Mesh segmentation apparatus and method for initializing the approximate plane in mesh segmentation

Abstract

To properly perform the initial setting of approximate planes for a mesh without giving the number of planes in advance.SOLUTION: A mesh segmentation apparatus comprises a face selection unit 11a for selecting one face from among a plurality of faces included in a mesh, an approximate plane setting unit 11b for setting an approximate plane for the selected face, and an area growing unit 11c for capturing the face whose error with the set approximate plane satisfies a first condition as the face of the area with respect to the approximate plane. The processing of each of these units 11a to 11c is repeatedly executed a plurality of times until a second condition is satisfied to obtain the plurality of areas and the plurality of approximate planes set by the plurality of times of the processing as the area and approximation plain for initial setting, so that the initial setting of the approximate plane can be automatically performed to suppress an error with the mesh, with an appropriate area division number, without the user having to specify the number of planes in advance.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a mesh segmentation apparatus and a method for initializing an approximate plane in mesh segmentation, and is particularly suitable for use in segmentation techniques that divide the mesh constituting measurement data of the surface shape of an object into regions according to the type and part of the object's surface. [Background technology]

[0002] Reverse engineering, a technique for converting physical measurement data into CAD data, has seen increasing demand in many industrial sectors in recent years. When converting measurement data of an object's surface shape into a CAD surface, a process called "segmentation" is necessary, which divides the mesh constituting the measurement data into regions based on the type and part of the object's surface. Here, each individual triangle constituting the mesh is called a face, and a set of one or more connected faces is called a region. As a result of segmentation, the mesh becomes a set of adjacent regions, and each face of the mesh belongs to exactly one region. Various improved techniques related to this segmentation have been known to date (see, for example, Patent Documents 1-3).

[0003] Patent Document 1 discloses a segmentation method as prior art in which, after dividing an input mesh into a group of regions, the geometric fit between the group of triangles and the group of surfaces is tested for each region based on indicators such as normal vectors and principal curvatures, and the divided group of regions is approximated by simple analytical surfaces (planes, cylindrical surfaces, spheres, conical surfaces, torus surfaces). Patent Document 1 proposes a method to overcome the problems of this prior art, such as the low accuracy of region extraction and its applicability only to simple shapes.

[0004] In other words, the segmentation device described in Patent Document 1 calculates principal curvature for non-sharp vertices from the input mesh model data, and generates a seed region consisting of a set of connected vertices that can be considered to belong to a certain analysis surface based on the calculated principal curvature. Then, by expanding this seed region, analysis surface regions are extracted, and the boundaries of the multiple analysis surface regions thus extracted are extracted as feature edges. Furthermore, fillet surface regions, etc., are recognized for each of the multiple connected analysis surface regions that have been extracted, and solid model data is generated from the feature edge information extracted in the feature edge extraction process and the surface region information recognized in the surface recognition process.

[0005] The three-dimensional model division device described in Patent Document 2 detects a plane that is a collection of small planes, which are triangles connected to each other and whose normal directions are common or opposite, within the three-dimensional model represented by the input triangular mesh. Here, the domain is expanded by collecting and merging child planes that satisfy certain conditions, and data about the final plane is obtained. At this time, the domain is gradually expanded until it is no longer possible to expand the child planes. That is, the child planes are gradually merged until it is no longer possible to merge any more child planes.

[0006] The manufacturing apparatus for three-dimensional structures described in Patent Document 3 takes 3D mesh model data represented by a plurality of mesh elements as input, and creates a plurality of 3D segments, which are sets of a plurality of mesh elements and are parts of a three-dimensional object corresponding to each assembled member, based on the input 3D mesh model data. Patent Document 3 discloses a method using Platonic solids, a method using the identification of the surface type of the mesh segments, and a method using the region growth method as segmentation algorithms. The method using the identification of the surface type is effective when it is necessary to accurately identify the type of curved surface (plane, quadratic surface, cylindrical surface, spherical surface, torus surface, wire-woven surface, etc.). The method using the region growth method is a method that can divide a 3D model with a complex shape and merge the 3D segments while minimizing the number of 3D segments.

[0007] Incidentally, one segmentation technique known as VSA (Variational Shape Approximation) is a well-known method. VSA is an algorithm that aims to approximate a complex mesh with k planes (where k is a predetermined number of planes). Segmentation using VSA is performed according to the procedure shown in Figure 5.

[0008] First, k faces are randomly selected, and a region and its approximation plane are initialized for each of the selected k faces (step S11). Here, each of the k regions consists of the selected faces and multiple faces connected to them sequentially. Next, for each of the k regions, the face that minimizes the error with respect to the corresponding approximation plane (the error between the normal vector of the face and the normal vector of the approximation plane) is searched for as the seed (starting point for growth) for the next region growth (step S12).

[0009] Then, by performing region growth from the face searched as a seed, each of the k regions is updated (step S13). Here, at faces where region growths collide, the region corresponding to the approximation plane with the smaller error is given priority for growth. Next, each approximation plane before region update is updated with the approximation plane corresponding to the updated region (step S14). The above process from steps S12 to S14 is repeated a predetermined number of times until the determination in step S15 is Yes, and finally the object surface shape of the measurement data is converted into a CAD surface using the k updated approximation planes.

[0010] VSA reduces distortion errors due to approximation by repeatedly clustering the mesh faces into regions that best fit their shape through the loop processing in steps S12 to S15. However, VSA has a drawback in that it requires the user to pre-specify the number of planes (number of regions to be divided) k in the initial setup process in step S11. Generally, the number of regions that should be the result of segmentation differs depending on the object surface shape, making it difficult for the user to pre-specify an appropriate number of planes k depending on the complex object surface shape. [Prior art documents] [Patent Documents]

[0011] [Patent Document 1] Patent No. 4568843 [Patent Document 2] Patent No. 5445199 [Patent Document 3] Patent No. 6198107 [Overview of the project] [Problems that the invention aims to solve]

[0012] This invention was made to solve such problems, and aims to enable appropriate initial setup of approximation planes for a mesh without having to specify the number of planes in advance. [Means for solving the problem]

[0013] To solve the above-mentioned problems, the present invention involves selecting one face that has not yet been selected from among multiple faces included in the mesh, setting an approximate plane for the selected face, and performing region growth by incorporating faces whose error with the most recently set approximate plane (most recent approximate plane) satisfies the first condition as faces of the region relative to the most recent approximate plane. This process is repeated multiple times until the second condition is met, so that the multiple regions and multiple approximate planes set by these multiple processes become the regions and approximate planes related to the initial settings. [Effects of the Invention]

[0014] According to the present invention configured as described above, when initializing multiple regions and corresponding approximation planes for a mesh, the user does not need to provide the number of planes in advance. Initialization is performed automatically by repeatedly executing the process of setting the approximation planes and growing the regions until the second condition is met. At that time, region growth is performed so that the error between the approximation plane and the face satisfies the first condition, so that the overall shape specified by the set of multiple approximation planes has reduced error relative to the mesh shape. Thus, according to the present invention, the initialization of approximation planes for a mesh can be performed appropriately without providing the number of planes in advance. [Brief explanation of the drawing]

[0015] [Figure 1] This is a block diagram showing an example of the functional configuration of a mesh segmentation device according to this embodiment. [Figure 2A] This is a schematic diagram illustrating the processing content (state before processing starts) of the initial setup unit according to this embodiment. [Figure 2B] This is a schematic diagram illustrating the processing content (first processing content) of the initial setup unit according to this embodiment. [Figure 2C] This is a schematic diagram illustrating the processing content (second processing content) of the initial setup unit according to this embodiment. [Figure 3]This is a diagram illustrating the allowable error angle related to the setting of a predetermined threshold for the second condition. [Figure 4] This flowchart shows an example of the operation of the mesh segmentation apparatus according to this embodiment (processing procedure for the approximation plane initial setting method performed by the initial setting unit). [Figure 5] This flowchart shows the segmentation processing procedure using VSA. [Modes for carrying out the invention]

[0016] Hereinafter, one embodiment of the present invention will be described with reference to the drawings. Figure 1 is a block diagram showing an example of the functional configuration of the mesh segmentation apparatus 10 according to this embodiment. The mesh segmentation apparatus 10 of this embodiment performs mesh segmentation using the VSA algorithm. That is, the mesh constituting the measurement data of the surface shape of an object is divided into a plurality of regions, and each of the plurality of regions is approximated by a plane.

[0017] As shown in Figure 1, the mesh segmentation apparatus 10 of this embodiment includes an initial setting unit 11 and an update processing unit 12 as its functional configuration. The initial setting unit 11 specifically includes a face selection unit 11a, an approximate plane setting unit 11b, and a region growth unit 11c.

[0018] The above-mentioned functional blocks 11 and 12 can be configured using hardware, a DSP (Digital Signal Processor), or software. For example, when configured using software, the above-mentioned functional blocks 11 and 12 are actually configured using a computer's CPU, RAM, ROM, etc., and are realized by the operation of programs stored in storage media such as RAM, ROM, hard disk, or semiconductor memory.

[0019] The initial setup unit 11 initializes multiple regions and multiple approximation planes for each region of the mesh. In this embodiment, the user does not need to specify the number of planes in advance, and the initial setup is performed automatically with an appropriate number of planes. The specific processing details of the initial setup unit 11 will be described later.

[0020] The update processing unit 12 updates the multiple regions and multiple approximation planes that were initially set by the initial setting unit 11 so that the error between the mesh and the approximation plane is reduced. The processing performed by the update processing unit 12 is as shown in steps S12 to S15 of Figure 5.

[0021] As described above, in the mesh segmentation device 10 of this embodiment, similar to the VSA algorithm, the mesh is divided into multiple regions, an approximate plane is initially set for each region, and then each region and its corresponding approximate plane are updated by region growth, thereby approximating the mesh with a plane for each of the multiple divided regions.

[0022] The specific processing details of the initial setup unit 11 are described below. The initial setup unit 11 repeatedly executes the processes of the face selection unit 11a, the approximation plane setting unit 11b, and the region growth unit 11c multiple times, thereby designating the multiple regions and multiple approximation planes set by these multiple processes as the regions and approximation planes related to the initial setup. The processes of the face selection unit 11a, the approximation plane setting unit 11b, and the region growth unit 11c are repeatedly executed until the second condition, described later, is met.

[0023] The face selection unit 11a selects multiple faces F included in the mesh. i Select one face from (i=1,2,...) that has not yet been selected. Specifically, the face selection unit 11a selects the face F that has not yet been selected. i From among them, the approximate plane P set by the approximate plane setting unit 11b j The current error d is calculated by the region growth unit 11c for (j=1,2,···) p_iSelect the single face where it is maximum. In the present embodiment, the region growing unit 11c calculates the error per unit area between the normal vector at the centroid position of the face F i and the normal vector of the approximate plane P j .

[0024] The current error d p_i refers to, for each of the plurality of faces F i included in the mesh, the minimum value among the errors between one or more approximate planes P j set by the approximate plane setting unit 11b and the face F i , and indicates the current value of the error that is appropriately updated for each face F i by the processing of the region growing unit 11c. The details of this current error d p_i will be described later. In the following description, among the plurality of current errors d i calculated for each of the plurality of faces F p_i , the maximum one is referred to as the maximum error d p_imax .

[0025] Note that at the stage of starting the processing of the initial setting unit 11, the values of the current error d i for all the faces F p_i are initialized to a huge value (for example, ∞). Therefore, immediately after starting the processing of the initial setting unit 11, the face selection unit 11a randomly selects any one face from all the faces F p_i for which the value of the current error d i is initialized to ∞.

[0026] The approximate plane setting unit 11b sets the approximate plane P j for the face selected by the face selection unit 11a. The approximate plane P j set here is an infinite plane such that the normal vector of the selected face and the normal vector of the approximate plane P j are parallel. An infinite plane refers to a plane that is assumed to extend infinitely.

[0027] The region growing unit 11c calculates, for each of the plurality of faces Fi Of these, the most recently set approximate plane P by the approximate plane setting unit 11b j Region growth is performed by incorporating faces whose error with (hereinafter referred to as the nearest approximate plane) satisfies the first condition as faces of the region relative to the nearest approximate plane. In the following explanation, the nearest approximate plane is referred to as P n This is denoted as (n=1,2,...,N, where N is the number of iterations = the final number of approximation planes to be initialized).

[0028] Here, the region growth section 11c is located in the nearest approximate plane P. n and Face F i The error (hereinafter referred to as the most recent error d) n_i (This refers to the approximation of the nearest approximation plane P) set by the approximation plane setting unit 11b. n One or more approximation planes set before (hereinafter referred to as existing approximation plane P) m (m <n))とフェイスF i The error (hereinafter referred to as the existing error d) m_i The first condition is that the current error d is below the minimum value, and then the region is grown. p_i Introducing the concept of the most recent error d n_i The current error is d p_i If it falls below the most recent error d, n_i The current error is d p_i Update this and then proceed with domain growth. This current error d p_i This is a multiple face F i For each of these, there is an existing error d of 1 or more. m_i This represents the minimum value among them, and the most recent error d n_i The current error is d p_i Each time it falls below the current error d, p_i The value of gradually decreases.

[0029] Figures 2A to 2C are schematic diagrams illustrating the processing content of the initial setup unit 11 according to this embodiment. For the sake of simplicity, it is assumed that the mesh has a total of six faces F1 to F6. Although the actual mesh has a three-dimensional shape, it is shown in a two-dimensional form here.

[0030] FIG. 2A is a diagram showing the state before starting the processing of the initial setting unit 11. At this stage, for all faces F1 to F6, the current errors d p_1 ~d p_6 are all initialized with huge values (for example, ∞).

[0031] FIG. 2B is a diagram showing the content of the first processing of the face selection unit 11a, the approximate plane setting unit 11b, and the region growing unit 11c. FIG. 2B(a) shows the processing of the face selection unit 11a and the approximate plane setting unit 11b, and FIG. 2B(b) shows the processing of the region growing unit 11c.

[0032] As shown in FIG. 2B(a), the face selection unit 11a selects one face with the maximum value among the current errors d p_1 ~d p_6 from the faces F1 to F6 that have not been selected yet. Here, since all of the current errors d p_1 ~d p_6 are ∞, the face selection unit 11a randomly selects one face. In the example of FIG. 2B(a), face F1 is selected. Next, the approximate plane setting unit 11b sets an approximate plane P1 for the selected face F1. In this case, the latest approximate plane P n is plane P1, and there is no existing approximate plane P m (m < n).

[0033] Next, as shown in FIG. 2B(b), the region growing unit 11c calculates the latest errors d 1_1 ~d 1_6 between the plurality of faces F1 to F6 included in the mesh and the latest approximate plane P1 set by the approximate plane setting unit 11b. In FIG. 2B(b), for the plurality of faces F1 to F6, the values of the latest errors d 1_1 ~d 1_6 are shown respectively. Then, with the face F1 selected by the face selection unit 11a as the starting point of region growth, the region growing unit 11c uses the latest errors d 1_1 ~d 1_6 of each face F1 to F6 calculated as above as the current errors d p_1~d p_6 On condition that it is less than the most recent error d 1_i the current error d p_i is updated, and then region growing is advanced.

[0034] Here, the most recent errors d 1_1 ~d 1_6 of the six faces F1 to F6 are all the current error d p_1 ~d p_6 (=∞). Therefore, region growing is advanced for all the faces F1 to F6, and all the faces F1 to F6 belong to the most recent approximate plane P1. Also, in all the faces F1 to F6, the most recent errors d 1_1 ~d 1_6 the current error d p_1 ~d p_6 are updated.

[0035] FIG. 2C is a diagram showing the content of the second processing of the face selection unit 11a, the approximate plane setting unit 11b, and the region growing unit 11c. FIG. 2C(a) shows the processing of the face selection unit 11a and the approximate plane setting unit 11b, and FIG. 2C(b) shows the processing of the region growing unit 11c. As shown in FIG. 2C(a), the current errors d p_1 ~d p_6 of each of the faces F1 to F6 are all the values updated in FIG. 2B(b).

[0036] As shown in FIG. 2C(a), the face selection unit 11a selects one face having the maximum value among the faces F2 to F6 for which selection has not yet been made, from the current errors d p_2 ~d p_6 . Here, among the current errors d p_2 ~d p_6 the current error d p_5 of the face F5 is the maximum. Therefore, the face selection unit 11a selects the face F5. Next, the approximate plane setting unit 11b sets an approximate plane P2 for the selected face F5. In this case, the most recent approximate plane P n is the plane P2, and the existing approximate plane P m (m < n) is the plane P1.

[0037] Next, as shown in FIG. 2C(b), the region growing unit 11c calculates the nearest errors d 2_1 ~d 2_6 between the plurality of faces F1 to F6 included in the mesh and the nearest approximation plane P2 set by the approximate plane setting unit 11b. In FIG. 2C(b), the values of the nearest errors d 2_1 ~d 2_6 between the plurality of faces F1 to F6 and the nearest approximation plane P2 are shown respectively. Then, starting from the face F5 selected by the face selection unit 11a, the region growing unit 11c updates the current error d 2_1 ~d 2_6 with the nearest error d p_1 ~d p_6 for each of the faces F1 to F6 calculated as above, on the condition that the nearest error d 2_i is less than the current error d p_i , and then proceeds with the region growth.

[0038] Here, since the nearest errors d 2_3 ~d 2_6 for the four faces F3 to F6 are less than the current error d p_3 ~d p_6 , the region growth is advanced for the four faces F3 to F6, and the four faces F3 to F6 become those belonging to the nearest approximation plane P2. Also, for the four faces F3 to F6, the current error d 2_3 ~d 2_6 is updated with the nearest error d p_3 ~d p_6 . For the two faces F1 to F2 for which the nearest error d 2_1 ~d 2_2 is not less than the current error d<00oooo99>~d p_2 , they remain belonging to the existing approximation plane P1, and the current error d p_1 ~d p_2 is not updated and remains the existing error d 1_1 ~d 1_2 .

[0039] Although not shown for the third process, the face selection unit 11a selects from the faces F2 to F4, F6 that have not yet been selected, the current error d p_2 ~dp_4 , d p_6 Select the face with the maximum value among them. Here, since the current error d p_6 of face F6 is the maximum, the face selection unit 11a selects face F6. Next, the approximate plane setting unit 11b sets an approximate plane P3 for the selected face F6. In this case, the most recent approximate plane P n is plane P3, and the existing approximate planes P m (m < n) are planes P1 and P2. For any of the faces F1 to F6, at this point, the current error d p_1 ~d p_6 is the smaller value (the minimum value) of the error from the first existing approximate plane P1 and the error from the second existing approximate plane P2.

[0040] Similarly, the processes of the face selection unit 11a, the approximate plane setting unit 11b, and the region growing unit 11c are repeatedly executed. And by executing this repeated process N times, the initial setting of approximating the mesh with N planes is completed. Each of the N approximate planes has a plurality of connected faces belonging to it, and a region is formed by the set of this plurality of faces. That is, the N regions corresponding to the N approximate planes as a result of the repeated process are the regions where the mesh is divided for each part of the surface of the object.

[0041] As described above, in this embodiment, the number N (the number of planes) of the repeated process is not specified in advance by the user, but is automatically determined. That is, in this embodiment, for each of the plurality of faces F i in the mesh, the minimum value of the error between one or more existing approximate planes P m and face F i (the current error d p_i ) is used as the error for determining the second condition, and until the maximum value (the maximum error d i ) of the current error d p_i calculated for each of the plurality of faces F p_imax is smaller than a predetermined threshold Th, the processes of the face selection unit 11a, the approximate plane setting unit 11b, and the region growing unit 11c are repeatedly executed N times.

[0042] Here, the predetermined threshold Th can be set arbitrarily, but it is preferable to set it from the following perspectives. For example, the predetermined threshold Th is a value calculated according to the angle set as the allowable error angle between the normal vector of the approximation plane and the normal vector of the face. The method for setting the predetermined threshold Th in this case is described below.

[0043] As described above, in this embodiment, Face F i and approximate plane P j As an error, Face F i Normal vector Fn i → and approximate plane P j The normal vector Pm j →This uses the error per unit area. This error per unit area can be expressed as the square of the norm of the difference in unit normal vectors, as shown in (Equation 1) below.

[0044]

number

[0045] Therefore, if we let θ be the allowable error angle between the two normal vectors, it is reasonable to set the predetermined threshold Th as shown in (Equation 2) below, based on the relationship shown in Figure 3.

[0046]

number

[0047] Here, the smaller the tolerance angle θ, the greater the number of approximate planes. Users can arbitrarily set the tolerance angle θ according to whether they want to increase or decrease the number of approximate planes. Alternatively, a recommended tolerance angle θ may be stored in advance, allowing users to arbitrarily increase or decrease it.

[0048] Figure 4 is a flowchart showing an example of the operation of the mesh segmentation apparatus 10 according to this embodiment configured as described above. This Figure 4 shows the processing procedure of the approximate plane initial setting method performed by the initial setting unit 11. Note that at the stage before the processing of the initial setting unit 11 starts, all faces F included in the mesh i Regarding the current error d p_i All of these values ​​are initialized to extremely large values ​​(for example, infinity).

[0049] First, the face selection unit 11a selects the face F that has not yet been selected. i From among them, the current error d p_i The face that maximizes this value is selected (step S1). Next, the approximation plane setting unit 11b determines the current error d of the face selected by the face selection unit 11a. p_i (=maximum error d p_imax Step S2 determines whether ) is smaller than a predetermined threshold Th.

[0050] Here, the maximum error d p_imax If it is determined that the value is not smaller than a predetermined threshold Th, the approximation plane setting unit 11b sets an approximation plane P for the face selected by the face selection unit 11a. j (nearest approximate plane P) n ) is set (step S3). Next, the region growth section 11c has multiple faces F included in the mesh. i Of these, the nearest approximation plane P n The most recent error d is the error between the two. n_i The current error is d p_i A face that satisfies the first condition of being below the nearest error d n_i The current error is d p_i After updating, the most recent approximate plane P n Region growth is performed by incorporating the region as a face for that region (step S4). After that, the process returns to step S1.

[0051] In step S2 above, the maximum error d p_imaxIf it is determined that the value is smaller than a predetermined threshold Th, the initial setup unit 11 terminates the initial setup process. After this, the update processing unit 12 executes the processes shown in steps S12 to S15 in Figure 5.

[0052] As explained in detail above, in this embodiment, in mesh segmentation by the VSA algorithm, multiple faces F included in the mesh i Select one face from among those that has not yet been selected, and apply the approximate plane P to the selected face. j Set the most recently set approximate plane P j (nearest approximate plane P) n The nearest approximate plane P is the face whose error with ) satisfies the first condition. n By repeatedly performing a series of processes, including incorporating the region as a face of the region, to grow the region, until the second condition is met, multiple regions and multiple approximate planes P set by these multiple processes are obtained. j This is set to be the area and approximate plane related to the initial settings.

[0053] According to this embodiment configured as described above, when initializing multiple regions and corresponding approximation planes for a mesh, the user does not need to provide the number of planes in advance. Initialization is performed automatically by repeatedly executing the process of setting the approximation planes and growing the regions until the second condition is met. At that time, region growth is performed so that the error between the approximation plane and the face satisfies the first condition, so that the overall shape identified by the set of multiple approximation planes has reduced error relative to the mesh shape. Thus, according to this embodiment, the initial setup of approximation planes for a mesh can be performed appropriately without providing the number of planes in advance.

[0054] In the above embodiment, the current error d p_i An example of using to determine the first condition has been described, but the example is not limited to this one. For example, multiple F included in the mesh i For each, one or more existing approximate planes P mand Face F i The error d m_i Each of these is stored in memory, and when determining the first condition, Face F i Error d for each m_i Alternatively, we could try to identify the minimum value from (m=1,2,...). However, the current error d p_i It is preferable to store the data while updating it, as this reduces the computational load.

[0055] Furthermore, the above embodiments are merely examples of how the present invention may be implemented, and the technical scope of the invention should not be interpreted as being limited by them. In other words, the present invention can be implemented in various ways without departing from its gist or its main features. [Explanation of Symbols]

[0056] 10 Mesh segmentation device 11 Initial setting section 11a Face selection section 11b Approximate plane setting section 11c Area Growth Department 12 Update Processing Unit

Claims

1. A mesh segmentation device that divides the mesh constituting measurement data of the surface shape of an object into multiple regions, and approximates each of the multiple regions with a plane, An initial setup unit that initializes the above-mentioned multiple regions and multiple approximate planes for each of the above regions for the above-mentioned mesh, The system includes an update processing unit that updates the multiple regions and multiple approximation planes initially set by the initial setting unit so as to reduce the error between the mesh and the approximation planes. The above initial setup section is, A face selection unit that selects one face from among the multiple faces included in the above mesh that has not yet been selected, An approximation plane setting unit sets the approximation plane for the face selected by the face selection unit, The region growth unit performs region growth by incorporating, among multiple faces included in the above mesh, faces whose error with the most recent approximation plane (which is the most recent approximation plane set by the above approximation plane setting unit) satisfies the first condition as faces of the region relative to the most recent approximation plane. The above face selection unit selects one face from among the faces that have not yet been selected that maximizes the minimum error between the face and one or more existing approximate planes, which are approximate planes set by the above approximate plane setting unit before the most recent approximate plane. The above-mentioned region growth section is performed under the first condition that the error between the nearest approximate plane and the face is less than the minimum error between the one or more existing approximate planes and the face. The minimum value of the error between the one or more existing approximate planes calculated for each of the multiple faces included in the mesh and the face is used as the determination error for the second condition. The processes of the face selection unit, the approximate plane setting unit, and the region growth unit are repeatedly executed multiple times until the maximum value of the determination error calculated for each of the multiple faces becomes smaller than a predetermined threshold, thereby satisfying the second condition. The multiple regions and multiple approximate planes set by these multiple processes are then set as the regions and approximate planes related to the initial settings. A mesh segmentation apparatus characterized by the following:

2. The mesh segmentation apparatus according to claim 1, characterized in that the region growth unit stores the minimum value of the error between one or more existing approximate planes and the face for each of the multiple faces included in the mesh as the current error, and updates the current error with the error between the nearest approximate plane and the face, with the first condition being that the error between the nearest approximate plane and the face is less than the current error, and then proceeds with region growth.

3. The mesh segmentation apparatus according to claim 1 or 2, characterized in that the predetermined threshold is a value calculated according to the angle set as the allowable error angle between the normal vector of the approximate plane and the normal vector of the face.

4. A mesh segmentation device that initializes multiple regions and multiple approximation planes for each region in a mesh constituting measurement data of the surface shape of an object, and then updates the initialized multiple regions and multiple approximation planes so as to reduce the error between the mesh and the approximation planes, wherein the initial initialization is performed by a mesh segmentation device, The first step is for the face selection unit of the mesh segmentation apparatus to select one face that has not yet been selected from among the multiple faces included in the mesh, The mesh segmentation apparatus performs a second step of setting the approximate plane for the faces selected by the face selection unit, The region growth unit of the mesh segmentation apparatus has a third step of performing region growth by incorporating, among a plurality of faces included in the mesh, faces whose error with the nearest approximate plane, which is the approximate plane most recently set by the approximate plane setting unit, satisfies a first condition, as region faces with respect to the nearest approximate plane. The above face selection unit selects one face from among the faces that have not yet been selected that maximizes the minimum error between the face and one or more existing approximate planes, which are approximate planes set by the above approximate plane setting unit before the most recent approximate plane. The above-mentioned region growth section is performed under the first condition that the error between the nearest approximate plane and the face is less than the minimum error between the one or more existing approximate planes and the face. The minimum value of the error between the one or more existing approximate planes calculated for each of the multiple faces included in the mesh and the face is used as the determination error for the second condition. The processes of the face selection unit, the approximate plane setting unit, and the region growth unit are repeatedly executed multiple times until the maximum value of the determination error calculated for each of the multiple faces becomes smaller than a predetermined threshold, thereby satisfying the second condition. The multiple regions and multiple approximate planes set by these multiple processes are then set as the regions and approximate planes related to the initial settings. A method for initializing the approximate plane in mesh segmentation, characterized by the above.

Images