a communication system, according to some embodiments. [Figure 2] FIG. 1 is a schematic diagram of a simplified block diagram of a streaming system, according to some embodiments. [Figure 3] FIG. 1 is a diagram of a subdivision scheme, according to some embodiments. [Figure 4] FIG. 10 illustrates an example of ordered displacement coefficients, according to some embodiments. [Figure 5] 1 is an operational flowchart illustrating steps performed by a program for encoding vertex displacements of a dynamic refinement mesh, according to some embodiments. [Figure 6] FIG. 1 is a diagram of a computer system suitable for implementing embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0012] The following detailed description of the exemplary embodiments refers to the accompanying drawings, in which the same reference numbers in different drawings may identify the same or similar elements.

[0013] A mesh may contain several polygons that describe the surface of a volumetric object. Its vertices in 3D space and information about how the vertices are connected can define each polygon, referred to as connectivity information. Optionally, vertex attributes, such as color and normals, can be associated with mesh vertices. Attributes may also be associated with the surface of a mesh by utilizing mapping information that parameterizes the mesh with a 2D attribute map. Such mappings are sometimes defined using a set of parametric coordinates, called UV coordinates or texture coordinates, associated with mesh vertices. 2D attribute maps can be used to store high-resolution attribute information, such as texture, normals, and displacements. Such information can be used for various purposes, such as texture mapping, shading, and mesh reconstruction.

[0014] This disclosure proposes several methods that improve upon existing approaches to compressing vertex displacements of dynamic refinement meshes. These methods can be applied individually or in any combination. Furthermore, each of the methods (or embodiments), encoders, and decoders may be implemented by processing circuitry (e.g., one or more processors or one or more integrated circuits). In one example, the one or more processors execute a program stored on a non-transitory computer-readable medium.

[0015] 1-2, one embodiment of the present disclosure for implementing the encoding and decoding structures of the present disclosure will be described.

[0016] 1 shows a simplified block diagram of a communication system 100 according to one embodiment of the present disclosure. The system 100 may include at least two terminals 110, 120 interconnected via a network 150. In the case of unidirectional data transmission, the first terminal 110 may code video data, which may include mesh data, at a local location for transmission to the other terminal 120 via the network 150. The second terminal 120 may receive the coded video data of the other terminal from the network 150, decode the coded data, and display the recovered video data. The unidirectional data transmission may be used in media serving applications, etc.

[0017] 1 shows a second pair of terminals 130, 140 provided to support bidirectional transmission of coded video, such as may occur during a video conference. For bidirectional transmission of data, each terminal 130, 140 can code video data captured at a local location for transmission to the other terminal over network 150. Each terminal 130, 140 can also receive coded video data transmitted by the other terminal, decode the coded data, and display the recovered video data on a local display device.

[0018] In FIG. 1 , terminals 110-140 may be, for example, servers, personal computers, and smartphones, and / or any other type of terminal. For example, terminals 110-140 may be laptop computers, tablet computers, media players, and / or dedicated videoconferencing equipment. Network 150 represents any number of networks that convey coded video data between terminals 110-140, including, for example, wired and / or wireless communication networks. Communication network 150 may exchange data over circuit-switched and / or packet-switched channels. Exemplary networks include telecommunications networks, local area networks, wide area networks, and / or the Internet. For purposes of this discussion, the architecture and topology of network 150 may not be important to the operation of the present disclosure, unless described herein below.

[0019] 2 illustrates the arrangement of a video encoder and a video decoder in a streaming environment as an example of an application for the disclosed subject matter. The disclosed subject matter may also be used in other video-enabled applications, including, for example, video conferencing, digital TV, storage of compressed video on digital media including CDs, DVDs, memory sticks, etc.

[0020] 2, the streaming system 200 may include a capture subsystem 213 that includes a video source 201 and an encoder 203. The streaming system 200 may further include at least one streaming server 205 and / or at least one streaming client 206.

[0021] The video source 201 may create a stream 202 including, for example, a 3D mesh and metadata associated with the 3D mesh. The video source 201 may include, for example, a 3D sensor (e.g., a depth sensor) or 3D imaging technology (e.g., a digital camera) and a computing device configured to generate the 3D mesh using data received from the 3D sensor or 3D imaging technology. The sample stream 202 may have a high amount of data compared to an encoded video bitstream and may be processed by an encoder 203 coupled to the video source 201. The encoder 203 may include hardware, software, or a combination thereof that enables or implements aspects of the disclosed subject matter, as described in more detail below. The encoder 203 may also generate an encoded video bitstream 204. The encoded video bitstream 204 may have a low amount of data compared to the uncompressed stream 202 and may be stored on a streaming server 205 for later use. One or more streaming clients 206 can access the streaming server 205 and retrieve a video bitstream 209 , which may be a copy of the encoded video bitstream 204 .

[0022] The streaming client 206 may include a video decoder 210 and a display 212. The video decoder 210 may, for example, decode a video bitstream 209 that is a copy of the input encoded video bitstream 204 and create an output video sample stream 211 that can be rendered on the display 212 or another rendering device (not shown). In some streaming systems, the video bitstreams 204, 209 may be encoded according to a particular video coding / compression standard.

[0023] As mentioned above, dynamic mesh sequences can consist of a significant amount of information that changes over time and therefore can require a large amount of data. Subdivision-based methods can be utilized to compress dynamic mesh sequences, and because the displacements of the vertices of the subdivided meshes are signaled, efficient coding of the displacements is necessary for high-performance compression of dynamic meshes.

[0024] A subdivision scheme can be utilized to efficiently compress dynamic meshes, a 2D diagram of which is shown in Figure 3, where the original curve is first decimated and subdivided. The subdivided polyline is then deformed to obtain a better approximation of the original curve. More precisely, a displacement vector is calculated for each vertex of the subdivided mesh such that the shape of the displaced curve is as close as possible to the shape of the original curve. The main advantage of a subdivided curve is that it has a subdivision structure that allows for efficient compression while providing a faithful approximation of the original curve.

[0025] In some embodiments, it is assumed that the vertex displacements (displacement vectors) of the subdivided mesh are calculated and transformed, so that the output of the transform (i.e., the coefficients) has lower entropy compared to the original displacements and can therefore be compressed more efficiently. For example, the magnitude of the scaling coefficients (low-frequency components) of a wavelet transform is generally larger than the wavelet coefficients (high-frequency components). Therefore, when the coefficients are quantized and ordered in a sequence from low level of detail (LOD) to high LOD, the magnitudes of the quantized coefficients are statistically descending, with most of the coefficients near the end of the sequence being zero. An example of the distribution of coefficients is shown in FIG. 4. Taking these assumptions into account, the following method of coding the coefficients described above is proposed. In some embodiments, the above assumptions may not need to be true for the following method to apply.

[0026] In some embodiments, the current frame is coded using only intra information. Existing methods, such as arithmetic coding, can be used to encode the coefficients. In addition, if the coefficients have a tree structure, where high-frequency coefficients are descendants of low-frequency components, the tree structure can be utilized to improve coding performance, such as a zero-tree structure.

[0027] In some embodiments, the current frame is coded using inter-picture information. These embodiments propose first predicting the coefficients of the current frame and then encoding the prediction residual using the method used for intra-coding frames. The residual can be calculated as the difference between the original and predicted coefficients. Specifically, in inter-frame mode, the current mesh frame is tracked with the previous frame, meaning that there is a one-to-one correspondence between the vertices of the current frame and the previous frame. As a result, the coefficients of each vertex of the current frame can be predicted by using the coefficients of the corresponding vertex in a reference frame, e.g., the previous frame. Entropy coding can then be performed on the prediction residual. In some embodiments, the prediction residual is encoded, while in other embodiments, the original coefficients are encoded. A signaling flag for each frame can be used to indicate such a selection. Because the distribution of the prediction residual is different from that of the original coefficients, separate coding contexts can be used to code the prediction residual and the original coefficients to further improve coding efficiency.

[0028] In some embodiments, different coding methods can be used for coefficients or coefficient residuals in inter-coded frames depending on the distribution of the coefficients / residuals. In some embodiments, a syntax structure is proposed in which coefficients with absolute values ​​greater than 1 are identified and their position in the sequence as well as their value are signaled. Syntax elements for indicating such purposes can include the number of these large coefficients, the distance from the last large coefficient to the next large coefficient, etc. After that, the remaining coefficients are always either 0, +1, or −1. To encode such a sequence, some embodiments simply use a flag for each position to indicate whether it is 0; if not, a separate sign flag is signaled to indicate whether it is a positive 1 or a negative 1.

[0029] 5 is a flowchart of an example process 500 for encoding vertex displacements of a dynamic refinement mesh. In some implementations, one or more process blocks of FIG. 5 may be performed by any of the elements described above.

[0030] As shown in FIG. 5, process 500 may include deriving a curve of a mesh sequence from a frame of a video bitstream, the curve including a plurality of vertices (block 510).

[0031] As further shown in FIG. 5, the process 500 may include subdividing the curve by adding a plurality of subdivided vertices (block 520).

[0032] As further shown in FIG. 5, process 500 may include calculating one or more displacement vectors between each of a plurality of vertices on the curve and each of a plurality of subdivided vertices on the subdivided curve (block 530).

[0033] As shown in FIG. 5, the process 500 may include transforming one or more displacement vectors and outputting one or more original coefficients (block 540).

[0034] As further shown in FIG. 5, process 500 may include determining whether the current frame is coded using inter-picture or intra-picture information (block 550).

[0035] As further shown in FIG. 5, in response to determining that the current frame is coded using interpicture information, process 500 may include tracking the current frame with the previous frame to obtain a one-to-one correspondence between a plurality of vertices of the current frame and a plurality of vertices of the previous frame (block 561).

[0036] As further shown in FIG. 5, the process 500 may include predicting one or more coefficients for each of a plurality of vertices in the current frame based on a one-to-one correspondence (block 571).

[0037] As further shown in FIG. 5, process 500 may include performing entropy coding on one or more prediction residuals (block 581).

[0038] As further shown in FIG. 5, the process 500 may include encoding one or more prediction residuals based on the one or more predicted coefficients (block 591).

[0039] As further shown in FIG. 5, in response to determining that the current frame is coded using intra-picture information, process 500 may include encoding one or more coefficients using arithmetic coding (block 562).

[0040] 5 illustrates example blocks of process 500, in some implementations, process 500 may include additional, fewer, different, or differently arranged blocks relative to those illustrated in FIG 5. Additionally or alternatively, two or more blocks of process 500 may be performed in parallel.

[0041] The techniques described above can be implemented as computer software using computer-readable instructions and physically stored on one or more computer-readable media. For example, Figure 6 illustrates a computer system 900 suitable for implementing certain embodiments of the present disclosure.

[0042] The computer software may be coded using any suitable machine code or computer language that can undergo mechanisms such as assembly, compilation, linking, etc. to produce code containing instructions that can be executed by a computer central processing unit (CPU), graphics processing unit (GPU), etc. directly, or via interpretation, microcode execution, etc.

[0043] The instructions may be executed on various types of computers or components thereof, including, for example, personal computers, tablet computers, servers, smartphones, gaming consoles, Internet of Things devices, and the like.

[0044] 6 for computer system 900 are examples and are not intended to suggest any limitation as to the scope of use or functionality of the computer software implementing embodiments of the present disclosure. The arrangement of components should not be interpreted as having any dependency or requirement regarding any one or combination of components illustrated in the non-limiting embodiment of computer system 900.

[0045] The computer system 900 may include certain human interface input devices. Such human interface input devices may respond to input by one or more human users, for example, via tactile input (e.g., keystrokes, swipes, data glove movements), audio input (e.g., voice, clapping), visual input (e.g., gestures), or olfactory input (not shown). The human interface devices may also be used to capture certain media not necessarily directly associated with conscious human input, such as audio (e.g., voice, music, ambient sounds), images (e.g., scanned images, photographic images, still image captured from a camera), and video (e.g., two-dimensional video, three-dimensional video including stereoscopic video).

[0046] The input human interface devices may include one or more of a keyboard 901, a mouse 902, a trackpad 903, a touchscreen 910, a data glove, a joystick 905, a microphone 906, a scanner 907, and a camera 908 (only one of each is shown).

[0047] The computer system 900 may also include certain human interface output devices. Such human interface output devices may stimulate one or more of the human user's senses, for example, through tactile output, sound, light, and smell / taste. Such human interface output devices may include haptic output devices (e.g., haptic feedback via a touchscreen 910, data gloves, or joystick 905, although haptic feedback devices that do not function as input devices may also be present). For example, such devices may be audio output devices (such as speakers 909, headphones (not shown)), visual output devices (such as screens 910 including CRT screens, LCD screens, plasma screens, and OLED screens, each with or without touchscreen input capability, each with or without haptic feedback capability, some of which may be capable of outputting two-dimensional visual output or output in more than three dimensions through means such as stereoscopic output, virtual reality glasses (not shown), holographic displays, and smoke tanks (not shown)), and printers (not shown).

[0048] The computer system 900 may also include human-accessible storage devices and their associated media, such as optical media including CD / DVD ROM / RW 920 with CD / DVD or similar media 921, thumb drives 922, removable hard drives or solid state drives 923, legacy magnetic media such as tape and floppy disks (not shown), and specialized ROM / ASIC / PLD-based devices (not shown) such as security dongles.

[0049] Those skilled in the art should also understand that the term "computer-readable medium" as used in connection with the subject matter of this disclosure does not encompass transmission media, carrier waves, or other transitory signals.

[0050] The computer system 900 may also include interfaces to one or more communication networks. The networks may be, for example, wireless, wired, or optical. The networks may also be local, wide area, metropolitan, vehicular, industrial, real-time, delay-tolerant, etc. Examples of networks include local area networks such as Ethernet, WLAN, etc.; cellular networks including GSM, 3G, 4G, 5G, LTE, etc.; TV wired or wireless wide area digital networks including cable TV, satellite TV, and terrestrial broadcast TV; and vehicular and industrial networks including CANBus. Certain networks generally require an external network interface adapter attached to a particular general-purpose data port or peripheral bus 949 (e.g., a USB port of the computer system 900, etc.), while other networks are generally integrated into the core of the computer system 900 by attachment to the system bus as described below (e.g., an Ethernet interface to a PC computer system, or a cellular network interface to a smartphone computer system). Using any of these networks, the computer system 900 can communicate with other entities. Such communications may be one-way receive only (e.g., broadcast TV), one-way transmit only (e.g., a CANbus to a particular CANbus device), or two-way, for example, to other computer systems using local-area or wide-area digital networks. Such communications may include communications to a cloud computing environment 955. Certain protocols and protocol stacks may be used with each of these networks and network interfaces, as described above.

[0051] The aforementioned human interface devices, human-accessible storage devices, and network interface 954 may be attached to core 940 of computer system 900 .

[0052] The core 940 may include one or more central processing units (CPUs) 941, graphics processing units (GPUs) 942, dedicated programmable processing units in the form of field programmable gate arrays (FPGAs) 943, hardware accelerators 944 for specific tasks, etc. These devices may be connected via a system bus 948, along with read-only memory (ROM) 945, random access memory 946, and internal mass storage 947, such as a non-user-accessible internal hard drive or SSD. In some computer systems, the system bus 948 may be accessible in the form of one or more physical plugs to allow expansion with additional CPUs, GPUs, etc. Peripheral devices may be attached directly to the core's system bus 948 or via a peripheral bus 949. Architectures for peripheral buses include PCI, USB, etc. A graphics adapter 950 may also be included in the core 940.

[0053] The CPU 941, GPU 942, FPGA 943, and accelerator 944 may combine to execute specific instructions that may constitute the aforementioned computer code, which may be stored in ROM 945 or RAM 946. Persistent data may be stored in, for example, internal mass storage 947, while temporary data may also be stored in RAM 946. Rapid storage and retrieval in any of the memory devices may be enabled through the use of cache memory, which may be closely associated with one or more of the CPU 941, GPU 942, mass storage 947, ROM 945, RAM 946, etc.

[0054] The computer-readable medium may bear computer code for performing various computer-implemented operations. The medium and computer code may be those specially designed and constructed for the purposes of the present disclosure, or they may be of the kind well known and available to those skilled in the computer software arts.

[0055] By way of example and not limitation, computer system 900 having the architecture, and specifically core 940, may provide functionality as a result of a processor (including a CPU, GPU, FPGA, accelerator, etc.) executing software embodied in one or more tangible computer-readable media. Such computer-readable media may be user-accessible mass storage as introduced above, as well as media associated with specific storage of core 940 that is non-transitory in nature, such as core-internal mass storage 947 or ROM 945. Software implementing various embodiments of the present disclosure may be stored on such devices and executed by core 940. The computer-readable media may include one or more memory devices or chips, depending on particular needs. The software may cause core 940, and specifically the processor therein (including a CPU, GPU, FPGA, etc.), to perform particular processes or particular portions of particular processes described herein, including defining data structures stored in RAM 946 and modifying such data structures according to the software-defined processes. Additionally or alternatively, a computer system may provide functionality as a result of logic hardwired or otherwise embodied in circuitry (e.g., accelerator 944), which may operate in place of or in conjunction with software to perform particular processes or portions of particular processes described herein. References to software may also encompass logic, where appropriate, and vice versa. References to computer-readable media may encompass circuitry (such as an integrated circuit (IC)) that stores software for execution, circuitry that embodies logic for execution, or both, where appropriate. The present disclosure encompasses any suitable combination of hardware and software.

[0056] While this disclosure describes several non-limiting embodiments, there are alterations, substitutions, and various substitute equivalents that fall within the scope of this disclosure. It will thus be appreciated that those skilled in the art will be able to devise numerous systems and methods that, although not explicitly shown or described herein, embody the principles of the present disclosure and are therefore within the spirit and scope of the present disclosure. [Explanation of symbols]

[0057] 100 Communication Systems 110 Terminal / First Terminal 120 Terminal / Second Terminal 130 terminals 140 terminals 150 Communication Network 200 Streaming System 201 Video Sources 202 Sample Stream 203 Encoder 204 encoded video bitstream 205 Streaming Server 206 Streaming Client 209 Video Bitstream 210 Video Decoder 211 video sample streams 212 Display 213 Capture Subsystem 500 processes 510 blocks 520 blocks 530 blocks 540 blocks 550 blocks 561 blocks 562 blocks 571 blocks 581 blocks 591 blocks 900 Computer Systems 901 Keyboard 902 Mouse 903 Trackpad 905 Joystick 906 Microphone 907 Scanner 908 Camera 909 Speaker 910 Touchscreen 920 CD / DVD ROM / RW 921 CD / DVD / similar media 922 thumb drive 923 Removable Hard Drive / Solid State Drive 940 cores 941 Central Processing Unit (CPU) 942 Graphics Processing Unit (GPU) 943 Field Programmable Gate Area (FPGA) 944 Hardware Accelerator 945 Read-Only Memory (ROM) 946 Random Access Memory (RAM) 947 Internal Mass Storage 948 System Bus 949 Peripheral Bus 950 graphics adapter 954 network interface 955 Cloud Computing Environment

Claims

1. A method executed by at least one processor, the method comprising: deriving a curve of a mesh sequence from frames of a video bitstream, the curve including a plurality of vertices; subdividing the curve by adding a plurality of subdivided vertices; calculating one or more displacement vectors between each of the plurality of vertices on the curve and each of the plurality of subdivided vertices on the subdivided curve; transforming the one or more displacement vectors to output one or more original coefficients; determining whether the current frame is coded using inter-picture information or intra-picture information; Including, In response to determining that the current frame is coded using inter-picture information, tracking the current frame with a previous frame to obtain a one-to-one correspondence between the vertices of the current frame and the vertices of the previous frame; predicting one or more coefficients of each of the plurality of vertices in the current frame based on the one-to-one correspondence; performing entropy coding on one or more prediction residuals; encoding the one or more prediction residuals based on the one or more predicted coefficients; Including, in response to determining that the current frame is coded using intra-picture information, encoding one or more coefficients using arithmetic coding A method comprising:

2. The method of claim 1 , wherein the one or more original coefficients are encoded.

3. The method of claim 2, wherein a signaling flag is used for each frame to indicate that one or more original coefficients should be encoded.

4. The method of claim 3 , wherein one or more separate coding contexts are used to code the prediction residuals and the original coefficients.

5. The method of claim 4 , wherein the prediction residuals or the original coefficients are encoded using a syntax structure such that a corresponding position in a sequence and a corresponding value are signaled for each prediction residual or each original coefficient.

6. The method of claim 5 further comprising the step of indicating each corresponding location using a flag.

7. The method of claim 1 , wherein the step of subdividing the curve comprises forming a thinned curve by thinning the curve and adding the plurality of subdivided vertices to the thinned curve.

8. An apparatus configured to perform the method of any one of claims 1 to 7.

9. A computer program for causing a computer to execute the method according to any one of claims 1 to 7.

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