JP2017102855A - Average shape calculation method of three-dimensional shape object and program thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a body shape data standardization system, a method, a program and a recording medium which can improve size error of an average size and can get interchangeability with existing average size.SOLUTION: A body shape data standardization system comprises a calculation device calculating a statistical average shape (average person) from 3D human body shape data of many people and a drawing device drawing the calculated average shape, and calculates average of length of edge of each polygon forming multiple 3D human body shape data. An average shape of the human body is obtained by calculating a coordinate value of a 3D object that error square sum with the calculated length of the edge average becomes very small.SELECTED DRAWING: Figure 5

Description

  The present invention relates to a method for obtaining a statistical average shape (average person or average object) from, for example, a three-dimensional human body or object shape data (3D data) measured by a 3D scanner.

  When designing clothes, conventionally, for example, a prototype of a clothing was made based on a full-scale human body model called a “body”, and the clothes produced based on the prototype were attached to this “body”. Is more fit to the body, or when worn, the pattern is modified so that the appearance looks good.

  When producing this “body”, the producer considers the basic average dimensions, for example, 3 sizes (bust, waist, hips), based on the measured dimensions (existing average dimensions) measured using a measure. Based on his experience, he created an average three-dimensional shape. Since the creation of this “body” requires a great deal of labor and manual work by craftsmen, for example, if it is a “body” for women's clothing, it is limited to No. 7, No. 11, No. 13, etc. Only size was produced, and changes in body shape by age and differences in body shape by race were not taken into account. Therefore, the “body” produced by the production method is not an ideal human body shape.

  On the other hand, it is not a measurement dimension measured with a measure, but recently, using a “3D scanner” or the like, the three-dimensional coordinates (called xyz coordinates) of the surface points of the human body are measured, and not only the dimensions but also the three-dimensional shape Anthropometric measurements that can be reproduced visually are performed. According to this three-dimensional shape measurement, it is possible to visually recognize the three-dimensional shape of one person in three dimensions. Hereinafter, a set of coordinate values obtained by measuring the xyz coordinates of each point on the surface of the human body is referred to as “human body shape data”.

  If a plurality of human body shape data can be measured using the “3D scanner” described above, the obtained human body shape data can be used for various purposes. For example, it is conceivable that statistical processing is performed using a plurality of human body shape data to obtain a standard shape (average shape) of the human body.

  However, in order to obtain the average of human body shape data of a plurality of people, that is, the average of the shape expressed in xyz coordinates, it is necessary that all human body shape data is composed of the same number of points, and that each coordinate is anatomical. Must have the same meaning. There is a “homology model” as a human body shape model developed to satisfy these conditions and perform statistical processing (Patent Document 1). In this specification, when measuring the xyz coordinates of the body surface of each person, the process of aligning the number and position of the measured coordinates based on the homology model is referred to as “homology”. In the homology, the standard template of the homologous model is fitted to 3D data indicating the whole body shape of the human body, for example, 3D data obtained by measuring the surface of the human body three-dimensionally in a mesh pattern with several mm pits. By performing homology on the 3D data of each person, all human body shapes can be expressed as polygon data having the same number of points and the same geometric structure.

JP 2008-171074 A

  As an example of a conventional method for obtaining an average shape, there is a method in which an average is obtained for coordinate values obtained by homogenizing a plurality of human bodies, and a shape constituted by the average is used as an average shape. FIG. 6 is a schematic diagram for explaining a comparison between the conventional method and the method according to the present invention described later. In FIG. 6, each part of the human body at each part when the origin is between both soles of the human body, for example, the head, shoulders, chest, elbows, navel, base of legs, hands, knees, soles, etc. It is the figure which plotted the position of the coordinate value and the average (average coordinate) of each coordinate value.

  In the figure, in the conventional method (left side in the figure), the variation between the average point and the coordinate point of each person is small at a position near the origin, for example, the position of the knee, but at a location away from the origin, for example, a shoulder. In the position of the head, the variation between the respective distribution points and the average point is large, and the hand is more widely dispersed. That is, there is a large difference in the variation in the coordinates of each person in each part of the body, so if the shape formed by the average coordinates is the average shape, it cannot be said that an appropriate shape is necessarily obtained.

  An object of the present invention is to provide a method for generating an average dimension with improved dimensional errors.

  The present invention pays attention to the amount invariable to the position of the origin (coordinate conversion), that is, the length of each triangle side (joint condition) constituting the shape of the human body surface, and obtains the average of these. .

を算出する工程と、前記複数の三次元オブジェクトと同一点数及び同一幾何学構造のポリゴンとして表現された平均形状の三次元オブジェクトについて、該平均形状三次元オブジェクトの各辺の長さ（l_i）と前記各辺の平均値

との誤差二乗和を最小にする、前記平均形状三次元オブジェクトの座標値を算出する工程と、を実行することで、三次元オブジェクトの平均形状を算出する事を特徴とする。 One of the representative methods for calculating the average shape of a three-dimensional object according to the present invention is to calculate the average value of each side for a plurality of three-dimensional objects expressed using a plurality of polygons.

And calculating the length (l _i ) of each side of the average shape three-dimensional object with respect to the average shape three-dimensional object expressed as a polygon having the same number of points and the same geometric structure as the plurality of three-dimensional objects. And the average value of each side

The average shape of the three-dimensional object is calculated by executing the step of calculating the coordinate value of the average shape three-dimensional object that minimizes the sum of squared errors.

とl_iの誤差二乗和を最小にする、前記平均形状三次元オブジェクトの座標値を算出する工程では、たとえば準ニュートン法を用いることができる。準ニュートン法を用いる場合、複数の三次元オブジェクトのうち、ひとつの三次元オブジェクトの座標値を平均形状三次元オブジェクトの初期座標値とし、準ニュートン法によって前記初期座標値を反復的に補正することで、前記平均形状三次元オブジェクトの座標値を算出する。

For example, a quasi-Newton method can be used in the step of calculating the coordinate value of the average shape three-dimensional object that minimizes the sum of squared errors of and l _i . When using the quasi-Newton method, the coordinate value of one of the three-dimensional objects is used as the initial coordinate value of the average shape three-dimensional object, and the initial coordinate value is repeatedly corrected by the quasi-Newton method. Then, the coordinate value of the average shape three-dimensional object is calculated.

  According to the present invention, it is possible to obtain body shape data that can improve the dimensional error of the average dimension and can be compatible with the existing average dimension.

  Further, it is possible to obtain body shape data in which the size of one person's whole body can match the average value of a plurality of individual data.

  For example, a body sample (product sample) is created by cutting out the body shape (average person / model) with the actual size based on the body shape data obtained by this system or method, and the sample of the clothes is average person. When mounted on a (model), it can be expected to improve product quality that is comfortable to wear.

  Problems, configurations, and effects other than those described above will become apparent from the following description of embodiments.

It is a block diagram which shows the structural example of the body shape data standardization system which concerns on one Example of this invention. It is a figure which shows the example of the program run with a calculation apparatus (processor). It is a figure which shows the vertex sample of a triangle. It is a figure which shows the length sample of a triangle. 5 is a flowchart illustrating a procedure for calculating an average shape in the first embodiment. It is a figure showing the problem of the conventional method. It is a comparison figure of the average shape calculated | required from the coordinate average of nine triangles, and the average shape calculated | required from the length average of a side. It is a figure which shows an example of the effect of this invention. 10 is a flowchart illustrating a procedure for calculating an average shape in the second embodiment. 10 is a flowchart illustrating a procedure for calculating an average shape in the third embodiment. It is an example of the change of a human body shape when changing a 1st main component. It is an example of the change of a human body shape when changing a 2nd main component. It is an example of the result of having performed principal component analysis about the length of the edge. It is an example of the result of having performed the principal component analysis about the angle.

  Embodiments of the present invention will be described below with reference to the drawings. In the following description, the contents of processing may be described with “program” as the subject, but in reality, the program is read by a computer (for example, a CPU (Central Processing Unit)) included in the server or the like. By executing, the processing is executed. In the following description, when the contents of the process are described with the program as the subject, it means that the process is actually executed by the CPU of the server that executes the program. The program may be installed on each computer from a program source. The program source may be provided by, for example, a program distribution server or a storage medium.

  First, discussions by the present inventors and an outline of the examples will be described. As described above, the homogenized human body shape data is expressed as polygon (specifically, triangle) data having the same number of points and the same geometric structure. In considering the “average” shape of the three-dimensional shape object, first, the average shape of the triangles forming the three-dimensional shape object will be described.

  FIG. 7 is a conceptual diagram for comparing and explaining “coordinate average” (conventional method) and “side length average” (method of the present invention) of nine triangles. A and B in FIG. 7 are average shapes obtained by calculating the average of the coordinates of nine triangles. On the other hand, C in FIG. 7 is an average shape obtained by calculating the average length of the sides of nine triangles.

  In the figure, in the conventional method for obtaining the average of coordinates, there are several results depending on the “alignment” of the triangles. In other words, the result greatly varies depending on the setting of parameters completely unrelated to the shape, such as which vertex (or center of gravity, etc.) is used as the origin, and in which direction the x-axis and y-axis are set. A and B in the figure show such a state. For example, it has been found that when the coordinates of nine triangles are averaged by changing the origin and coordinate axes that are generally used in the past, the results are greatly different. This means how unstable the coordinate average is.

  However, as in the present invention, when the lengths of the sides of the triangle are averaged, the result is stable regardless of the position of the triangle and the direction of the triangle. C in FIG. 7 shows such a state, and the average shape is determined in one way.

  The concept of 3D data is basically the same as described above. The 3D data of the human body is basically composed of triangular polygons. Therefore, if an average is taken of the lengths of the sides of each triangle constituting the whole body, it is considered that it represents an average shape (average). In an ideal homologous model with an infinitely small triangle size, the length of this side corresponds to the geodesic distance.

  The average value of the measurement dimension on the body surface of the 3D data is consistent with the dimension at the corresponding position of this model. That is, it can be said that the average person made by this method has a shape in which the whole body is composed of average dimensions. Actually, since the size of the triangle is finite, some error will appear, but unlike the average shape of coordinates, which is completely unrelated to the average size, the whole body is basically composed of the average size. This average shape is much easier to use, for example, in the field of garment manufacture.

  Therefore, the present inventor pays attention to the “triangle side length” constituting the 3D data, and all the triangles forming the 3D shape data from all the 3D shape data for which the average shape is obtained. A calculation method has been devised in which the average of the lengths of the sides is obtained, and three-dimensional shape data having a length equal to (or closest to) the average of the obtained side lengths is used as the average shape.

  In the following description, an example in which an average shape is obtained by using human body shape data for K people will be described (K is an integer of 1 or more). Prior to the description of the principle of calculating the average shape, the meanings of terms and symbols used below will be described.

Each side of the triangle constituting the three-dimensional shape data (human body shape data) is managed by assigning a number or code to each side so that each side can be identified. For example, as shown in FIGS. 3 and 4, identification numbers such as edge 1, edge 2,... Are attached to each side of the triangle, and identification numbers such as vertex 1. Attached and managed. In the following, it is assumed that one human body shape data has m vertices (in the case of a homologous model, m is an integer value such as 3346), and the i-th human body shape data (1 ≦ i ≦ K) Is expressed as P _ij (j is an integer not less than 1 and not more than m). When the vertex P _ij is expressed by xyz coordinates, it is expressed as P _ij = (x _ij , y _ij , z _ij ). Note that vertices having the same subscript j mean vertices at the same position on the body surface. For example, the vertex P _{aj of the} a-th human body shape data and the vertex P _bj of the b-th human body shape data mean vertices at the same position on the body surface.

Further, it is assumed that one (for one person) human body shape data has n (for example, 10032) triangular sides, and the length of the jth side in the i-th human body shape data is l _ij (here I and j are integers satisfying the relations 1 ≦ i ≦ K and 1 ≦ j ≦ n). Naturally, the length of each side is the distance between two vertices (for example, P _ia and P _ib ) among the three vertices of the triangle constituting the human body shape data. Therefore l _ij is, when representing the length between the top point P _ia and P _ib, and l _ij and the vertex P _ia and P _ib coordinates are in a relationship represented by the following formula (1).

と表記する。なお、表現が冗長になることを避けるために、以下ではＫ人分の人体形状データから算出された辺の平均値

のことを、単に「各辺の平均値」あるいは「各辺の長さの平均値」と呼ぶ。

は一般的な平均値の算出方法、つまり以下の式（２）によって算出される。

In the average shape calculation method described in the examples (particularly, Example 1) of the present specification, the average value of the lengths of the sides of the human body shape data is used. Below, among the average values of the sides calculated from the human body shape data for K people, the average value of the jth side is shown.

Is written. In order to avoid redundant expressions, the average value of the sides calculated from the human body shape data for K people below.

This is simply referred to as “average value of each side” or “average value of lengths of each side”.

Is calculated by a general average value calculation method, that is, the following equation (2).

Further, in this specification, a set of vertices constituting an average shape of human body shape data for K persons (this is called “average shape data”) is expressed as (P ₁ , P ₂ ,... P _m ). I will do it. The coordinates of this vertex (for example, P _i ) are expressed as (x _i , y _i , z _i ). Further, the set of lengths of the sides constituting the average shape of the human body shape data for K persons is expressed as (l ₁ , l ₂ ,..., L _n ) or L.

と等しい。つまり、以下の実施例１における平均形状の各頂点算出方法では、平均形状を構成する各辺(l₁,l₂,…,l_n)の長さが各辺の平均値

と等しくなる時の、人体形状データの各頂点の座標値を求める。ただし、この座標値の厳密解(解析解)を求めることは困難であるため、以下の式（３）で表される、各辺の長さと各辺の平均値の誤差二乗和

を最小化（極小化）する解(各頂点の座標値)を数値計算により求めることで、平均形状を構成する各頂点の座標値とする。Eが0になる時の解が理想解である。 Hereinafter, the calculation principle of the average shape will be outlined. In the definition of the (ideal) average shape described in Example 1 below, the length of each side (l ₁ , l ₂ ,..., L _n ) constituting the average shape is the average value of each side.

Is equal to That is, in each average shape vertex calculation method in the following first embodiment, the length of each side (l ₁ , l ₂ ,..., L _n ) constituting the average shape is the average value of each side.

The coordinate value of each vertex of the human body shape data when it becomes equal to is obtained. However, since it is difficult to obtain an exact solution (analysis solution) of this coordinate value, the error square sum of the length of each side and the average value of each side represented by the following formula (3)

The value (coordinate value of each vertex) that minimizes (minimizes) is obtained by numerical calculation to obtain the coordinate value of each vertex constituting the average shape. The solution when E is 0 is the ideal solution.

Note that although the coordinate value (x _i , y _i , z _i ) is not (explicitly) included in the above equation for the sum of squared errors (Equation (3)), it has been explained in Equation (1) above. As described above, the side length l _ij is a function of two vertices (for example, (x _ia , y _ia , z _ia ) and (x _ib , y _ib , z _ib )). Therefore, the error sum of squares E expressed by the expression (3) is expressed by the coordinate values ((x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m )) of all vertices constituting the average shape. It is a function. Therefore, the calculation to find a solution that minimizes (minimizes) E in Eq. (3) above is for each vertex when E takes the minimum value (strictly speaking, it is called the minimum value below). It can be said that the coordinate values ((x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m )) are calculated. Hereinafter, a specific example of a method for obtaining each vertex when the error square sum E takes the minimum value (minimum value) will be described.

  This example is based on 3D data (see FIG. 3) of the human body as a large number of statistical data. Further, as an example of the shape analysis of the body shape data, the length of a triangle side is taken as an example. In the description of this embodiment, the 3D data may be referred to as body shape data or body shape data.

  FIG. 1 is a block diagram illustrating a configuration example of a body shape data standardization system for calculating an average shape in the present embodiment. In the present embodiment, an example in which an average shape of a plurality of persons is obtained will be described. However, the body data standardization system and the average shape calculation method described below can also be used when obtaining the average shape of a three-dimensional object other than the human body.

  The body data standardization system 1 is configured by a computer such as a server, for example. Hereinafter, the figure data standardization system 1 may be expressed as “server 1”. The server 1 includes a computing device (processor) 11 (hereinafter referred to as “processor 11”), a storage device 12, an input device 13, an output device (display, printer) 15, and a program memory 16.

  The processor 11 controls the operation of each device, and controls each of the above devices according to a program stored in the program memory 16. Further, the server 1 executes at least a measurement data collection program 111 and an average shape (shape) output program 116 for calculating the average shape. These programs are stored in the storage device 12 before the average shape calculation processing is performed. When the computing device 11 executes the average shape calculation process, the server 1 stages these programs in the program memory 16, and the processor 11 reads and executes the staged programs in the program memory 16.

  The storage device 12 is a device for accumulating and storing 3D data (body shape data) indicating the shape of a large number of people in addition to the programs described above. The storage device 12 is a non-volatile storage device such as an HDD (Hard Disk Drive), for example. The 3D data of the human body is basically composed of a plurality of polygons (triangles) as described above, and includes a large number (a little less than 7000) of polygons constituting the whole body of the human body.

  The input device 13 is a device for a user (user) of the server 1 to input data. The input device 13 includes a keyboard, a mouse, operation buttons, and the like. The output device 15 is a device such as a display for displaying an average shape (average person) or a printer for printing.

  FIG. 2 is a diagram showing main programs executed by the computing device (processor) 11. The processor 11 executes at least a measurement data collection program 111 and an average shape (shape) output program 116.

  The measurement data collection program 111 collects 3D data (body shape data) indicating the body shape of a large number of people (several tens to thousands) measured by a 3D measuring instrument, for example, a 3D scanner, and performs homology. The stored 3D data is accumulated and stored in the storage device 12. When collecting the 3D data, it is preferable to collect people whose predetermined age range and body size (for example, bust size) are included in the predetermined range and collect data of those people. However, even if arbitrary human 3D data is collected, it is possible to calculate the average shape described in the present embodiment.

  The average shape (shape) output program 116 is a program for calculating an average shape (coordinate values thereof) using the collected body shape data of a large number of people. The average shape (shape) output program 116 also has a function of generating a human body shape using the calculated coordinate value of the average shape and outputting it to the output device 15.

  FIG. 3 is a diagram illustrating an example of vertex samples of 3D data for a large number of people collected by the measurement data collection program 111, and is a diagram illustrating xyz coordinates of vertices of a triangle with respect to the data for a large number of people. For example, the first person's data indicates that the X coordinate of vertex 1 is “30.4594”, the Y coordinate of vertex 1 is “700.145”, and the Z coordinate of vertex 1 is “−33.5433”. Show. A part of the data is omitted.

  FIG. 4 is a diagram illustrating an example of length of 3D data for a large number of people collected by the measurement data collection program 111, and is a diagram illustrating the lengths of the sides of a triangle for the data for a large number of people. For example, the data of the first person indicates that the length of the side 1 is “28.2783”, the length of the side 2 is “25.74598”, and so on. In the figure, a part of the data is omitted.

  The procedure of the average shape calculation process performed by the processor 11 of the server 1 will be described with reference to the flowchart shown in FIG. The alphabet “S” added to the beginning of the reference number in the figure is an abbreviation for “step”.

First, in step 1111, the measurement data collection program 111 collects 3D data (body shape data) for a large number of people. Similar to the example described in the outline description, for example, measurement data of the whole body of K people are collected, and the coordinate values (x _ij , y _ij , vertices) of the vertex P _ij of the human body shape data homogenized from the collected measurement data z _ij ) is obtained, and the obtained coordinate values are stored in the storage device 12. FIG. 4 shows an example of coordinate values collected and stored. Since homology is a well-known process, detailed description thereof is omitted here.

  In step 1111, the measurement data collection program 111 calculates the length of each side of the triangle constituting the human body shape based on the coordinate value of the human body shape data of each person, and stores the calculated length of each side. Store in device 12. FIG. 4 shows an example of information on the length of each side stored in the storage device 12. Instead of collecting the measurement data in step 1111, the homogenized coordinate value and side length information may be stored in the storage device 12 in advance. In that case, the server 1 does not need to execute the measurement data collection program 111.

を算出する。ただし別の実施形態として、ステップ１１１２で平均形状（カタチ）出力プログラム１１６が各辺の長さの平均値

を算出する代わりに、あらかじめ算出された各辺の長さの平均値を記憶装置１２に格納しておいてもよい。その場合、ステップ１１１２が実行される必要はない。 Next, in step 1112, the average shape (shape) output program 116 reads out the length of each side of the triangle constituting the 3D data from the storage device 12 with respect to the 3D data for all members collected in step 1111. Subsequently, the average value of the length of each side of the triangle that makes up the 3D data based on it

Is calculated. However, as another embodiment, in step 1112, the average shape (shape) output program 116 calculates the average length of each side.

Instead of calculating, the average value of the lengths of the sides calculated in advance may be stored in the storage device 12. In that case, step 1112 need not be executed.

との誤差二乗和を算出し、誤差二乗和が最も小さくなる人のデータを座標値の初期値とする。各辺の長さが最も各辺の長さの平均値

に近い人の座標値を用いると、この後の計算速度が向上するためである。 Subsequently, in step 1113, the average shape (shape) output program 116 stores variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z) for storing coordinate values constituting the average shape. _m ) is prepared. Then, the average shape (shape) output program 116 selects the coordinate value of the 3D data for one person as the initial value from the 3D data for K persons, and the variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ). Any method can be used as a method for selecting an initial value. However, in the average shape (shape) output program 116 according to the present embodiment, the lengths (l _i1 , l _i2 ,..., L _in ) of triangles constituting each person's 3D data and (i is 1 or more) (It is an integer less than or equal to K), the average length of each side

And the data of the person with the smallest error square sum is used as the initial coordinate value. The average length of each side is the length of each side

This is because the calculation speed after this increases when the coordinate value of a person close to is used.

In step 1114 to step 1115, the average shape (shape) output program 116 calculates a coordinate value that minimizes the sum of squared errors between the length of each side constituting the average shape and the average value of each side (strictly speaking, As will be described later, a coordinate value when the sum of squared errors is less than a predetermined threshold value is obtained). The average shape (shape) output program 116 according to the present embodiment uses a quasi-Newton method in order to obtain a coordinate value that minimizes the sum of squared errors. Specifically, the average shape (shape) output program 116 uses the coordinate values stored in the variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ) in step 1113 as initial values. The coordinate value that minimizes the error sum of squares E in equation (3) is calculated (exactly, l _i in equation (3) is converted into variables (x ₁ , y ₁ , z using equation (1)). ₁ ) to (x _m , y _m , z _m ) are used).

As is well known, calculation methods such as the quasi-Newton method are stored in variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ) by performing iterative calculations. The value is updated (corrected). Then, iterative calculation is performed until the slope ∇E (x ₁ , y ₁ , z _1,..., X _m , y _m , z _m ) of the error sum of squares falls below 0 or a predetermined threshold value. A minimum value is obtained (step 1114). Of course, as another embodiment, the iterative calculation may be terminated when the number of iterations exceeds a predetermined number.

In step 1115, an error sum of squares E is calculated, and it is determined whether E is equal to or less than a predetermined threshold. If E is a predetermined threshold value (step 1115: Y), the values stored in the variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ) are average shapes ( Is a set of coordinate values). In that case, the average shape (shape) output program 116 outputs the values stored in the variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ) to the output device 15 or the storage device. 12 to finish the processing (step 1116). On the other hand, if E exceeds a predetermined threshold value in step 1115 (step 1115: N), step 1114 is executed again.

Note that by executing Step 1114 and Step 1115, a set of coordinate values ((x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m )) constituting the average shape is obtained. As a method for outputting this to the output device 15, various output methods can be adopted other than simply outputting coordinate values (numerical values). For example, the average shape (shape) output program 116 may create an image of the human body using the obtained coordinate values and output it to the display. Further, the average shape (shape) output program 116 may use a 3D printer as the output device 15 so as to create a three-dimensional human body shaped object with the obtained coordinate values.

との誤差二乗和Eを最小にする解（頂点の座標）を求める。もっとも理想的な場合は、誤差二乗和Eが０になる場合である。この場合、式（３）から明らかなように、平均形状を構成する各辺の長さl_iと、各辺の長さの平均値

は等しい。 An example of the effect of the average shape calculation method in the present embodiment will be described with reference to FIG. In the calculation method of the average shape in the present embodiment, as described above, the length l _{i of} each side constituting the average shape and the average value of the length of each side of the human body shape for K persons.

Find the solution (vertex coordinates) that minimizes the error sum of squares E. The most ideal case is when the error sum of squares E becomes zero. In this case, as is apparent from the equation (3), the length l _{i of} each side constituting the average shape and the average value of the lengths of each side

Are equal.

  In the above-described embodiment, an example in which a human body model (homology model) composed of a finite number of polygons (triangles) is used is explained. However, an average using a human body model composed of infinitely small polygons is used. A case where the shape is obtained is assumed. The distance of the arbitrary section on the body surface of the average human body shape obtained by this, for example, the waist circumference (waist dimension) is the waist dimension (for example, 692 mm, 578 mm, 691 mm) of plural persons used for calculating the average human body shape. It will correspond to the average of (654 mm). When actually obtaining the average shape, a human body model composed of a finite number of polygons will be used, so the waist size of the average shape does not necessarily match the average of the waist dimensions of multiple people, but the number of polygons should be increased So you can bring them closer together. Many body dimension measuring methods that exist in the past, as represented by a measuring method such as a waist, often calculate the distance (dimension) of a section on the human body surface. In the average shape calculation method according to the present embodiment, the distance of the section on the surface of the obtained average human body shape is expected to be extremely close to the average of the distances of the plurality of sections on the human body surface. There is an advantage that it matches well with the dimension measurement method.

  Next, a method for calculating the average shape of a three-dimensional object and a body shape data standardization system that performs this average shape calculation process according to the second embodiment will be described. Since the hardware configuration of the body shape data standardization system according to the second embodiment is the same as that described in the first embodiment, a description thereof is omitted here.

  In addition, the body shape data standardization system according to the second embodiment is similar to the one described in the first embodiment. The measurement data collection program 111 ′ for collecting 3D data for a large number of people and the collected body shape shapes for a large number of people An average shape output program 116 ′ for calculating an average shape (coordinate values thereof) using data is provided. The contents of the processing executed by the measurement data collection program 111 ′ and the average shape output program 116 ′ are common in many parts to the processing executed by the measurement data collection program 111 and the average shape output program 116 described in the first embodiment. Therefore, the following description will focus on the differences between the two.

  First, the principle of the average shape calculation method according to the second embodiment will be described before the details of the processing performed by each program. In the first embodiment, as a method for obtaining an average shape of a three-dimensional object, an average of the lengths of the sides of a polygon (triangle) constituting the three-dimensional object is obtained for a plurality of three-dimensional objects, and the length of each side is obtained. A method has been described in which a three-dimensional object that is equal to the average of the lengths obtained here (or the error sum of squares is minimized) is made an average shape of the three-dimensional object. On the other hand, in a second embodiment described below, a method will be described in which attention is paid to the angles of the vertices of each triangle constituting the three-dimensional object in order to obtain the average shape of the three-dimensional object.

Hereinafter, as in the first embodiment, an example in which an average shape is obtained using human body shape data for K persons will be described (K is an integer of 1 or more). As in the first embodiment, it is assumed that one human body shape data has m vertices, and each vertex of the i-th human body shape data (1 ≦ i ≦ K) is represented by P _ij (j is 1 to m). (Integer). When the vertex P _ij is expressed by xyz coordinates, it is expressed as P _ij = (x _ij , y _ij , z _ij ). Note that vertices having the same subscript j mean vertices at the same position on the body surface. For example, the vertex P _{aj of the} a-th human body shape data and the vertex P _bj of the b-th human body shape data mean vertices at the same position on the body surface.

In addition, it is assumed that one (for one person) human body shape data has n triangular corners, and the size of the j-th corner in the i-th human body shape data is θ _ij (where i and j are These are integers satisfying the relations 1 ≦ i ≦ K and 1 ≦ j ≦ n).

In the present embodiment, when the corner size is obtained, the corner size constituted by two sides constituted by three vertices of the triangle constituting the human body shape data is obtained. For example, in the case of a triangle composed of vertices P _ia , P _ib , and P _ic , the angle formed between the side that ends at P _ia and P _ib and the side that ends at P _ia and P _ic (that is, vertex P _Find the size of the corner formed at the position of _ia . Here, when the angle formed between the sides and end points P _ia and P _ics and theta _ij, theta _ij and vertex P _ia, the coordinates of P _ib and P _ics is represented by the following formula (4) There is a relationship.

と表記する。

は実施例１で説明した式（２）と同様に、一般的な平均値の算出方法で算出される（式（５））。

In addition, the average value of the jth angle of the human body shape data for K people is

Is written.

Is calculated by a general average value calculation method (formula (5)) in the same manner as formula (2) described in the first embodiment.

に等しくなる時の、三次元オブジェクトの頂点を求める。そしてこれを求める時に、以下の式（６）で表される、各角度と角度の平均値との誤差二乗和E´

を最小化する解を、準ニュートン法などの数値計算を用いて求める点も、実施例１で説明したものと同様である。 The calculation principle of the average shape of the three-dimensional object in the second embodiment is the same as that described in the first embodiment. In other words, in the second embodiment, the angles (θ ₁ , θ ₂ ,..., Θ _m ) of the respective triangles constituting the three-dimensional object expressing the average shape are

Finds the vertex of a 3D object when When obtaining this, the sum of squared errors E ′ of each angle and the average value of the angles expressed by the following equation (6):

The point that obtains a solution that minimizes using numerical calculation such as the quasi-Newton method is the same as that described in the first embodiment.

  Next, the flow of the average shape calculation process executed by the calculation device (processor) will be described with reference to FIG.

First, in step 1111 ′, the measurement data collection program 111 ′ collects 3D data (body shape data) for a large number of people. For example, the measurement data of the whole body of K people are collected, and the vertex P _ij (specifically, the coordinate value (x _ij , y _ij , z _ij )) of the human body shape data homogenized from the collected measurement data is obtained. The obtained and homogenized coordinate values are stored in the storage device 12.

  Here, the measurement data collection program 111 ′ calculates the angles of the vertices of all the triangles constituting the human body shape based on the coordinate values of the human body shape data of each person, and stores the calculated angles in the storage device 12. To store. The angle is obtained by using the equation (4) described above. Instead of collecting the measurement data in step 1111 ′, the coordinate values and the angles of the vertices that have been homologized in advance may be stored in the storage device 12. In this case, the calculation device 11 does not need to execute the measurement data collection program 111 '.

を算出する。ただし別の実施形態として、ステップ１１１２’で各角度の平均を算出する代わりに、あらかじめ算出された平均を記憶装置１２に格納しておいてもよい。 Next, in step 1112 ′, the average shape (shape) output program 116 ′ uses each angle information of the 3D data for all the members obtained in step 1111 ′ to obtain each of the triangles constituting the 3D data. Average vertex angle

Is calculated. However, as another embodiment, instead of calculating the average of each angle in step 1112 ′, the average calculated in advance may be stored in the storage device 12.

との誤差二乗和を算出し、誤差二乗和が最も小さくなる人のデータを座標値の初期値とするとよい。 Step 1113 ′ is the same process as step 1113 of the first embodiment. That is, the average shape (shape) output program 116 prepares variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ) for storing coordinate values constituting the average shape. Then, the average shape (shape) output program 116 selects the coordinate value of the 3D data for one person as the initial value from the 3D data for K persons, and the variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ). As the initial value selection method, any method may be used as described in the first embodiment. As an example, the angle (θ ₁ , θ ₂ , ..., θ _m ) and the average of each angle of the triangles that make up the 3D data of each person

It is preferable to calculate the sum of squared errors with the data of the person who has the smallest sum of squared errors as the initial coordinate value.

の誤差二乗和E´を最小にする座標値の算出を行う。ステップ１１１４’でも実施例１と同様に、準ニュートン法が用いられる。 In steps 1114 ′ to 1115 ′, the average shape (shape) output program 116 ′ is set to θ _i .

The coordinate value that minimizes the error sum of squares E ′ is calculated. In step 1114 ′, the quasi-Newton method is used as in the first embodiment.

In step 1115 ′, the average shape (shape) output program 116 ′ calculates an error square sum E ′ and determines whether E ′ is equal to or less than a predetermined threshold. If E ′ is a predetermined threshold value, the values stored in the variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ) are the coordinate values constituting the average shape ( Set). Finally, the average shape (shape) output program 116 ′ uses the values stored in the variables (x ₁ , y ₁ , z ₁ ) to (x _m , y _m , z _m ) as the output device 15 or the storage device 12. To terminate the process (step 1116 ′). In step 1115 ′, if E ′ exceeds a predetermined threshold value, step 1114 ′ is executed again.

  Next, a method for calculating the average shape of a three-dimensional object and a body shape data standardization system that performs this average shape calculation process according to the third embodiment will be described. Since the hardware configuration of the body shape data standardization system according to the second embodiment is the same as that described in the first embodiment, a description thereof is omitted here.

  The body shape data standardization system according to the third embodiment is a shape obtained by deforming the average shape using the measurement data collection program 111 and the collected body shape data of a large number of people (this is called a deformed shape in this embodiment). Has a deformed shape output program 117 for calculating. The measurement data collection program 111 is the same as the measurement data collection program 111 described in the first embodiment. The deformed shape output program 117 includes the same function as the average shape output program 116 described in the first embodiment, and performs processing for generating deformed shape data (hereinafter referred to as “deformed shape generation processing”). The contents of the deformed shape generation process will be mainly described below.

  As in the first embodiment, an example in which human body shape data for K persons is used as original data will be described. In the following description, the notation of vertices, vertex coordinates, and side lengths is the same as that described in the first embodiment.

In the deformed shape generation process according to the third embodiment, principal component analysis is performed on human body shape data for K people. Principal component analysis is a statistical technique in which each data is represented by a low-dimensional subspace that is designed to suppress information loss as much as possible. In the deformed shape generation process according to the third embodiment, first, the length of each side is obtained for the human body shape data for K people. In the following, the length of each side of the human body shape data for one person is expressed as a vector. Hereinafter, this vector is referred to as an “edge vector”. When the length of the jth side of the i-th human body shape data is expressed as l _ij , the side vector L _i of the i-th human body shape data is expressed as the following Expression (7).

と表記する。また主成分分析の結果として得られる部分空間の基底をp₁, p₂, p₃,…, p_rとするとき、部分空間上の辺ベクトルLは、部分空間の基底を用いると以下の式（８）で表現することができる。なお、p₁は、第１主成分ベクトルを表し、p₂, p₃…はそれぞれ第２主成分ベクトル、第３主成分ベクトル…を表す。

In deformed shape generation process according to the third embodiment, the side vector _{L 1, L 2, L 3} , ..., principal component analysis is performed on the L _K. In the following, a vector of average values of the side lengths of human body shape data for K people is

Is written. When the subspace basis obtained as a result of the principal component analysis is p ₁ , p ₂ , p ₃ ,..., _Pr , the edge vector L on the subspace can be expressed as It can be expressed by (8). P ₁ represents a first principal component vector, and p ₂ , p ₃ ... Represent a second principal component vector, a third principal component vector,.

When the vector s = (s _1, s _2, ... _, S _r ) is 0, the edge vector L represents an average shape. Further, by changing the vector S, various human body shapes (length vectors of sides of the human body shape) can be generated. When changing the vector, for example, only s ₁ or s ₂ may be changed, or all values of s _1, s _2, ... May be changed.

  As a result of collecting a large number of human body shape samples and performing principal component analysis on each side (side vector) of the human body shape, the inventor of the present application has found that the first principal component and the second principal component constitute the human body shape. I found it dominant. FIG. 13 shows an example of the result of principal component analysis for the length of the side. The horizontal axis of the graph of FIG. 13 represents the principal component, and the vertical axis represents the eigenvalue of each principal component. Referring to FIG. 13, it can be seen that only the eigenvalues of the first principal component and the second principal component are larger than the other principal components.

The inventors of the present application have also found that the first main component is a component representing the size of the human body, and the second main component is a component representing the thickness of the human body (obesity level). FIG. 11 shows an example of a change in the human body shape when the first principal component is changed. (B) in FIG. 11 represents an average shape, and (a) in FIG. 11 represents an example of a human body shape when the first principal component is increased (s ₁ in the above equation (8) is increased). ing. On the other hand, FIG. 11C shows an example of a human body shape when the first main component is reduced (s ₁ in the above equation (8) is reduced).

FIG. 12 shows an example of a change in the human body shape when the second principal component is changed. FIG. 12B shows an average shape as in FIG. 11B. 12D shows an example of the human body shape when the second main component is reduced (s ₂ in the above equation (8) is reduced), and FIG. 12E shows the second main component. was larger components represent examples of (significantly and the s ₂ of the above equation (8)) human when the shape.

That is, by changing only the element s ₁ in the vector S to a value other than 0, a human body shape (average vector) having a physique larger (or smaller) than the average shape can be obtained, while s ₂ is By changing, it is possible to obtain a human body shape (an average vector thereof) having a physique that is thicker (or thinner) than the average shape. Hereinafter, the element s _{1 is referred} to as a “first principal component deformation degree”, and the element s ₂ is referred to as a “second principal component deformation degree”.

  Next, the flow of processing of the deformed shape generation method performed by the body shape data standardization system according to the third embodiment will be described with reference to FIG. This process flow is common in many parts with the process flow of FIG. 5 of the first embodiment. For this reason, the following description will focus on the differences from FIG.

  Steps 1111 and 1112 are the same as steps 1111 and 1112 described in the first embodiment. Here, the length of each side of the triangle that constitutes the 3D data is obtained for the 3D data for all members, but the deformed shape output program 117 determines the length of the side of the triangle that constitutes the 3D data of each person. It is stored in the storage device 12 as an edge vector like Expression (7). However, in the present embodiment, the process of obtaining the average of the lengths of the sides of the triangles constituting the 3D data may be performed, but is not an essential process.

Subsequently, in step 2111, the deformed shape output program 117 performs principal component analysis on the edge vector obtained in step 1112, and the subspace bases (p ₁ , p ₂ , p ₃ ,. )

以下では、L´の各要素をL´=（l₁´,l₂´,l₃´,…,l_n´）と表記する。 As described above, when the edge vector is expressed using the basis (p ₁ , p ₂ , p ₃ ,...), It is ideally expressed as Expression (8). However, the deformed shape output program 117 according to the third embodiment ignores the third and subsequent principal components and calculates the deformed shape (calculates the side vector L ′) according to the following equation (9). This is because the first principal component and the second principal component are dominant as elements representing the human body shape.

Hereinafter, each element of L ′ is expressed as L ′ = (l ₁ ′, l ₂ ′, l ₃ ′,..., L _n ′).

  In step 2112, the deformed shape output program 117 allows the user to specify the first principal component deformation degree and the second principal component deformation degree (step 2112). Specifically, the deformed shape output program 117 displays an input screen for the first principal component deformation degree and the second principal component deformation degree on the output device 15 (display), and displays the first principal component deformation degree and the second main component deformation degree to the user. Input the principal component deformation degree. When the user designates the first principal component deformation degree and the second principal component deformation degree, the deformed shape output program 117 calculates the deformed side vector L ′ using Expression (9).

  Note that 0 can also be specified for the first principal component deformation degree or the second principal component deformation degree. When 0 is designated for both the first principal component deformation degree and the second principal component deformation degree, the deformed shape output program 117 outputs the average shape as in the first embodiment.

を用いる代わりに、上で求めた変形後の辺ベクトルL´（つまり（l₁´,l₂´,l₃´,…,l_n´））を用いる。 The following steps 2113 to 2116 are the same processes as steps 1113 to 1116 of the first embodiment. However, when the deformed shape output program 117 executes step 2113 to step 2116, the average value of the lengths of the respective sides

Instead of using the modified edge vector L ′ (that is, (l ₁ ′, l ₂ ′, l ₃ ′,..., L _n ′)) obtained above.

との誤差二乗和が最も小さくなる人のデータを座標値の初期値としてもよい。この場合、ステップ１１１２で３Ｄデータを構成する三角形の各辺の長さの平均を求める処理を行っておく必要がある。 Specifically, in step 2113, the deformed shape output program 117 selects, as an initial value, human shape data that minimizes the sum of squares of errors with the side vector L ′ obtained in step 2112 when selecting an initial value. select. However, as in Example 1, the average length of each side

It is also possible to use the data of the person with the smallest sum of squared errors as the initial coordinate value. In this case, it is necessary to perform processing for obtaining the average length of each side of the triangle constituting the 3D data in step 1112.

の誤差二乗和を最小にする座標値の算出ではなく、l_iと式（９）で求めたL´の要素（l_i´）との誤差二乗和を最小にする座標値の算出を行う点が、実施例１のステップ１１１４及びステップ１１１５と異なる。それ以外の点は、実施例１の図５で説明した処理と同じである。 Step 2114 and step 2115 are the same as step 1114 and step 1115 of the first embodiment. Where l _i and

Rather than a calculation of the coordinate value minimizing the error sum of squares, the point to calculate the coordinate value of the error sum of squares of the L'elements obtained in l _i and equation (9) (l _i') minimizes However, it differs from step 1114 and step 1115 of the first embodiment. The other points are the same as the processing described in FIG.

  Finally, the deformed shape output program 117 outputs the calculated deformed shape to the output device 15 and ends the process.

  By using the method according to the third embodiment, shapes other than the average shape of the human body shape data collected in advance for K persons can be generated. In the method according to the first embodiment, a shape equal to the average value of the lengths of the sides of the polygons (triangles) constituting the human body shape for K people can be generated. On the other hand, in the method according to Example 3, in addition to the shape equal to the average value of the length of each side, the triangle constituting the human body shape data, the shape larger than the average value of the length of each side, or a smaller shape, etc. Various human body shapes can be generated.

  In generating the average shape described in the first embodiment, for example, a large number of shape data of a person whose height and age belong to a predetermined range are collected, and an average value of the shape data (side length or angle) is obtained. Therefore, it is necessary to follow a procedure for calculating a shape suitable for it. For example, if shape data of a person whose height is 150 cm to 165 cm and a weight of 45 to 55 kg is collected and the method described in the first embodiment is used, average shape data of a person whose height is 150 cm to 165 cm can be generated. For example, in order to generate an average shape of a person having a height of 170 cm to 180 cm, the shape data of a person having a height of 170 cm to 180 cm must be collected again in the method described in the first or second embodiment. According to the method described in the present embodiment, even if there is no shape data of a desired range (height, weight, age, etc.), average shape data of a human body belonging to the range can be generated. .

  According to the embodiment described above, it is possible to create an average shape (average person) from 3D data of a large number of people. In addition, it is possible to create full-sized bodies by age, size, and L size. You can also check how all the dimensions of the sample differ from the average dimension by just putting the sample on the average person once. It can also be used for the manufacture and grading of paper patterns.

  In the average shape calculation method in the above-described embodiment, the length of each side (or the angle of each vertex) of the polygon (triangle) constituting the three-dimensional shape object (for example, the human body shape) is calculated from the length of the side ( Alternatively, the coordinates of each polygon are determined by making it equal to the average value of angles). For example, when a human body shape is measured, an error is likely to occur in the coordinates at a position far from the origin, so that a portion with a large error and a portion with a small error are generated depending on how the origin is determined. In addition, depending on how the origin is determined, the required average shape may change.

  On the other hand, the length and angle of a side are determined depending on the coordinates of adjacent vertices, so that errors are unlikely to occur. In addition, no matter where the origin is when measuring the shape, a difference in the required side length or angle is unlikely to occur. Therefore, if the average shape is calculated by paying attention to the length and angle of the side, a shape with less error can be obtained.

  In addition, in the average shape calculation method focusing on the length of the side, compatibility with existing dimensions such as a waist and a hip is easily obtained. In addition, since 3D measurement data is processed by the calculation device, it is easy to design a body that suits the characteristics of any category, for example, by age or by race, and fits the human body more easily. Garment design is possible.

  Further, in the field of regenerative medicine due to body defects or the like, it is possible to obtain an average of the body shapes of a plurality of persons belonging to a specific category and reproduce more natural shapes as three-dimensional data. Furthermore, it is possible to measure a three-dimensional shape such as a living body such as an animal or a plant with an irregular shape and grasp shape characteristics, not limited to humans.

  In addition, this invention is not limited to the Example mentioned above, Various modifications are included. For example, the above-described embodiments have been described in detail for easy understanding of the present invention, and are not necessarily limited to those having all the configurations described. Further, a part of the configuration of one embodiment can be replaced with the configuration of another embodiment, and the configuration of another embodiment can be added to the configuration of one embodiment. Further, it is possible to add, delete, and replace other configurations for a part of the configuration of each embodiment.

  For example, in each of the embodiments described above, the example in which the coordinate values of the vertices constituting the average shape are obtained by the quasi-Newton method has been described. However, the calculation method for obtaining the coordinate values of the vertices constituting the average shape or the deformed shape is not limited to the quasi-Newton method, and other numerical calculation algorithms may be used. In the third embodiment described above, the example in which the edge vector of the deformed shape is obtained by changing the first principal component deformation degree or the second principal component deformation degree has been described. The deformed shape may be calculated using the edge vector obtained by changing the degree.

  In the third embodiment described above, principal component analysis is performed on the length of the side, and a deformed shape is calculated by using a method similar to the method described in the first embodiment based on the principal component analysis. Explained. However, as another embodiment, a deformed shape may be calculated by performing a principal component analysis on the angle and using a method similar to the method described in the second embodiment based on the analysis.

  An example in which the principal component analysis is performed on the angle is shown in FIG. The horizontal axis of the graph of FIG. 14 represents the principal component, and the vertical axis represents the eigenvalue of each principal component. As can be seen from the graph of FIG. 14, when the principal component analysis is performed on the angle, only the first principal component is larger than the other principal components. Therefore, when calculating a deformed shape by changing the angle, only the first principal component needs to be changed. However, the deformed shape may be calculated using the main components after the second main component.

  In addition, each of the above-described configurations, functions, processing units, processing means, and the like may be realized in hardware by designing a part or all of them with, for example, an integrated circuit.

1 3D body data standardization system (server)
2 3D Scanner 3 Scanned Person (Human Body / Model)
11 processor 12 storage device 13 input device 15 output device

Claims (10)

For a plurality of three-dimensional objects expressed using a plurality of polygons, calculating a mean value of the lengths of the sides of the polygons;
For a target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, the sum of squared errors between the length of each side of the target object and the average value of the lengths of the sides is Obtaining a coordinate value at the time of minimization, and setting the obtained coordinate value as a coordinate value of an average shape three-dimensional object;
The computer calculates the shape of the three-dimensional object. The step of obtaining the coordinate value of the average shape three-dimensional object calculates the coordinate value of the average shape three-dimensional object using a quasi-Newton method.
The shape calculation method for a three-dimensional object according to claim 1, wherein: The step of obtaining the coordinate value of the average shape three-dimensional object includes, among the plurality of three-dimensional objects, the coordinate value of the three-dimensional object that is closest to the average value of the lengths of the sides. As the initial coordinate value of the average shape three-dimensional object, by correcting the initial coordinate value by performing a predetermined iterative calculation, it approaches the coordinate value of the average shape three-dimensional object,
The shape calculation method for a three-dimensional object according to claim 1, wherein the shape calculation method is used. The method for calculating the shape of a three-dimensional object according to any one of claims 1 to 3, further comprising:
Calculating one or more principal component vectors by performing principal component analysis on each side of a plurality of three-dimensional objects expressed using a plurality of polygons;
Calculating the length of each side of the deformed object using the one or more principal component vectors;
For the target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, instead of the step of obtaining the coordinate value of the average shape three-dimensional object, the length of each side of the target object And obtaining a coordinate value when an error sum of squares between each side of the deformed object is minimized,
A method wherein the computer executes. Calculating a mean angle value of each vertex of the polygon for a plurality of three-dimensional objects expressed using a plurality of polygons;
For a target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, the sum of squared errors between the angle of each vertex of the target object and the angle average value of each vertex is minimized. Obtaining a coordinate value at a time, and using the obtained coordinate value as a coordinate value of an average shape three-dimensional object,
The computer calculates the shape of the three-dimensional object. The method for calculating a shape of a three-dimensional object according to claim 5, further comprising:
Calculating one or more principal component vectors by performing principal component analysis on the angle of each vertex of a plurality of three-dimensional objects expressed using a plurality of polygons;
Calculating an angle of each vertex of the deformed object using the one or more principal component vectors;
For the target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, instead of the step of obtaining the coordinate value of the average shape three-dimensional object, the angle of each vertex of the target object And obtaining a coordinate value when the sum of squared errors between the angle of each vertex of the deformed object is minimized,
A method wherein the computer executes. For a plurality of three-dimensional objects expressed using a plurality of polygons, calculating a mean value of the lengths of the sides of the polygons;
For a target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, the sum of squared errors between the length of each side of the target object and the average value of the lengths of the sides is Obtaining a coordinate value at the time of minimization, and setting the obtained coordinate value as a coordinate value of an average shape three-dimensional object;
A program that causes a computer to execute. The program according to claim 7, further comprising:
Calculating one or more principal component vectors by performing principal component analysis on each side of a plurality of three-dimensional objects expressed using a plurality of polygons;
Calculating the length of each side of the deformed object using the one or more principal component vectors;
For the target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, instead of the step of obtaining the coordinate value of the average shape three-dimensional object, the length of each side of the target object And obtaining a coordinate value when an error sum of squares between each side of the deformed object is minimized,
A program that causes a computer to execute. Calculating a mean angle value of each vertex of the polygon for a plurality of three-dimensional objects expressed using a plurality of polygons;
For a target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, the sum of squared errors between the angle of each vertex of the target object and the angle average value of each vertex is minimized. Obtaining a coordinate value at a time, and using the obtained coordinate value as a coordinate value of an average shape three-dimensional object,
A program that causes a computer to execute. The program according to claim 9, further comprising:
Calculating one or more principal component vectors by performing principal component analysis on the angle of each vertex of a plurality of three-dimensional objects expressed using a plurality of polygons;
Calculating an angle of each vertex of the deformed object using the one or more principal component vectors;
For the target object expressed using polygons having the same number of points and the same geometric structure as the plurality of three-dimensional objects, instead of the step of obtaining the coordinate value of the average shape three-dimensional object, the angle of each vertex of the target object And obtaining a coordinate value when the sum of squared errors between the angle of each vertex of the deformed object is minimized,
A program that causes a computer to execute.

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