Mesh segmentation apparatus and method for setting termination conditions in mesh segmentation

Abstract

To enable a threshold used as a termination condition of area connection to be appropriately set regardless of the mesh to be processed.SOLUTION: A mesh segmentation device includes a permissible error value setting part 11a for setting a permissible error value showing a degree of a permissible error between a normalized mesh in the case of assuming that an input mesh is expanded or reduced to be placed so as to be inscribed in a unit cube and an approximate shape set to the normalized mesh, and a threshold calculation part 11b for calculating a threshold by a function having the set permissible error value and a surface area of the mesh as variables, and can calculate and set an appropriate threshold by the function only by setting the permissible error value by using the matter that an error between the input mesh and an approximate shape corresponding to it can be approximated by the function with the error between the normalized mesh and the approximate shape corresponding to it and the surface area of the input mesh as variables even in the input mesh generated from an object having any kind of a surface shape.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a mesh segmentation apparatus and a method for setting termination conditions 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] That is, in the segmentation device described in Patent Document 1, for vertices that are not sharp vertices in the input mesh model data, the principal curvatures are calculated, and based on the calculated principal curvatures, a seed region consisting of a set of connected vertices that can be regarded as belonging to a certain analysis surface is generated. Then, the analysis surface region is extracted by expanding this seed region, and the boundary lines of the plurality of analysis surface regions thus extracted are extracted as characteristic ridge lines. Further, for each of the plurality of connected analysis surface regions extracted, a fillet surface region or the like is recognized, and solid model data is generated from the information of the characteristic ridge lines extracted by the characteristic ridge line extraction process and the information of the surface regions recognized by the surface recognition process.

[0005] In the three-dimensional model segmentation device described in Patent Document 2, a plane is detected that is formed by gathering small planes in a three-dimensional model represented by an input triangular mesh, where the triangles are connected to each other and the normal directions of the triangles are common or opposite. Here, by gathering and merging child planes that satisfy certain conditions, the region is expanded to obtain data regarding the final plane. At this time, the region is gradually expanded until the child planes cannot be expanded any further. That is, the child planes are gradually merged until all the child planes can no longer be merged.

[0006] In the manufacturing device for a three-dimensional structure described in Patent Document 3, 3D mesh model data represented by a plurality of mesh elements is input, and based on the input 3D mesh model data, a plurality of 3D segments that are a set of a plurality of mesh elements and are part of a solid corresponding to each assembly member are created. Patent Document 3 discloses, as segmentation algorithms, a method using Platonic solids, a method using identification of the surface type of mesh segments, and a method using the region growing method. The method using identification of the surface type is an effective method when it is necessary to accurately identify the type of the surface (plane, quadratic surface, cylindrical surface, spherical surface, toroidal surface, wire-woven surface, etc.). The method using the region growing 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] By the way, as one of the segmentation techniques, a technique called HMS (Hierarchical Mesh Segmentation) is known. HMS is an algorithm based on fitting to basic shapes such as planes, spheres, and cylindrical surfaces, and is an effective segmentation algorithm for mesh models of object surface shapes that contain many basic shapes like industrial products. The segmentation by HMS is executed according to the procedure shown in FIG. 4.

[0008] First, as an initial state, each face included in the mesh is regarded as an independent region. Then, from each region (in the initial state where there is no combined region, each face) included in the mesh, a pair of adjacent regions is selected, and the error L between the combined region composed of the pair and the basic shape (any one of a plane, a sphere, and a cylindrical surface) approximating it 2 is obtained such that it is minimized (step S11). The error L 2 is calculated by the area-weighted sum of the squared distances between the centroid points of each face included in the combined region and the basic shape, as shown in the following (Equation A).

[0009] L 2 = min{L 2 (plane), L 2 (sphere), L 2 (cylindrical surface)} = min{Σa i h pi 2 , Σa i h si 2 , Σa i h ci 2} ··· (Equation A) Here, i = 1, 2, ···, n (n is the number of faces included in the combined region) a i is the area of each face h pi is the distance between each face and the plane h si is the distance between each face and the sphere h ci is the distance between each face and the cylindrical surface

[0010] Here, the minimum error L calculated based on (Equation A) above 2 min It is determined whether the value exceeds the threshold Th (step S12), and if it does, the process is terminated. Meanwhile, the minimum error L 2 min If the threshold Th is not exceeded, the pair of regions obtained in step S11 are joined, and the joined region becomes a new region (step S13). Then, the process returns to step S11 and continues.

[0011] The key to HMS is that it creates a hierarchy of regions by repeatedly combining pairs of adjacent regions that best approximate each other with a common base shape. The larger the given threshold Th, the more region pairs are combined, resulting in fewer regions in the partitioned area, while the error L between the combined region and the base shape increases. 2 The error becomes larger. Figure 5 shows the number of region joins and the overall approximation error (the error between the mesh and the entire approximation shape, which is the set of joined regions, and the error L for each joined region) when HMS is applied to a certain mesh. 2 This figure shows the relationship with the sum of the values. From Figure 5, it can be seen that the approximation error increases as the number of regions is joined, and that the approximation error becomes rapidly larger after a certain number of region joins.

[0012] Setting the threshold Th in HMS is equivalent to determining how much increase in approximation error is tolerable as region joining progresses. However, in general, in HMS, as mentioned above, the error L is calculated using a formula such as the area weighted sum of the squared distances between the centroid of each face included in the joined region and the basic shape. 2 Because of the calculation involved, the approximation error of the approximate shape relative to the mesh is determined by complex factors such as the mesh's shape, size, and number of faces. This presented a problem in that it was difficult for users to intuitively set an appropriate threshold Th. [Prior art documents] [Patent Documents]

[0013] [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]

[0014] This invention was made to solve these problems, and aims to enable the appropriate setting of a threshold value used as a termination condition for region joining, regardless of the mesh being processed. [Means for solving the problem]

[0015] To solve the above-mentioned problems, the present invention performs mesh segmentation by a region growth process in which a joined region consisting of one or more faces is sequentially expanded within a range that satisfies the condition that the error between the joined region and the basic shape approximating it is below a threshold. Before starting the region growth process, a threshold that serves as the termination condition for the region growth process is set in advance as follows. That is, the present invention sets a value that indicates the degree of tolerance error between the normalized mesh, which is assumed to be enlarged or reduced to fit inscribed within a unit cube, and the overall approximate shape obtained when the divided regions set in the normalized mesh are assumed to be approximated by the basic shape. The threshold is calculated using a function that has the set tolerance value and the surface area of ​​the mesh as variables. [Effects of the Invention]

[0016] The inventors of the present invention, configured as described above, have found that, regardless of the surface shape of the object from which the mesh is generated, if we assume that the normalized mesh is enlarged or reduced to fit inscribed within a unit cube, the error between the mesh and the overall approximate shape obtained by assuming that each of the divided regions set in the mesh is approximated by the basic shape can be approximated by a predetermined function. The predetermined function is a function in which the error between the normalized mesh and the overall approximate shape obtained by assuming that each of the divided regions set in the normalized mesh is approximated by the basic shape, and the surface area of ​​the mesh are variables. Since the surface area of ​​the mesh is a calculable value, by setting a value that indicates the degree of allowable error between the normalized mesh and the approximate shape, and using this value in place of the above error, a threshold indicating the degree of allowable error for the original mesh can be obtained. Thus, according to the present invention, it is possible to appropriately set the threshold used as the termination condition for region joining, regardless of the mesh being processed. [Brief explanation of the drawing]

[0017] [Figure 1] This is a block diagram showing an example of the functional configuration of a mesh segmentation device according to this embodiment. [Figure 2] This figure shows an example of a normalized mesh. [Figure 3] This flowchart shows an example of the operation of the mesh segmentation device according to this embodiment (processing procedure for the termination condition setting method executed by the threshold setting unit). [Figure 4] This flowchart shows the segmentation processing procedure using HMS. [Figure 5] This figure shows the relationship between the number of region joins and the approximation error when HMS is applied to a certain mesh. [Modes for carrying out the invention]

[0018] 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 HMS algorithm. That is, by repeatedly performing a region growth process in which a combined region consisting of one or more faces is sequentially expanded within a range that satisfies the condition that the error between the combined region and the basic shape approximating it is below a threshold, the mesh constituting the measurement data of the object surface shape is divided into multiple regions, each approximated by a basic shape.

[0019] As shown in Figure 1, the mesh segmentation apparatus 10 of this embodiment includes a threshold setting unit 11 and a region growth unit 12 as its functional configuration. The threshold setting unit 11 specifically includes an allowable error value setting unit 11a and a threshold calculation unit 11b.

[0020] 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.

[0021] The threshold setting unit 11 pre-sets a threshold that will serve as the termination condition for the region growth process before the region growth process by the region growth unit 12 begins. The region growth unit 12 divides the mesh into multiple regions by sequentially expanding a combined region consisting of one or more faces within a range that satisfies the condition that the error between the combined region and the basic shape approximating it is less than or equal to the threshold. The process performed by this region growth unit 12 is as shown in Figure 4.

[0022] The tolerance value setting unit 11a sets a value (hereinafter referred to as the tolerance value d) that indicates the degree of tolerance between the normalized mesh, which is obtained when it is assumed that the mesh to be processed is enlarged or reduced so that it fits inscribed within a unit cube, and the overall approximate shape obtained when it is assumed that the divided regions set in the normalized mesh are approximated by the basic shape. The user's instructions are given through input operations on a predetermined input screen using an input device such as a keyboard, mouse, or touch panel.

[0023] Figure 2 shows an example of a normalized mesh. Figure 2(a) is the mesh before scaling, and is the input mesh to be processed, consisting of measurement data of the object's surface shape. Figure 2(b) is the normalized mesh assuming that the input mesh is contained within a unit cube, and here we show an example of normalization by scaling down the input mesh. A unit cube is a cube where the length of each side is unit length (=1). Inscription means that a part of the input mesh is in contact with one of the six faces of the unit cube, and the volume of the normalized mesh is maximized within the unit cube.

[0024] The normalized mesh shown in Figure 2(b) (and the input mesh shown in Figure 2(a)) is divided into multiple regions by segmentation. Each divided region is approximated by a basic shape (either a plane, a sphere, or a cylindrical surface). As a result, the normalized mesh is represented as an approximate shape in which multiple basic shapes approximated for each divided region are connected. In this case, an approximation error occurs between the normalized mesh and the approximate shape. The tolerance error value setting unit 11a sets a tolerance error value d, which indicates how much of this approximation error is tolerable, based on instructions from the user.

[0025] The threshold calculation unit 11b calculates a threshold that serves as the termination condition for the region growth process by the region growth unit 12, using a function that has the tolerance error value d set by the tolerance error value setting unit 11a and the surface area of ​​the input mesh as variables. When the surface area of ​​the input mesh is A and the threshold is Th, the threshold calculation unit 11b calculates the threshold Th using the function shown in (Equation 1) below. The surface area A of the input mesh is a value that can actually be calculated. Th=A 2 d 2 ...(Formula 1)

[0026] The validity of calculating the threshold Th using (Equation 1) is explained below. Now, assume that the input mesh is replaced with a normalized mesh by scaling it up or down by a factor s.

[0027] As explained above (Equation A), the approximation error L between the input mesh and the overall approximate shape obtained when assuming that the input mesh and the divided regions set in the input mesh are each approximated by the basic shape is o 2 This is calculated using the area weight sum of the squared distances between the centroid of each face and the base shape, as shown in (Equation 2) below. L o 2 =Σa j h j 2 ...(Formula 2) j = 1, 2, ..., N (where N is the number of faces in the input mesh) a j The area of ​​each face h j This is the distance between each face and the base shape (either a plane, a sphere, or a cylindrical surface).

[0028] In contrast, the approximation error L between the normalized mesh and the overall approximate shape obtained by assuming that the divided regions set in the normalized mesh are each approximated by the basic shape is different. s 2 This can be expressed using a magnification factor s as follows (Equation 3): L s 2 =Σ(s 2 aj )(sh j ) 2 =s 4 Σa j h j 2 =s 4 L o 2 ...(Formula 3)

[0029] Here, the surface area A of the input mesh is given by A = Σa j Let (j=1,2,···,N) be the surface area s of the normalized mesh. 2 Assuming that A is equal to 1, the following equation (Equation 4) holds. L o 2 =L s 2 / s 4 = (1 / s 2 ) 2 L s 2 =A 2 L s 2 ...(Formula 4)

[0030] Based on the above analysis, we specify the tolerance value d between the normalized mesh and its approximate shape, and use this in (Equation 4) L s 2 By using this instead, it can be seen that the threshold Th can be expressed as shown in (Equation 1) above. Here, the smaller the tolerance value d, the more finely the region will be divided into. For example, a recommended tolerance value d can be set as the initial value, and the system can be configured to allow adjustment of the tolerance value d according to the user's specifications.

[0031] Figure 3 is a flowchart showing an example of the operation of the mesh segmentation device 10 according to this embodiment, configured as described above. This Figure 3 shows the processing procedure for the termination condition setting method executed by the threshold setting unit 11.

[0032] First, the tolerance value setting unit 11a sets a tolerance value d, which indicates the degree of tolerance between the normalized mesh corresponding to the input mesh and the overall approximate shape obtained by assuming that the divided regions of the normalized mesh are each approximated by the basic shape, based on instructions from the user (step S1). Next, the threshold calculation unit 11b calculates and sets a threshold Th using a function (Equation 1 described above) that has the tolerance value d set by the tolerance value setting unit 11a and the surface area A of the input mesh as variables (step S2). This completes the processing of the threshold setting unit 11. After this, the processing of the region growth unit 12 is carried out according to the flowchart shown in Figure 4.

[0033] As explained in detail above, in this embodiment, when setting the threshold Th which is the termination condition for the region growth process in mesh segmentation using the HMS algorithm, an tolerance value d is set which indicates the degree of tolerance error between the normalized mesh, which is assumed to be enlarged or reduced to fit inscribed within a unit cube, and the overall approximate shape obtained by assuming that the divided regions set in the normalized mesh are approximated by the basic shape. The threshold Th is then calculated using a function (Equation 1) which has the set tolerance value d and the surface area A of the mesh as variables.

[0034] As explained using (Equations 1) to (4) above, the inventors have found that, regardless of the surface shape of the object from which the input mesh was generated, if we assume that the normalized mesh is obtained by scaling it up or down so that it is inscribed within a unit cube, then the approximation error L between the input mesh and the corresponding approximate shape is o 2 The approximation error L between the normalized mesh and its corresponding approximate shape. s 2 We also found that it can be approximated by a function of (Equation 4) with the surface area A of the input mesh as a variable.

[0035] Since the surface area A of the input mesh is a calculable value, by setting an allowable error value d that indicates the degree of tolerance between the normalized mesh and the approximate shape and calculating the function in (Equation 1), a threshold Th indicating the degree of allowable error for the input mesh can be obtained. Thus, according to this embodiment, regardless of the mesh to be processed, it is possible to appropriately set the threshold Th used as the termination condition for region joining when executing the region growth process by the region growth unit 12.

[0036] In the above embodiment, when the processing of the region growth unit 12 is completed, the user may be notified by displaying the number of divided regions on the display screen. The user may check the displayed number of regions and, if necessary, readjust the tolerance value d to re-execute the processing of the region growth unit 12 to adjust the number of divided regions.

[0037] 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]

[0038] 10 Mesh segmentation device 11. Threshold setting section 11a Tolerance value setting section 11b Threshold calculation unit 12 Area Growth Department

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 basic shape, A region growth unit that sequentially expands a joint region consisting of one or more faces within a range that satisfies the condition that the error between the joint region and the basic shape approximating it is below a threshold, The system includes a threshold setting unit that pre-sets the threshold before starting the processing of the region growth unit, The threshold setting unit described above is A tolerance value setting unit sets a value that indicates the degree of tolerance error between the normalized mesh obtained when the above mesh is assumed to be enlarged or reduced so as to be inscribed within a unit cube, and the overall approximate shape obtained when the divided regions set in the normalized mesh are assumed to be approximated by the above basic shape, The system includes a threshold calculation unit that calculates the threshold value using a function Th = A²d² (where Th is the threshold value) which has the tolerance value d set by the tolerance value setting unit and the surface area A of the mesh as variables. A mesh segmentation apparatus characterized by the following:

2. The mesh segmentation apparatus according to claim 1, characterized in that the above-mentioned tolerance value setting unit is configured to initially set the recommended tolerance value and to be adjustable according to the user's specifications.

3. A mesh segmentation device that divides the mesh constituting measurement data of an object's surface shape into multiple regions approximated by the basic shape by repeatedly performing a region growth process in which a joined region consisting of one or more faces is sequentially expanded within a range that satisfies the condition that the error between the joined region and a basic shape approximating the joined region is below a threshold, a method for setting the threshold that serves as the termination condition for the region growth process before starting the region growth process, A first step in which the computer's tolerance value setting unit sets a value indicating the degree of tolerance between the normalized mesh, which is obtained when it is assumed that the mesh is enlarged or reduced so that it fits inscribed within a unit cube, and the overall approximate shape obtained when it is assumed that the divided regions set in the normalized mesh are approximated by the basic shape; The above computer's threshold calculation unit has a second step of calculating and setting the threshold using a function Th = A 2 d 2 (where Th is the threshold) which has the tolerance value d set by the tolerance value setting unit and the surface area A of the mesh as variables. A method for setting termination conditions in mesh segmentation, characterized by the above.

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