JP6342180B2 - 3D CAD model similarity search method - Google Patents

Description

  The present invention relates to a retrieval method capable of easily retrieving necessary data including an assembly structure, which is difficult to retrieve by a conventional method, from a large amount of 3D CAD data stored in various formats.

Although 3D CAD data is used in various production sites, it is required to make effective use of past data to improve the efficiency of design work. There is a problem that it is difficult to extract desired data from the data. In addition, there is a problem that an assembly structure cannot be detected by a search system using a normal graph.
Therefore, various 3D CAD search systems that solve these problems have been proposed.
For example, in Patent Document 1, a design system adapted to both layout adjustment and part editing work is realized, and information on a part model created by a three-dimensional layout adjustment CAD is processed in order to improve the applicability of part elements. A three-dimensional placement adjustment CAD part information processing apparatus, which comprises a part table storing part data in a spreadsheet format, and the parts stored in the part table Only the placement information necessary for placement adjustment is extracted from the data, and the placement adjustment tool that adjusts the placement of the component, and only the component element editing information that is necessary for editing the component element is extracted from the part table to edit the component element. There has been proposed a part information processing apparatus for three-dimensional layout adjustment CAD, which is characterized by comprising a part element editing tool to be performed.
Patent Document 2 discloses a character string for acquiring character string information from CAD data having character string information as a device for creating understanding support data in which CAD data is associated with a database storing attribute information related to the CAD data. Information acquisition means, related information acquisition means for searching and acquiring attribute information related to the character string information from the database, understanding support data creation means for creating and outputting understanding support data based on the acquired related information, The one with is proposed.

JP 2005-108023 A JP 2006-344095 A

Hiroyuki Onishi, Hisashi Suzuki, Takashi Arimoto, “Detection of rotation and translation using Hough and Fourier transform”, IEICE Transactions, D-, Information / System, Information Processing, J80-D-2 ( 7), pp.1668-1675, 1997 Atsuhiko Tsuboi and Shinichi Hirai, “Plane motion detection of multiple objects using Radon transform and one-dimensional phase-only correlation”, IEICE Transactions D-Vol.J87-D- No.10 pp1963-1972 2004 Ding-Yun Chen, Xiao-pei Tian, Yu-te Shen and Ming Ouhyoung, “On Visual Similarity Based 3D Model Re-trieval”, The Eurographics Association and Blackwell Pub-lishers 2003 Jin Aragaki and Kazuhiro Fukui, “Examination of high-precision identification of 3D objects with similar shapes by multi-view images”, IEICE technical report. PRMU, pattern recognition / media understanding 107 (539), 151-156, 2008-03-03 Nobuhara Shohei, Matsuyama Takashi, U Small Army, Matsuura Nobuhiko, “Simultaneous estimation of 3D shape and target area under complex environment using multi-view images”, MIRU2011 Junpei Ishii, Shuji Sakai, Koichi Ito, Takafumi Aoki, “High-precision 3D reconstruction using SIFT and POC and its application”, ITE Technical Report, Vol. 35, No. 33, pp.17-20 , 2011 Tajima, Yuichiro and Fudano, Kinya and Ito, Koichi and Aoki, Takafumi, “Object recognition from local scale invari-ant features”, IEICE Transactions, pp826-835, 2013

However, in the system according to the above proposal, since CAD data is to be recognized and processed as characters, the search may not be possible or the search accuracy may be lowered depending on the data storage format. Further, in the case of character data, when it is made three-dimensional, if it is attempted to process detailed data such as how members are applied, positions, and directions, it takes an enormous amount of time for the search. There is a problem that, if such reconstruction is performed, necessary data is insufficient and it is difficult to obtain desired three-dimensional data.
Attempts have also been made to recognize and process three-dimensional CAD data as images, but the conventionally proposed methods only show the appearance of the data, and the details of the internal structure and components, and the positional relationship. However, there is a problem that data useful for actual manufacturing such as the relationship between parts cannot be obtained.
The following introduces the method of detecting the rotation angle between two data, the method of detecting the enlargement / reduction ratio, and the research for the 3D volume model using projection data.
Arimoto et al. (Non-Patent Document 1, etc.) proposed an algorithm that estimates the rotation angle and translation amount between two images using Hough transform and Fourier transform, and positioning and seal of mechanical parts placed on a plane. Proposed application for verification.
Tsuboi et al. (Non-Patent Document 2) proposed a method for detecting the position and orientation of a target object using Radon transform and one-dimensional phase-only correlation.
Ding-YunChen et al. (Non-patent Document 3) defined the vertices of an icosahedron with an object as the center, obtained a set of 20 silhouette images from each vertex, and called this image a light field descriptor. This light field descriptor was obtained from various angles, and matching that allowed rotation of the 3D model was made possible. Aragaki et al. (Non-Patent Document 4) used images taken from multiple viewpoints for matching 3D objects. Furthermore, we extracted HLAC and contour features from this image, and compared the accuracy of each method. They used constrained mutual subspace method and mutual subspace method for matching. Nobuhara (Non-Patent Document 5) et al. Do not use prior information such as multi-viewpoint silhouettes, and perform estimation of the target region and shape even in a complex environment including the background, etc. We proposed a method using.
Ishii (Non-Patent Document 6) and others proposed a 3D shape reconstruction from multi-viewpoint images of 3D models using phase-only correlation and SIFT.
In a study that dealt with volume models, Tajima (Non-Patent Document 7) and others expanded the corresponding point search by the phase-only correlation method to three dimensions, and matched the volume models with subpoxel accuracy, thereby registering non-rigid bodies. A high-precision and high-speed registration method for medical volume models was proposed.
Accordingly, an object of the present invention is to provide a retrieval method that can easily retrieve necessary data including assembly structures, which is difficult to retrieve by a conventional method, from a large amount of 3D CAD data stored in various formats. There is.

The present invention has been made in view of the above object, and provides the following inventions.
A method for retrieving 3D CAD data for specifying 3D CAD data relating to a structure similar to a specific 3D structure from a data group consisting of a plurality of 3D CAD data,
A modeling step for modeling the three-dimensional CAD data into a three-dimensional model;
Projection mapping step of obtaining a plurality of two-dimensional projections by scanning the obtained three-dimensional model from a plurality of directions 3D CAD data to be searched is converted into a three-dimensional model, and 2 indicating a three-dimensional structure to be searched A target data acquisition step of obtaining a target projection by scanning so as to obtain a three-dimensional projection;
A selection step of selecting a two-dimensional projection having the highest correlation with the target projection from the obtained two-dimensional projections;
A search method comprising a display step of accessing three-dimensional CAD data from which a selected two-dimensional projection map is obtained and displaying the three-dimensional CAD data as a search result.

According to the 3D CAD data search method of the present invention, necessary data including an assembly structure, which is difficult to search by the conventional method, can be easily searched from a large amount of 3D CAD data stored in various formats. it can.
In particular, according to the present invention, it is an assembly model composed of a plurality of parts, which is difficult to search with the existing technology, and is a model or part composed of parts of different materials even if the shape is the same. It is possible to search for models having different arrangements.

FIG. 1 is a schematic diagram showing a mode in which vertex coordinates are stored in a three-dimensional array. FIG. 2 is an explanatory diagram showing a surface model and a volume model. FIG. 3 is an explanatory diagram showing an algorithm for three-dimensional modeling. FIG. 4 is a schematic diagram showing how to obtain three projection data. FIG. 5 is a schematic diagram showing an embodiment of the two-dimensional radon transform. FIG. 6 is an explanatory diagram showing an example in which the projection data is two-dimensional radon transformed. FIG. 7 is an explanatory diagram illustrating an example of a three-dimensional model. FIG. 8 is an explanatory diagram showing an example of projection data of the three-dimensional model shown in FIG. FIG. 9 is a reference diagram showing an example of conventional rotation angle detection. FIG. 10 is an explanatory diagram showing an example of similar projection data.

Embodiments of the present invention will be described below with reference to the accompanying drawings.
<Overall configuration>
The three-dimensional CAD data search method of the present invention is a three-dimensional CAD data search method for specifying three-dimensional CAD data related to a structure similar to a specific three-dimensional structure from a data group composed of a plurality of three-dimensional CAD data. And
A modeling step for modeling the three-dimensional CAD data into a three-dimensional model;
Projection mapping step of obtaining a plurality of two-dimensional projections by scanning the obtained three-dimensional model from a plurality of directions 3D CAD data to be searched is converted into a three-dimensional model, and 2 indicating a three-dimensional structure to be searched A target data acquisition step of obtaining a target projection by scanning so as to obtain a three-dimensional projection;
A selection step of selecting a two-dimensional projection having the highest correlation with the target projection from the obtained two-dimensional projections;
This can be implemented by accessing the three-dimensional CAD data from which the selected two-dimensional projection drawing is obtained and performing a display step of displaying the three-dimensional CAD data as a search result.
The search method of the present invention can be performed using a normal computer. Specifically, a central processing unit (CPU), a recording medium such as a hard disk that stores data and programs, a memory that temporarily stores data and programs, an input device such as a keyboard, and a liquid crystal that displays calculation results It can be performed using a computer having a display medium such as a monitor, and a program for operating the computer can be stored in the recording medium so that the method can be performed.

<Modeling step>
This step is a step of modeling the three-dimensional CAD data into a three-dimensional model.
In the present specification, the three-dimensional modeling includes both a case where a three-dimensional array is meant and a case where a modeling which is not related to physical realization is meant.
Here, the three-dimensional CAD data means data created using various CAD software, and the format thereof is not particularly limited.
Three-dimensional modeling is to convert CAD data into a three-dimensional model, and can be carried out without particular limitation using a method for reading data with ordinary 3D model creation software and creating a 3D model on a computer. it can.
An example of a method that can be used in the present invention is a ply file (surface model) published by McGill University. Vertex information (x; y; z) is extracted from the ply file, and a three-dimensional array corresponding to the vertices is filled with 1 as shown in FIG. 1 (FIG. 1) to create a volume model. The processing procedure is shown in Algorithm 1 of FIG. FIG. 2 shows an example of creating a volume model from a surface model.

<Projection mapping step>
In this step, the obtained three-dimensional model is scanned from a plurality of directions to obtain a plurality of two-dimensional projection diagrams (hereinafter also referred to as projection data).
Here, the plurality of directions are directions that are arbitrarily selected, but are set according to the shape of the object, the number of parts, and the like in addition to the so-called six-plane direction.
When scanning, “projection” is implemented and projection data is obtained from the 3D model.
In the conventional method, it is difficult to perform matching correctly when the model is the same silhouette or multi-viewpoint image and the assembly structure is different. Therefore, in the present invention, even if the target is an assembly model, in order to grasp the structure and the like accurately and realize a highly accurate search, projection data is obtained instead of silhouettes, and these are used as feature quantities.
Since the projection data includes internal information in addition to model shape information such as silhouettes and multi-viewpoint images, it is possible to consider the assembly structure. In order to obtain projection data from the 3D model, the 3D model is rotated at appropriate intervals in the range of 0 ≤ η <π and 0 ≤ ζ <2π as shown in Fig. 1, and the sum perpendicular to the projection plane S is obtained. To obtain projection data. The flow of processing for obtaining projection data is shown in Algorithm2.

<Target data acquisition step>
In this step, 3D CAD data to be searched is separately converted into a 3D model and scanned so as to obtain a 2D projection showing the 3D structure to be searched to obtain the target projection.
For the three-dimensional data to be searched, the projection data of the query data may be referred to as query projection data.
A three-dimensional model of this data can also be obtained in the same manner as the modeling step described above.
Further, the method for obtaining the target projection map in this step can be performed in the same manner as in the projection mapping step.

<Selection step>
This step is a step of selecting a two-dimensional projection diagram having the highest correlation with the target projection diagram from the obtained two-dimensional projection diagrams.
This will be described in detail below.
The 3D model is projected and calculated in the range of 0 ° ≦ η <180 ° and 0 ° ≦ ζ <360 °, and the stored one is used as the 3D model database. The query data is treated as a 3D model with an unknown internal structure, and it is unknown how the 3D model exists. In the so-called matching, which selects the two-dimensional projection map having the highest correlation, it is determined whether or not the projection data stored in the three-dimensional model database and the query projection data are the same based on the correlation values.
In the present invention, matching is performed using projection data obtained from a three-dimensional model. Since the projection data of the 3D model is obtained from the combination of η and ζ, the query projection data of the same 3D model as the 3D model database is obtained by calculating the projection data stored in the 3D model database at fine intervals. When input, there is a high possibility that almost the same thing exists. However, as the size of the 3D model database increases, matching accuracy improves while processing time increases.
In order to solve this problem, in the present invention, rotation angle detection using Radon transform is used for the obtained projection data. Conventionally, rotation angle detection using Radon transform is performed on two identical images as shown in FIG. The amount of rotation of the two objects is replaced with the amount of translation, and the amount of translation is obtained by the phase-only correlation method. When a high correlation value is detected, the rotation amount is detected from the coordinates of the correlation value.
That is, in the past,
・ High correlation value is detected → The algorithm flow is to obtain the rotation angle.
On the other hand, since the purpose of the present invention is not the posture detection but the data detection,
-A high correlation value is detected-> it is detected that there is query data.
The algorithm flow.
For this reason, in the present invention, the rotation angle of a similar projected image as shown in FIG. 9 is detected instead of the same image as shown in FIG. By using this method, even when the stored projection data and the query projection data are slightly different, a high correlation value is detected and it can be determined that the projections are the same object.

In the present invention, the matching can be performed using the mutual subspace method or in combination with the above-described method.
The mutual subspace method is an extension of the subspace method proposed by Maeda et al. The mutual subspace method is applied when a plurality of input data can be used. Features are extracted from the input pattern to create an input subspace, and identification is performed based on the minimum angle θ1 formed by the subspace of each class registered as a dictionary. In the mutual subspace method, the M-dimensional subspace V and the N-dimensional subspace
The cosine of the minimum angle formed by U (M ≦ N) is defined below, and this is the similarity.
This angle θ1 is the maximum eigenvalue of the matrix S defined below.
We also generalize the mutual subspace method using the canonical angle, which is the angle between the two subspaces. N canonical angles can be defined between M-dimensional space V and N-dimensional space U. Here, un (1 ≦ n ≦ N) and vm (1 ≦ m ≦ M) are orthonormal bases, respectively. The second canonical angle θ2 is the minimum angle measured in the direction orthogonal to the first canonical angle θ1, and the third canonical angle θ3 is the minimum angle measured in the direction orthogonal to θ1 and θ2. In the same manner, N canonical angles can be obtained sequentially. This can be written as follows:
Where ui ∈ U, vi ∈ V, || ui || ≠ 0, || vi || ≠ 0, ui⊥uj (= 1
,..., I-1), vi⊥vj (= 1,..., I-1). In addition, the i-th largest eigenvalue in the above equation (4) is cos ² θi with respect to the i-th canonical angle θi.
As a measure to measure the structural similarity between two subspaces, we define the similarity S [n] (n ≧ 1) considering the nth canonical angle as follows.
In the present invention, matching is performed using the first canonical angle cos ² θ ₁ and S [n], and the two are compared.

Further, in the present invention, a nuclear nonlinear mutual subspace method known as an effective technique for identifying a nonlinear pattern distribution can be used. This nuclear nonlinear mutual subspace method is an application of the kernel principal component analysis proposed by Scholkopf to the mutual subspace method. We define a non-linear mapping to the collection space as: RN → F. When the vector x which is a feature vector is mapped to the feature space, (vector x) is obtained. Since F is high-dimensional or infinite-dimensional, it is difficult to directly find these inner products. Therefore, by using Kernel Principal Component Analysis, calculation can be performed in finite time. If the vectors on the feature space of classes V and U are Vi (1 ≤ i ≤ m) and Uj (1 ≤ j ≤ n), the inner product of them can be obtained by the following equation.

Here, k (-,-) is a kernel function, {αl} i, {α′l ′} j is a coefficient, and is obtained from a vector xvl and a vector xul ′ that are feature vectors. The vectors xvl and xul ′ are V and U feature vectors. Specifically, in order to calculate the angle between the bases obtained by the kernel principal component analysis, it may be substituted into the mathematical formula of Equation 4.

The case where matching is performed using the nuclear nonlinear mutual subspace method in the present invention will be described in detail.
When the projection data is obtained by the method in the projection mapping step described above and matching is performed by the mutual subspace method using the plurality of projection data, the projection data varies greatly depending on the angle and becomes a non-linear distribution. In the subspace method, the projection data and the recognition rate are lowered as they are. This point can be improved. In addition, the projection data is Fourier-transformed so that matching can be performed even if the 3D model moves in parallel, and alignment by the center of gravity is used.
-Alignment by Center of Gravity In the present invention, in order to enable matching even when the three-dimensional model is moved in parallel, experiments were performed in two ways using the Fourier transform and using alignment by the center of gravity. This section describes the alignment based on the center of gravity. The center of gravity of each piece of projection data is obtained and moved so that the position of the center of gravity matches the center of the image. Here, assuming that the value at the position (xn, yn) (1 ≦ n ≦ N) of the projection data is f (xn, yn), the centroid (xg, yg) of the image of the projection data is defined as follows.

The coordinates (xg, yg) of the center of gravity obtained in this way are aligned with the center of the projection data.
These data are .ply format files, and the .ply format files store the vertex coordinates of the 3D model. In the modeling step, in order to convert the surface data into volume data, first, the voxel value 1 is stored as a weight in a three-dimensional array of addresses corresponding to the vertex coordinates. Since the inside is empty as it is, volume data is obtained by assigning the value 1 to the empty portion as well. In addition, the internal structure was changed by partially changing the internal weight value to a value other than 1. In this experiment, a model was created in which the weight (voxel value) was changed to 20-45.

(Learning phase)
Specifically, for the three-dimensional model on the dictionary side, projection data is appropriate within the range of 0 ° ≦ ζ <180 ° and η within the range of 0 ° ≦ ζ <360 ° by three-dimensional radon transformation. Find multiple sheets at intervals. Projection data is a collection of a plurality of images. Next, perform the Fourier transform or alignment by the center of gravity so that matching can be performed even if the 3D model is translated. Next, a subspace on the dictionary side is constructed from the projection data for matching using the mutual subspace method.
Each image of projection data is vectorized.
A matrix K ^v _ij = k (vector vi, vector vj) is created from the vector vi (1 ≦ i ≦ M) using a kernel function, and an eigenvector α ^v is obtained. The eigenvectors are sorted and normalized in ascending order of eigenvalues. In the case of the mutual subspace method, eigenvalues and eigenvectors are obtained by eigenvalue decomposition of a matrix in which vectors are arranged after vectorization. Sort the eigenvectors in descending order of eigenvalues, and construct the subspace V from this. Here, M is the number of input query projection data.
The algorithm is shown in Equation 9.

(Classification phase)
Similar to the learning phase, the projection data of the 3D model of the class μ on the query side is created. A basis vector u ^u _j (1 ≦ j ≦ N) is created from the projection data, and a matrix Ku is created from this using a kernel function to obtain an eigenvector αu. The eigenvectors are sorted and normalized in ascending order of eigenvalues. By substituting the eigenvector αv obtained in the learning phase and vi obtained by vectorizing the input data into the formula (7), the matrix S of the formula (4) is created. However, not all eigenvectors are used, but the number of vectors set from the dictionary side and the input side can be used. Find cos ² θ1 and S [n] from the largest eigenvalue of this matrix, and classify the query into the class with the highest value.
In the case of the mutual subspace method, as in the learning phase, the base vectors are arranged to form a matrix, and the eigenvectors are sorted and normalized in the order of eigenvalues obtained by eigenvalue decomposition. The eigenvector obtained in the learning phase and the eigenvector obtained in the classification phase may be obtained.
The algorithm is shown in Equation 10.

<Display step>
This step is a step of accessing the three-dimensional CAD data from which the selected two-dimensional projection map is obtained and displaying the three-dimensional CAD data as a search result.
In this step, target CAD data is selected from a large number of three-dimensional CAD data existing in the database, the corresponding CAD data is displayed on the screen, and can be appropriately edited and saved under a different name. Therefore, a normal method can be used without any particular limitation.

As described above, the search method of the present invention takes projections uniformly from the periphery of the assembly model and stores them in the database. Therefore, the search accuracy increases as the number of projections increases.
When a model to be searched is given, an appropriate number of projections are taken from a random angle. Here, it is not necessary to be the same as the projection method for the model in the database, but here the search accuracy increases as the number of projections increases.
One piece of projection data is selected from the model to be searched, and projection data having the highest correlation value is searched from the database. A series of these operations are performed on all projection data, and the projection data in the database having the highest correlation value with any of the projection data of the model to be searched is selected, and the original assembly model is used as the search result.
Here, there are the following problems. In the present invention, these problems are solved, and this point is characteristic.
[Problems in the above search method]
・ Problems related to rotation Projection varies depending on the projection angle even in the same assembly model. If the number of projection data per assembly model is increased so that the difference in projection angle is reduced, the search accuracy increases, but the processing time and data capacity increase.
・ Problems related to parallel movement When taking the projection of the assembly model, the position of the projection is also shifted depending on the position of the model.
[Solution adopted in the present invention]
When comparing two projection data, radon conversion is performed for each and the correlation value is obtained by the phase-only correlation method. By using the Radon transform and the Fourier transform together, the problems related to rotation and parallel movement can be solved. Since the influence of the projection angle can be reduced, the number of necessary projection data can be reduced.
<Others>
In addition to the above steps, other steps can be introduced as necessary.

  Although the three-dimensional CAD data search method of the present invention has been described above, the present invention is not limited to these, and various modifications can be made without departing from the spirit of the present invention.

Hereinafter, the present invention will be described more specifically with reference to examples, but the present invention is not limited thereto.

[Example 1]
The data used for the experiment is summarized in Table 1.
In the 3D model database used in the experiment, the ranges of 0 ° ≦ η ≦ 180 ° and 0 ° ≦ ζ ≦ 360 ° are as follows: • η = 0 °, 5 °, 10 ° ··· 175 °, ζ = 0 3D model database DB1 that stores 36 × 72 = 2592 projections calculated at 5 ° intervals such as °, 5 °, 10 ° ... 355 °
・ 3D model database DB2 that stores 18 × 36 = 648 projections calculated at 10 ° intervals
・ 9 × 18 = 162 projections calculated at 20 ° intervals 3D model database DB3
Prepared. Here, η and ζ are as shown in FIG.

In the experiment, one of the three-dimensional models in Table 1 is selected as query data, and projection data of the three-dimensional model is randomly obtained in the range of 0 ° ≦ η ≦ 180 ° and 0 ° ≦ ζ ≦ 360 °. In addition, we conducted experiments using multiple query data instead of one, and evaluated accuracy and processing time. Using the proposed query projection data and 3D model database, the proposed method 4.4 is used to find correlation values for all combinations. Judge whether the query data and the 3D model database are the same from the height of the calculated correlation value. Examples of query data used in the experiment are summarized in Table 2, and the experimental results are summarized in Table 3. In Tables 7 to 18, Query is abbreviated as Q, TABLE as TA, HUMAN as HU, and SPIDER as SP because of the table space. In the table, the correlation value cells that are not correctly matched are shaded.

As a result of correlation value detection with DB1 and various numbers of query projection data, if the number of query projection data is as small as one, the correlation value is very low, and the internal structure is similar to TABLE1-1 and TABLE1-2. There is no difference between two very similar correlation values and matching is not performed correctly. It can be seen that the higher the number of query projection data, the higher the correlation value is detected, and the correct 3D data matching is performed. However, when the internal structure is similar, such as TABLE1-1 and TABLE1-2, TABLE2-1 and TABLE2-2, compared with the correlation value with a completely different 3D model database such as TABLE, HUMAN, or SPIDER. It turns out that it becomes high. On the other hand, there is a problem that the processing time becomes enormous as the query projection data increases.
As a result of correlation value detection with DB2 and various numbers of query projection data, if the number of query projection data is as small as one, the correlation value is very low, and the internal structure is similar to TABLE1-1 and TABLE1-2. There is no difference between two very similar correlation values, and matching is not performed correctly. In addition, the maximum correlation value has been detected from the two that differ greatly in appearance and internal structure like TABLE1-3 and TABLE2-1. Similar to DB1, if the internal structure is similar, such as TABLE1-1 and TABLE1-2, TABLE2-1 and TABLE2-2, the correlation value with a completely different 3D model database such as TABLE, HUMAN, or SPIDER It turns out that it becomes high compared with.
As a result of correlation value detection with DB3 and various numbers of query projection data, if the number of query projection data is 1, as in DB1 and DB2, the correlation value will be low if the internal structure is similar. , Can not match correctly.
When there is one query projection data, the correlation value is low regardless of the size of the 3D model database. The matching rate is very low regardless of the size of the 3D model database.
When the query projection data is 4, the correlation value is higher than that of 1 and the matching can be performed correctly. Depending on the projection data obtained at random, matching may not be performed correctly, but the probability of correct matching is higher than when only one query projection data is used.
When the query projection data is 9, the correlation value is higher than that of 1 or 4 images, and matching can be performed correctly. Depending on the projection data obtained at random, the matching may not be performed correctly, but the probability that the matching can be performed correctly is higher than when the query projection data is one or four. In addition, the larger the size of the 3D model database, the higher the accuracy but the processing time.
In the case of 16 query projection data, correct matching is almost certainly possible with DB1 and DB2, which have relatively many stored projection data, but the processing time has become enormous.
In this evaluation experiment, query projection data was obtained at random angles, but matching was not performed correctly depending on the query projection data. Table 4 shows the matching rate for each 3D model database and the number of query projection data. Table 4 shows that if the size of the 3D model database is small and the number of query projection data is small, the matching rate decreases and matching is not performed correctly. This is because the query projection data is obtained at random angles, so the rotation angle between the projection data stored in the 3D model database and the query projection data is not correctly detected, resulting in a low correlation value. Possible cause.
In this regard, in the present invention, it has been found that matching can be performed with high accuracy by using many query projections.

Here, the processing time of matching is shown in Tables 5 and 6.
Table 6 shows the calculation environment. Table 5 shows that the processing time increases in proportion to the number of processed sheets. Based on the matching rate (Table 4) and processing time (Table 5), the number of appropriate 3D model database and query projection data in this experiment is 18 × 36 = 648, which is calculated at 10 ° intervals. The number of data was determined to be nine.

As described above, the 3D CAD data search method of the present invention can perform matching including the internal structure, which cannot be taken into consideration by the conventional method, by using projection data. We evaluated the number of query projection data and the number of 3D model databases.

(Example 2)
The effectiveness of using projection data is evaluated by the similarity by mutual subspace method and nuclear nonlinear mutual subspace method. The experiment was performed on MATLAB 2012 on a machine with Xenon E31245 3.3GHz, main memory 16Gb. The surface data of the experimental data was the public dataset of McGill 3D Shape Benchmark [9]. This was converted to volume data by converting the previous chapter.
The volume data described above was used as a matching sample. Of these, the number of input R for constructing the query subspace was varied from 50 to 200, and the transition of similarity was examined. The 3D model of the database
(1) Same model
(2) Rotated model
(3) Translated model
(4) Rotated and translated model
(5) Five types of models with different internal values (weights) of volume data were used.
When using a nuclear non-linear mutual subspace, there are four dimensions: the dictionary-side subspace dimension number r _d , the input-side subspace dimension number r _i , the number of canonical angles used nca, and the scale parameter s. In this experiment, the number of canonical angles was made equal to the number of rows in the matrix in equation (5), that is, the number of dimensions r _{d in the} dictionary side subspace. The experiment was mainly performed this time with r _d = 6 and r _i = 5.
The following Gaussian RBF was used as the kernel function.

The scale parameter is used to determine the value of σ. Specifically, the average obtained from the vector obtained from the projection data and multiplied by the scale parameter s is defined as σ. A similar experiment was also performed using the mutual subspace method for accuracy comparison. In the case of the mutual subspace method, vectors obtained from projection data of the models to be compared are arranged to form a matrix. The similarity was obtained by substituting the eigenvector of the matrix into Equation (5).

First, we show the results of using the nuclear nonlinear mutual subspace method (KMSM) and the mutual subspace method (MSM) for different models.
First, the results of the similarity between the models without weights are shown. Here, table1-1-rot is obtained by rotating table1-1 by 5 ° for both θ and φ. Since the projection data is 10 ° at a time, the maximum error is set to 5 °. The numerical value of the experimental result is the value of cos ² θ1 expressed by using the angle θ between the spaces and S [n].
This time, we set n = 6 which is equal to the dimension r _d of the dictionary side subspace. The maximum similarity is 1 for both cos ² θ1 and S [n].
From Table1-1 and Table1-1-rot in Table 12, it can be seen that the similarity of the same object is the highest even when rotating. Taking R = 50 as an example, the similarity between table1-1 and table1-1-rot is 0.9871 in MSM, and the next highest similarity is not much different from 0.9746 of spider and human. On the other hand, in KMSM, the similarity between table1-1 and table1-1rot is 0.9492, and the similarity with the next highest spiderto human is 0.8176, indicating a large difference. From the difference of similar values, it can be confirmed that KMSM has higher discrimination performance than MSM.
Next, it was evaluated how much the difference in rotation appears as a difference in similarity.
The results are shown when the angle at which the projection is started for the same object is changed by 1 °. The experiment was conducted using Table1-2.
The greater the difference in rotation from Table 13, the lower the similarity. In KMSM, S [n] and cos ² θ1 are smaller than MSM. However, the highest similarity among the different human and spider objects in Table 12 is cos ² θ1 = 0.8176 and S [n] = 0.2505.
From this, it can be seen that the same object can be recognized even if it is rotated by 5 °, which is the maximum error. Also, from these experiments, the cos ² θ1 value is 0.9 as a threshold value, and if it is more than that, it will be judged as a matching model, and if it is less, it will be judged as a different model.
Next, the result when parallel movement and weight are taken into account is shown. A model table1-2-1 translated from table1-2 and a model table1-2-2 translated and rotated were used. Specifically, the volume data value was changed from 1 to 20.
From Table 14, it can be said that matching is possible even with parallel movement.
Moreover, if the shape is the same, a high degree of similarity is shown even if the object is translated and rotated. However, on the other hand, models with different structures, such as table1-2 and table1-3 0.9573, show high similarity. Next, the result when the alignment based on the center of gravity is performed will be shown. From Table 15, the similarity between table1-2 and table1-3 is 0.7804, which is higher than the similarity when table1-2 and table1-2-2, that is, the same object is moving and rotating. . From this, it can be confirmed that it is more effective than performing Fourier transform.
Furthermore, we changed the value of the volume data, which is weight, to 20-45, and also changed the number of weighted legs.
Table 16 shows that the similarity between table1-2 and table1-4,5,6 is low. From this result, if the weighted position is different, it also appears as a difference in similarity. The reason why the similarity between Table1-2 and Table1-2 in Table 14 is high is that there is only one leg difference and the weight is different only in one place. When the Fourier transform is applied, it can be seen that matching is possible when the position of the weight is different or when the difference in the value of the weight is large.
From Table 17, the similarity between table1-4 and table1-5 is 0.6189, which is below 0.9. From this, it can be seen that the Fourier transform can also distinguish the erroneously matched ones.
The number of projection data was changed to R = 50, 100, and 200, and the transition of the similarity value was examined. Similarity was obtained by aligning the 3D models with different shapes by the center of gravity. The results are shown below.
It can be seen from Tables 18, 19, and 20 that the similarity value tends to increase as the number of projection data increases.
The execution time of the present invention will be described. It can be seen that the calculation time of the projection data is much longer than the time for matching using the mutual subspace method.
As a result of the present invention, the three-dimensional model used this time can be matched even if it is rotated, moved, or rotated. Furthermore, it was confirmed that matching was possible with assembly models with different simple structures with different positions and weights of the desk legs.

Claims (1)

A method of causing a computer to execute a search for specifying 3D CAD data relating to a structure similar to a specific 3D structure from a data group consisting of a plurality of 3D CAD data,
And modeling step of three-dimensional modeling the three-dimensional CAD data,
A projection mapping step of obtaining a plurality of two-dimensional projections by scanning the obtained three-dimensional model from a plurality of directions ;
Separately three-dimensional model of the three-dimensional CAD data to be searched, the target data obtaining step of obtaining a target projection drawing by scanning such that two-dimensional projection view showing a three-dimensional structure to be searched is obtained,
A step of selecting a two-dimensional projection having the highest correlation with the target projection from the obtained two-dimensional projections, and performing Fourier transform after each of the two-dimensional projection and the target projection the correlation value by the phase-only correlation method for those converted, and selecting step of the highest correlation value is selected the two-dimensional projection view is detected,
A display step of accessing the three-dimensional CAD data from which the selected two-dimensional projection is obtained and displaying the three-dimensional CAD data as a search result ;
To let the computer run .