JP2018136946A - Three-dimensional cad model part search method and three-dimensional cad model search method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a three-dimensional CAD model similarity search method capable of performing search for every component configuring complicate three-dimensional CAD data, and performing various types of search such as accessing the three-dimensional CAD data as a finished product from the components.SOLUTION: A three-dimensional CAD model part search method includes: an arrangement step for three-dimensionally arranging three-dimensional CAD data; a disassembly step for disassembling the three-dimensional model for every component of the CAD data to obtain element data; sinogramming step for processing the element data to obtain a sinogram; an association step for associating the sinogram with the original three-dimensional CAD data; and an extraction step for performing search for each three-dimensional data with the sinogram as a mark to extract matching components by performing collation for every component data, or to extract the three-dimensional CAD data associated with the components.SELECTED DRAWING: Figure 1

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.

In recent years, in the manufacturing industry, etc., model design is performed using 3D CAD. In particular, in the manufacturing industry, designing is often performed using an assembly model that represents one model by combining parts.
In order to efficiently manage data that is increasing year by year, a search method for a three-dimensional assembly model is required. If efficient management is possible, the time required for the designer's design will be shortened, leading to more efficient design and production. As a main process, the search is generally performed by reflecting only the shape in the feature amount. In the 3D assembly model, it is necessary to have a search method to identify not only the shape but also the internal structure, the arrangement of each part, and the material used for the part. In addition, when data is reused, data can be reused more efficiently if the search can be performed in units of used parts. When searching in parts, a partial search technique that searches the entire model from a part is required. However, since the shapes of the models to be compared are different, it is difficult to realize by applying a technique that searches for similar models. There is a 3D model search using projection data from a plurality of viewpoints as a 3D model search method for identifying the arrangement and material of parts of an assembly model. The similarity of a plurality of projection images is calculated to obtain the similarity of the three-dimensional model. The model similarity is calculated by performing Radon transform on the projected image, performing Fourier transform, and comparing with the phase-only correlation method. However, the method of calculating the similarity of the obtained projection images can only know whether the objects are similar. In the case of partial search, there is a problem that the comparison target is not necessarily similar because the comparison target is one part constituting the model.

Many searches based on the shape of a three-dimensional model have been proposed so far (Non-Patent Document 1). Non-Patent Document 2 proposes a method for searching a shape of a three-dimensional model from a feature amount called “Light Field Descriptor (LFD)”. “LFD” renders a three-dimensional model from a plurality of directions and uses the obtained silhouette image for retrieval. Non-Patent Document 3 proposes a method of searching for a 3D model that is robust against fluctuations and noise of a handwritten line drawing sketch using a sketch written by a searcher. The position, size, and orientation of the three-dimensional model are arbitrary depending on the producer. As a three-dimensional model search method, there is a method of searching by matching the position and orientation of the model. In Non-Patent Document 4, as a process prior to performing a search, a point is randomly selected on the surface of the model, a principal component analysis of the point group is performed to determine the model axis, and an alignment method using the axis is used. Proposed. Rendering is performed on the aligned model, four shape representations are generated, respective Fourier spectra are calculated, and a search is performed using a combination of these low frequency components as a feature amount.
With respect to these methods, a three-dimensional model having no assembly model structure is a search target. Non-Patent Document 5 proposes a model search for identifying the internal structure of a model by converting the component of the model into a graph having a vertex and performing a graph search. As research on partial search, Non-Patent Document 6 proposes “KAZE feature value”. The scale space by "Gaussian Filter" used for SIFT and SURF is isotropic Gaussian Filter, so the outline of the model may be blurred and local features may not be taken well. In order to solve this problem, the “KAZE feature value” uses a non-linear scale space. In Non-Patent Document 7, a depth image of an object called “Depth Buffer” image is generated from multiple viewpoints, and “Vector of Locally Aggregated Descriptors (VLAD)” is used as an encoding method for KAZE features extracted from “Depth Buffer” images. The local feature amount is integrated as the feature amount of the three-dimensional model, and partial search of the three-dimensional object is realized. This method is different from the proposed method because it is not a partial search considering the assembly structure of the three-dimensional model.
Further, Patent Document 1 discloses a data group composed of a plurality of three-dimensional CAD data as a search method that can easily retrieve necessary data including an assembly structure from a large amount of three-dimensional CAD data stored in various formats. 3D CAD data search method for specifying 3D CAD data related to a structure similar to a specific 3D structure from 3D CAD data in 3D model, scanning 3D model from multiple directions Step of obtaining a plurality of two-dimensional projection views, separately modeling the three-dimensional CAD data to be searched for, and scanning the target projection drawing so as to obtain a two-dimensional projection drawing showing the three-dimensional structure to be searched. A step of selecting a two-dimensional projection having the highest correlation with the target projection from the obtained two-dimensional projections A search method has been proposed which includes a step of accessing the 3D CAD data from which the selected 2D projection map is obtained and displaying the 3D CAD data as a search result.

JP2015-158752A

J.H.Tangelder and R.C.Veltkamp, “A Survey of Content 3D Shape Retrieval Methods”, Multimedia Tools and Ap-plications, vol.39, no.3, pp.441-471, 2008 D.Y. Chen, X.P. Tian, Y.T. Shen, and M. Ouhyoung, “On Visual Similarity Based 3D Model Retrieval”, Computer Graphics Forum, vol.22, no.3, pp.223-232, 2003 Takahiko Furuya, Takahiro Matsuda, Yuki Kurita, “Retrieval of 3D models by sketches using manifolds of multi-view image features”, NICOGRAPH, 2013. Shinji Tatema, Yohei Seki, “Shape Similarity Search for 3D Models Based on Multi-Fourier Spectral Representation”, IEICE Transactions Vol.J91-D, No.1, pp.23-36, IEICE, 2008 A.S. Deshmukh, A.G. Banerjee, S.K.Gupta, R.D.Sriram, “Content-based assembly search: A step towards assemblyreuse”, Computer-Aided Design, vol.40, issue 2, pp.244-261,2008 Pablo F. Alcantarilla, Adrien Bartoli and Andrew J. Davi-son, “KAZE Features” European Conference on ComputerVision (ECCV), October 2012 Ryuichi Kosaka, Koji Tatema, Masaki Aono, “Partial Search Method for 3D Objects Using Local Features of Multiple Viewpoint Images”, ITE Technical Report Vol.37, No.56, ME2013-124, December 2013 Shiro Wakita and Masaki Aono, “Segmentation of 3D model focusing on protrusion shape”, ITE Technical Report Vol. 35, No. 9 AIT 2011-11, HI2011-11, ME2011-50 (Feb. 2011) K. Katayama and T. Sato, “Matching 3D CAD Assembly Models with Different Layouts of Components using Projec-tions”, IEICE Transactions on Information and Systems, Vol.E98-D (6), pp.1247-1250, 2015 [10 ] N. Chida, T. Sato, K. Katayama, “Retrieval Method of 3D Model by Projection Image Emphasized Parts and Its Experimental Evaluation” DEIM Forum 2016 E5-

In recent years, the number of 3D CAD models has been increasing due to the popularization of 3D CAD software used in the manufacturing industry. In order to reuse them, the demand for 3D model search is expected to increase. In order to further improve the efficiency of reuse, a partial search technique for searching the entire model from a part of the model is required.
However, the methods proposed in the past are still insufficient in terms of quick search, and the current various demands such as searching the whole map from the components of IU have not been met.
Accordingly, an object of the present invention is not only to quickly search complicated three-dimensional CAD data, but also to search for each component constituting the complicated three-dimensional CAD data, and to obtain three-dimensional CAD data as a finished product from such components. It is an object of the present invention to provide a three-dimensional CAD model partial search method capable of performing a wide variety of searches, such as accessing a database.

As a result of intensive studies to solve the above problems, the present inventors,
By providing the above, the above-mentioned problems are solved.
1. A three-dimensional CAD model partial search method for specifying three-dimensional CAD data including a specific three-dimensional structure from a data group consisting of a plurality of three-dimensional CAD data,
An arraying step for converting the three-dimensional CAD data into a three-dimensional array;
A decomposing step of decomposing the obtained three-dimensional model for each component of the CAD data to obtain element data;
A sinogramization step of processing the obtained element data to obtain a sinogram;
Associating the obtained sinogram with the original 3D CAD data;
An extraction step of searching for each three-dimensional data using the sinogram as a landmark and collating each component data to extract matching components or extracting three-dimensional CAD data associated with the components A three-dimensional CAD model partial search method comprising:
2. Furthermore, it has a position information acquisition step of subdividing the horizontal axis of the obtained sinogram and associating each element data to obtain a position information sinogram associated with the position information,
The association step is
The three-dimensional CAD model partial search method according to 1, comprising a step of comparing the position information sinogram with the position information sinogram in the original three-dimensional CAD data.
3. A 3D CAD model search method for specifying 3D CAD data including a specific 3D structure from a data group consisting of a plurality of 3D CAD data,
An arraying step for converting the three-dimensional CAD data into a three-dimensional array;
A decomposing step of decomposing the obtained three-dimensional model for each component of the CAD data to obtain element data;
A sinogramization step of processing the obtained element data to obtain a sinogram;
A position information acquisition step of subdividing the horizontal axis of the obtained sinogram and associating each element data to obtain a position information sinogram associated with the position information;
An associating step for associating the obtained sinogram with the original three-dimensional CAD data and comparing the positional information sinogram with the positional information sinogram in the original three-dimensional CAD data;
And a three-dimensional CAD model retrieval method for obtaining invariant data by performing Fourier transform on each position information sinogram in the radial direction and then performing Fourier transform in the angular direction, and performing retrieval based on the obtained invariant data.

  According to the 3D CAD model partial search method of the present invention, not only can complex 3D CAD data be searched quickly, but also search is performed for each component constituting the complex 3D CAD data, and the component is completed. Various searches such as accessing 3D CAD data, which is a product, are possible.

It is a perspective view which shows a search object model. It is the schematic which shows the example of the comparison of the columns of sinogram. It is the schematic which shows the example of the whole comparison of a sinogram. It is a schematic diagram which shows the example of the determination of the corresponding point in projection, (a) shows the projection point of a query model, (b) is a schematic diagram which shows the projection point of a database model. It is a perspective view which shows the components used for evaluation, (a) is Clutch, (b) is Die, (c) is Gear. It is a schematic diagram which shows the list of the used model. It is a chart which shows the coincidence degree of each model and query model by the method using the comparison of sinogram, (a) is a case where Clutch is a query model, (b) is a case where Die is a query model, (c) Indicates the case where Gear is a query model. It is a chart which shows the search accuracy of the method using the comparison using the sinogram and the method using the phase only correlation method. It is a chart which shows the change in the number of projections and the degree of coincidence of the database model in each query model, (a) when Clutch is a query model, (b) is when Die is a query model, (c) is Gear Each case is shown as a query model. It is a chart which shows the search system at the time of reducing the projection point used for a search. It is a chart which shows the search system at the time of changing the size of a model.

  Hereinafter, the present invention will be described in detail with reference to the drawings, but the present invention is not limited thereto.

The three-dimensional CAD model partial search method of the present invention includes:
A three-dimensional CAD model partial search method for specifying three-dimensional CAD data including a specific three-dimensional structure from a data group consisting of a plurality of three-dimensional CAD data,
An arraying step for converting the three-dimensional CAD data into a three-dimensional array;
A decomposing step of decomposing the obtained three-dimensional model for each component of the CAD data to obtain element data;
A sinogramization step of processing the obtained element data to obtain a sinogram;
Associating the obtained sinogram with the original 3D CAD data;
An extraction step of searching for each three-dimensional data using the sinogram as a landmark and collating each component data to extract matching components or extracting three-dimensional CAD data associated with the components It can be implemented by performing.

The present invention proposes a partial search method that considers not only the shape of a three-dimensional CAD assembly model but also the arrangement of parts. A three-dimensional array is used for the search (arraying step). In order to identify the parts constituting the assembly model, a numerical value is assigned to each type of part used. A projection image is generated from a plurality of viewpoints for the assembly model (decomposition step). In this way, the numerical value given to the component is reflected in the projection image (association step). Radon conversion is performed on the projection image to generate a sinogram (sinogram generation step). The sinograms thus obtained are compared (extraction step). In the following embodiment, the database model is prepared for three types of three-dimensional CAD assembly models, and three types of three-dimensional CAD assembly models having different component arrangements, each of three types and 27 types, and the proposed method is tested. Evaluated.
In the present invention, a method is proposed in which partial search is realized by performing two-dimensional radon transformation on a projected image and making a comparison using the properties of the obtained sinogram. As preparations for the search, removal of parts unnecessary for the search and weighting of the labels representing the parts are performed. It is assumed that the labels are uniquely determined for the parts among the designers. As for the label weighting, the value based on the volume is set for each part, thereby reducing the influence of the label value on the search result. Due to the nature of the sinogram, the translation and rotation amount of the three-dimensional assembly model is replaced by the vertical translation of the sinogram. In addition, there is a problem that it takes enormous time to compare sinograms. Therefore, the amount of calculation was reduced by calculating the amount of rotation and reducing the number of sinograms used to compare projection points for aperture comparison.

<Partial search>
The partial search handled in the present invention is defined as “searching a database model including all query models”. That is, it is to search for “a model in which a part of the database model matches the query model”. The partial search handled in this paper will be described using the Gear model shown in Fig. 1 as an example. As shown in FIG. 1, the assembly model represents a model in which a plurality of parts are combined to form one model. The partial search handled in the present invention represents searching the gear model of the database model using “Cap”, which is a component of the Gear model, as a query model. However, the Gear model has six “Caps”. If the query model has six “Caps” and is configured in the same arrangement as the database model, it is naturally a partial search. However, in the present invention, even if one query model “Cap” has the same shape as one of the six, it is treated as a partial search. In the case of shape search, since the purpose is to search a database model similar to the query model, there is a premise that the shape of the database model to be searched is similar to the query model. When the query model is the Gear model, searching for a database model whose shape is similar to the Gear model is called shape search. However, since partial search is part of the database model, the shape of the database model to be searched is not necessarily similar. Therefore, it is difficult to realize partial search only by calculating the similarity of images.

<Proposed method>
Hereinafter, each step of the partial search method of the present invention will be described.
(Array step)
The arrangement step is an arrangement step for converting the three-dimensional CAD data into a three-dimensional arrangement.
We propose a partial search method that takes into account the shape of the 3D CAD assembly model and the arrangement of the parts used. The format of the assembly model used for the search is a three-dimensional array. That is, since the three-dimensional CAD data is usually three-dimensionally arranged data, the three-dimensionally arranged data is used as it is. If it is expressed in a different format, it is converted into a three-dimensional array using a known function.
The size of the three-dimensional array is proportional to the size of the original three-dimensional assembly model.
By giving a label to each used part, a three-dimensional array including part information is obtained. For this label information, there is a common label list among designers, and parts are uniquely determined for the label.

Pretreatment is preferably performed before, simultaneously with, or after the sequencing step.
In general, in the case of partial search, since the type and number of parts used are different, the shape of the comparison target may be different and search may be difficult. In such a case, in order to increase the accuracy of the search, it is preferable to perform pre-processing of the search to eliminate unnecessary parts and reassign labels.
Deletion of unnecessary parts means deleting parts that are not included in the query model (described later) among the parts included in the database model. When the original label value is used in the search, the difference between the labels affects the search result. The effect of the label value is not completely eliminated, but the value of the label is reassigned to minimize the effect.
This preprocessing will be specifically described, for example, as follows.
Let V (m) be the number of elements of the three-dimensional array of the three-dimensional assembly model m. Similarly, let V (ck) be the number of elements of ck, which is a component of m. Also, let p be the model to be compared. At this time, the following method is performed as preprocessing. (1) A label 0 is assigned to a part ck that is not a constituent part of p 1 among constituent parts of m. (2) Reassign 1 = V (ck) as a label value to a component whose element is not 0 among ck which is a component of m.

(Disassembly step)
This step is a step of obtaining the element data by decomposing the obtained three-dimensional model for each component of the CAD data, and can be grasped as a step of obtaining the feature amount of the three-dimensional CAD assembly model.
Since the position and orientation of the three-dimensional model are different from each other, the posture is generally normalized in advance. In the case of searching for a 3D assembly model, there is a problem that the orientation is not uniquely determined because it has a symmetric shape to handle machine parts or because the parts are circular. In order to perform a universal search for translation and rotation of a three-dimensional model, a feature value that is robust against translation and rotation of the model is required. In order to obtain such feature quantities, projection images for the assembly model are obtained from various angles. The comparison between the query model and the database model uses the feature amount of the projection image. The projection image is a sum of values perpendicular to the projection plane of the three-dimensional array of assembly models, and the shape of the model and the arrangement of the component parts are also reflected in the image. In the present embodiment, the feature amount of the three-dimensional assembly model is obtained using the vertex coordinates of Geodesic Domain as projection points.

(Sinogram step)
A sinogramization step of processing the obtained element data to obtain a sinogram;
A sinogram is obtained by performing two-dimensional radon transform on the projection image thus obtained. As a property of the sinogram, a translation on the two-dimensional plane is represented by a translation in the radial direction, and a rotation on the two-dimensional plane is represented as a translation in the declination direction. Thereafter, one-dimensional discrete Fourier transform is performed on the radial direction to obtain an amplitude spectrum, and further, one-dimensional discrete Fourier transform is performed on the angular direction to obtain an amplitude spectrum. This makes it possible to obtain feature quantities that are robust against translation and rotation in a two-dimensional space.
In the present embodiment, the advantage of the method of the present invention will be described using a method of calculating an amplitude spectrum by the phase-only correlation method as a comparison method (described later). In addition, a sinogram obtained by two-dimensional radon transform of the projected image is used for comparison in order to realize partial retrieval with different shapes.

(Association step)
This step is a step of associating the obtained sinogram with the original three-dimensional CAD data. Specifically, when calculating the feature amount in the above-described decomposition step, it is associated with the data of the three-dimensional assembly model before projection, or the sinogram obtained in the above-described sinogram conversion step is traced back to the data before projection. To do so. In the present embodiment, the former method is adopted, and in the decomposition step, the data of the picture dimension assembly model is associated with each other through projection, calculation of feature values, and sinogram formation. Has been implemented.

(Extraction step)
In this step, each three-dimensional data is searched using the sinogram as a landmark, and a matching component is extracted by matching for each component data, or three-dimensional CAD data associated with the component is extracted. Is a step. In this step, the degree of agreement between assembly models>
Since the feature amount of the assembly model is obtained through projection as described above, it is represented by a two-dimensional array. A sinogram obtained by performing two-dimensional radon transformation on the projection image is used for calculating the degree of coincidence. The feature extraction procedure is shown in Algorithm 1 shown in Table 1. The two sinograms are compared and the degree of agreement between the sinograms is calculated. The procedure for calculating the coincidence between the two sinograms is shown in Algorithm 2 shown in Table 1 and Algorithm 3 shown in Table 1. Algorithm2 represents the procedure for calculating the coincidence between sinograms. Circ (syn, k) of Algorithm2 represents the process of storing values in order from the first array when the array is larger than the argument by shifting syn in the declination direction by k. ing. This is a process utilizing the property of sinogram in which the amount of rotation of an object on a two-dimensional plane is replaced by parallel movement in the declination direction. Algorithm3 represents the procedure for comparing sinogram columns. Extension (s,) I) of Algorithm 3 represents the process of shifting s by i in the radial direction and expanding the array and substituting 0 when the size of the array exceeds the radial direction. . Examples of sinogram comparison are shown in FIGS. Fig. 4 shows the sequence of comparison of the sinograms, and Fig. 3 shows the flow of the entire sinogram comparison. The parameters correspond to each Algorithm. FIG. 2 shows a comparison procedure of the sinogram rows S1 and S2. First, the difference between each element of S1 and s2 is calculated. A value greater than 0 among the calculated values is set to 0. This process is repeated by shifting S2 line by line in the radial direction. The total sum of N obtained is used as the coincidence between the sinogram columns. FIG. 3 shows a comparison procedure between the sinograms syn1 and syn2. First, the columns of each sinogram are taken out, and the degree of coincidence between the columns is calculated by the procedure of FIG. This process is repeated by shifting syn2 in the declination direction. Let mdegree2 be the minimum value of each column of mdegree1 obtained in this way.
The sum of mdegree2 is the degree of coincidence mdegree between sinograms. The calculated degree of coincidence is a difference. The numerical value is negative, but the larger the value, the more consistent the models are. However, if the degree of coincidence exceeds 0, it is excluded because it indicates that the query model is larger. The procedure for calculating the degree of coincidence between models is shown in Algorithm 4 shown in Table 2.

<Efficient calculation of coincidence>
A partial search is performed using a sinogram for calculating the degree of coincidence of the three-dimensional assembly model. There is a problem that it takes time to compare sinograms. Two measures are taken to reduce the time required for the search. The first is a reduction in the number of projections. Conventionally, projection images are compared by making the number of projections of the query model equal to the number of projections of the database model. In the present embodiment, efficiency is improved by performing a search by reducing the number of projections of the query model. As a second contrivance, the calculation amount was reduced by calculating the rotation amount between the projection points of the query model and reducing the number of sinograms for comparing and comparing the projection points of the database model. For example, when the projection image is generated from the six projection points A to F like the projection points of the query model shown in FIG. 4, the database model is generated for one projection image of the query model generated from the point A. The degree of coincidence with the projection image generated from all the projection points was calculated. If the projection point having the projection image with the highest degree of coincidence with the projection image of the query model is called a corresponding point, if the corresponding point of the first projection image of the query model is known, the second corresponding point The coordinates can be calculated from the rotation amount of the vertex coordinates of Geodesic Domain. The corresponding point of the projection image of the query model is calculated by calculating the degree of coincidence between the first projection image of the query model and all projection images of the database model, and the projection point of the projection image having the highest degree of coincidence is defined as the corresponding point. To do. For example, in FIG. 4, it is assumed that the corresponding point of the first projection image of the query model is the projection point G. If the point rotated by the rotation amount calculated from the vertex coordinates of the Geodesic Domain with respect to the projection point G is G ′, the corresponding point of the second projection image of the query model should be near G ′. Since it is unlikely to be projected from the same point, in this embodiment, five projected points that are close in distance from the calculated point coordinates are set as candidate points of corresponding points. For the coincidence calculation with the second and subsequent projection images of the query model, calculation is performed only with the projection image obtained from this candidate point, and the point at which the projection image with the highest coincidence among the candidate points is obtained is calculated. The degree of coincidence is calculated using the corresponding points thereafter.

<Evaluation experiment>
For the evaluation in this embodiment, an experimental evaluation was performed using a three-dimensional CAD assembly model in which the arrangement of parts is different. Three types of three-dimensional CAD assembly models shown in FIG. 5 having various parts selected from GrabCAD [9] were selected, and some parts were deleted for simplification. Each of the three models was classified from type 1 to type 3 depending on the model configuration. Type 1 is a model in which the total number of components is different, Type 2 is a model in which the number of components is the same and the number of component parts is different, and Type 3 is a model in which both the total number of components and the number of parts are different. Three types of models with different parts arrangements were created. For Clutch, Die, and Gear, three types of models A, B, and C were prepared as type 1. Let A be a correct model and B and C be incorrect models. For Type 2, D is the correct model and e and F are incorrect models. For Type 3, G is the correct model and H and I are the incorrect models.
Table 3 shows a list of models. An assembly model given as a query is called a query model, and an assembly model to be compared with a query model is called a database model. The database model was prepared in 9 patterns for 27 types of Clutch, Die, and Gear, a total of 27 assembly models. Three models of Clutch, Die, and Gear were prepared as query models. Ten types of assembly models, each of which was randomly translated and rotated, were prepared. We also added random translation and rotation to the database model. The model used for the experiment is shown in FIG. Differences in color represent differences in parts. The configuration of the Clutch model is also shown in Table 3. The model size is 64 × 64V64, the number of database model projections is 162, and the number of query model projections is 42. Visual C ++ 2012 and MATLAB 2013b were used on Windows 7 Professional 64 bits, and experiments were performed with a 2.8 GHz Intel Core i3 processor and 16 GB RAM computer.

  As a comparison method, a three-dimensional model search using a phase-only correlation method was performed. Similar to the method of the present embodiment, the shape of the three-dimensional model and the arrangement of parts were identified. The feature quantity used in the search is the power spectrum of the sinogram obtained with Algorithm1. The procedure for calculating the degree of coincidence between models is shown in Algorithm 5 of Table 4. POC (f (m1, v), f (m2, v)) of Algorithm 5 represents that the feature quantities f (m1, v) and f (m2, v) are compared by the phase-only correlation method.

<Identification of 3D CAD assembly models with different component arrangements>
The proposed method was experimentally evaluated using models with different component arrangements. The aforementioned 27 assembly models are used as database models, and projection images are generated in advance for these models. For each model, 162 projection images were prepared, and sinograms were generated for the projection images of 27 models, and these were used. Similarly, the query model generates 42 projection images and searches the database using them. FIG. 7 shows the degree of coincidence between the database models of Clutch, Die, and Gear and the query model calculated by the proposed method. The results showed that the correct model (A, D, G of each model) had the highest degree of agreement among the types of Clutch, Die, and Gear models. From this result, it can be seen that the assembly model used in the experiment can be classified by type according to the method of the present invention, and it is possible to identify partial searches of assembly models that differ not only in shape but also in component arrangement. The Clutch model type 3 model (Clutch G, H, I) is generally more consistent than the other type 1 and 2 results. Clutch H and I are incorrect models, but the degree of coincidence is higher than that of the type 2 correct model. In other words, it can be understood that the search can be performed with higher accuracy by classifying by type than by performing the search without classifying by type. The search accuracy of each method is shown in FIG. The search accuracy in the present embodiment is expressed as follows when a set of query models is Q.
Search accuracy = (| Among models with the highest degree of matching among types; Number of models that are correct models |) / | Q |

<Search accuracy and processing time when the number of projections is changed>
We experiment with database search by changing the number of projected images, and evaluate the search accuracy of our proposed method and the processing time required to calculate the degree of coincidence between models. In this paper, the number of projected images is determined by the number of vertices of GeodesicDome. Here, the number of vertices is changed to 42, 92, 162, 252 and 362, and the matching degree and processing of each model in the database when the number of projections is changed to 42, 92, 162, 252 and 362 Evaluate time. FIG. 9 shows the degree of agreement between the query model and each model in the database when the correct model is ClutchA, Die A, and Gear A, respectively. From Fig. 9, it can be seen that when the correct model is Clutch A and Die A, the correct model has the highest degree of matching even if the number of projections is changed. In other words, it can be said that the search is correctly performed for each type. However, when the correct model is Gear A, depending on the number of projections, the model that is not the correct model may have the highest match. This is probably because the number of projected images with a high degree of coincidence was small due to the influence of the model's posture, and the search was not possible.

<Effects on processing time due to reduction in calculation amount>
The longest processing time is the comparison of sinograms. To reduce processing time, reduce the number of comparisons of sinograms and reduce the amount of calculation. 3 for the proposed method. The amount of computation is reduced by the method described in Section 4, and the processing time required to calculate the search accuracy and the matching score between models is evaluated. FIG. 10 shows the processing time when the number of projection points used for the second and subsequent coincidence calculation is changed to 3, 5, 12, 42, 92, 162. FIG. 11 shows the change in the search accuracy of the proposed method when the number of projection points is reduced. From FIG. 11, it can be seen that even if the number of projection points is reduced to five, the search accuracy is not significantly affected. However, if the number of projection points is reduced to 3, the search accuracy will decrease. This seems to be due to the fact that correct corresponding points cannot be obtained due to the reduction of projection points. If projection points are not reduced, the number of projection points used for comparison is 162. In the proposed method, the number of projection points used for calculating the degree of coincidence for the second and subsequent sheets was reduced to 5, and the processing time for calculating the degree of coincidence between models could be reduced to 5%.

<Effect>
According to the method of the present embodiment, a partial search can be performed with high accuracy using the projection image in consideration of not only the shape of the three-dimensional CAD assembly model and the number of parts but also the arrangement of the parts. Comparison is performed using sinograms to realize partial searches with different shapes, and the time required for the comparison can be realized by reducing the number of projections and the number of projection points used for comparison.

In the search method of the present embodiment,
Furthermore, it has a position information acquisition step of subdividing the horizontal axis of the obtained sinogram and associating each element data to obtain a position information sinogram associated with the position information,
The association step is
A step of comparing the position information sinogram with the position information sinogram in the original three-dimensional CAD data may be included.

(Location information acquisition step)
This step is a step of subtracting the horizontal axis of the obtained sinogram and associating each element data to obtain a position information sinogram associated with the position information.
In the partial search, there are a case where a model included in the query model is searched and a case where a model including the query model is searched. In the present embodiment, the former is assumed. Note that the latter case can be dealt with by changing the direction of the difference described later.
The algorithm for this location information acquisition step is shown in Algorithm 1 in Table 5. Algorithm 1 compares the database model and the query model according to the following steps. Here, the arrangement step is omitted.
(1) Search for a combination as a candidate for correspondence from all combinations of database model and query model subassemblies (pre-processing step).
(2) The projection image from the vertex coordinates of “Geodesic Sphere” onto the two-dimensional plane is calculated for each subassembly of the database model and the query model (decomposition step).
(3) Construct a sinogram from the projected image by radon transformation (sinogram step).
(4) Calculate the difference between sinograms for the set of candidate subassemblies.
(5) Based on the obtained dissimilarity, the correspondence between the database model and the query model subassembly is determined, and the dissimilarity at that time is returned as the dissimilarity between the database model and the query model (4 and 5). In the location information acquisition step).
Here, a set of parts having the same material label in the assembly model is called a subassembly. A subassembly of the assembly model m is represented as a set SA (m), and a set composed of parts included in m is represented as C (m). Similarly, for subassembly saεSA (m), C (sa) represents a set of parts included in sa. In the present embodiment, it is assumed that only the same parts are included in C (sa).

(Pre-processing step)
When the database model m ^d and query model m ^q are given, since the correspondence between the material information between the two assembly model is unknown, for each sub-assembly is first included in the m ^d, the subassembly m ^q throat Judge whether the same parts are included. For subassemblies sa ^d ∈SA (m ^d) and sa ^q ∈SA (m ^q), and sa component contained in the ^d c ^d ∈ C volume Vol of ^{(sa d) (c d)} , components contained in sa ^d total | C (sa ^d) | a volume Vol of components c ^q ∈ C contained in ^{sa q (sa q) (c} q) and, sa parts total number included in the ^q | C (sa ^q) | and respectively compared To do. If the volume ratio | Vol (c ^q ) / Vol (c ^d ) −1 | is greater than the threshold value t, c ^q is regarded as a part different from c ^d and sa ^d is regarded as not included in sa ^q . When | C (sa ^d ) | is larger than | C (sa ^q ) |, sa ^d is obviously not included in sa ^q . Algorithm 2 in Table 6 shows an algorithm that determines the correspondence of each subassembly of m ^d and m ^q and returns a set CRP that stores the pairs that are candidates for correspondence.
Next, based on CRP, all combinations in which m ^q subassemblies correspond one-to-one to m ^d subassemblies are obtained, and a set CSA is formed. This processing is performed by the function MakeSubassemblyPairs (CRP) in the 10th line of Algorithm 1. For example, when CRP = {(sa ^d ₁ ; sa ^q ₁ ); (sa ^d ₁ ; sa ^q ₂ ); (sa ^d ₂ ; sa ^q ₁ ); (sa ^d ₂ ; sa ^q ₂ ))}, Return value CSA is CSA = {((sa ^d ₁ ; sa ^q ₁ ); (sa ^d ₂ ; sa ^q ₂ )); ((sa ^d ₁ ; sa ^q ₂ ); (sa ^d ₂ ; sa ^q ₁ ) )}. If the one-to-one correspondence of the material information cannot be taken and | CSA | = 0, it is determined that m ^d and m ^q are different assembly models, and the process is terminated.

(Disassembly step)
In general, since the position and orientation of a three-dimensional model in space vary depending on the manufacturer, a feature amount that is robust against translation and rotation of the model is required. Therefore, first, in order to obtain a feature quantity that is robust against rotation in the elevation and azimuth directions of the model, a projection image of the model on a two-dimensional plane perpendicular to a certain viewpoint is calculated. As the viewpoint to be used, the vertex coordinates of \ Geodesic Sphere "obtained by expanding the regular polyhedron can be used, which is different from the above-described decomposition step.
(Sinogram step)
Although this step is the same as the above-described sinogram generation step, it may be configured by calculating a projection vector while changing the angle and arranging the obtained projection vectors side by side. The sinogram is characterized by converting the rotation of the original image into angular translation and converting the translation into radial fluctuation.
A normal sinogram is constructed by calculating a projection vector in the range of 0 ° ≤ angle θ <180 °. In order to correspond to rotation in the projection axis direction by alignment of the sinogram, the sinogram on the query model m ^q side is used. Calculates a projection vector in the range of 0 ° ≦ angle θ <540 °. Algorithm 3 in Table 7 shows the feature extraction procedure for the 3D CAD assembly model m. As described above, | A ^d | = 180 for m ^{d and} | A ^q | = 540 for m ^q .

(Location information acquisition step)
For each corresponding candidate (sa ^q ; sa ^{d) of the} subassembly of m ^d and m ^q included in the set CRP, the sinograms are compared, and the difference in the candidate (sa ^d ; sa ^q ) is calculated. This process corresponds to the 14th to 18th lines in Algorithm 1.
The sinograms sng ^d and sng ^q are compared with the difference between sng ^q while moving sng ^d in the radial and angular directions in order to compensate for the deviation of the position and posture of m ^d and m ^{q in} the three-dimensional space. This is done by calculating in projection vector units. sng ^d and sng ^q reflect the component arrangement of subassemblies sa ^d and sa ^q , respectively, and the absolute value of the difference | sng ^q −sng ^d | represents the degree of difference, which is the degree of difference in component arrangement . Here, when C (sa ^q )> C (sa ^d ), a positive element remains in the difference sng ^q −sng ^d even if the component arrangements partially match. Therefore, by replacing all elements greater than 0 in the difference sng ^{q –} sng ^d with 0, and evaluating the dissimilarity, it is possible to evaluate the partial match of the component arrangement even if the total number of components is different. Also, by dividing | sng ^q −sng ^d | by Vol (sa ^d ), the difference calculation result by the subassembly with a large volume is prevented from becoming dominant.
Algorithm 4 and Algorithm 5 in Table 8 show the algorithm for calculating the difference between the sinograms sng ^d and sng ^q . Here, the index “:” in Algorithm 4 represents the process of extracting all elements of a specific dimension from the array. For example, for an array a of size n _y × n _x and k with 1 ≦ k ≦ n _x , a (:, k) returns the k th row vector of a with size n _y . The function sum (v) in Algorithm 4 returns the sum of all elements of the vector v. Furthermore, the function abs (x) in Algorithm 5 is a function that returns the absolute value of the scalar value x, and the function shift (pv, i) in Algorithm 5 shifts the projection vector pv by i so that the empty element is 0. It is a function to fill with.
However, if the position that best matches the radial direction and the angular direction is obtained from the degree of difference obtained for the candidate (sa ^d ; sa ^q ), the position for each corresponding sub-assembly candidate (sa ^q ; sa ^d ) is determined. Since the alignment results of the position deviation and the posture are different, the arrangement relation of the m ^d and m ^q subassemblies is lost. Therefore, as shown in the 19th to 27th lines of Algorithm 1, the difference calculated for each subassembly correspondence candidate (sa ^q ; sa ^d ) is calculated as a one-to-one correspondence between the m ^d and m ^q subassemblies. After adding according to the candidate csa∈CSA, the difference between m ^d and m ^{q in} the corresponding csa obtained by radial and angular alignment is added to the set CSAD [csa]. As a whole, m ^d and m ^q are aligned. Here, since the number of differences added depends on jSA (md) j, considering the accumulation of discrete errors, the difference obtained by registration is calculated as │SA (m ^d ) | In addition, the functions ArrayMin (a, dim) and ArraySum (a, dim) in Algorithm 1 are the functions for obtaining the minimum value in the dim dimension of the multidimensional array a and the functions for summing the elements in the dim dimension of a, respectively. . For example, for an array a of size n _y n _x , ArrayMin (a, 1) returns a vector of size n _{x with} the smallest element found for each column vector of a. ArraySum (a, 1) also returns a vector of size n _x for each column vector of a that is the sum of all the elements of that column vector.
For all combinations of the projected point v ^d ∈ V ^d and v ^q ∈ V ^q, is after seeking dissimilarity by comparing sinograms, among Csa∈CSA, most m ^d, the degree of difference between m ^q decreases Search for subassembly correspondences. The difference between m ^d and m ^{q at} this time becomes the final difference between the database model m ^d and the query model m ^q as it is. This process is shown in Algorithm 6 of Table 9. The processing in Algorithm 6 has the lowest dissimilarity based on the dissimilarity stored in CSAD [csa] for all combinations of projection points v ^d ∈V ^d and v ^q ∈V ^q in csa∈CSA This is a process of searching for a set of projection points while avoiding selecting the same viewpoint redundantly.
This position information acquisition step can be performed after extracting the constituent elements that are suitable in the extraction step described above. In other words, even if it is determined that the shape feature points are matched by the above-described extraction step, it is possible to accurately grasp the position and the arrangement angle of the parts in the whole by performing this position information acquisition step. It becomes.
In this case, in the associating step, retrieval is possible by associating the acquired position information with the original three-dimensional CAD data. This association can be performed using the association method described in the association step described above.

Next, an embodiment of a three-dimensional CAD model search method for searching the whole instead of the partial search method described above will be described. In the following description, parts different from the above-described three-dimensional CAD model partial search method of the present invention will be particularly described.
The 3D CAD model search method of this embodiment is:
A 3D CAD model search method for specifying 3D CAD data including a specific 3D structure from a data group consisting of a plurality of 3D CAD data,
An arraying step for converting the three-dimensional CAD data into a three-dimensional array;
A decomposing step of decomposing the obtained three-dimensional model for each component of the CAD data to obtain element data;
A sinogramization step of processing the obtained element data to obtain a sinogram;
A position information acquisition step of subdividing the horizontal axis of the obtained sinogram and associating each element data to obtain a position information sinogram associated with the position information;
An associating step for associating the obtained sinogram with the original three-dimensional CAD data and comparing the positional information sinogram with the positional information sinogram in the original three-dimensional CAD data;
Each position information sinogram can be Fourier transformed in the radial direction and then Fourier transformed in the angular direction to obtain invariant data, and can be performed by performing a retrieval step for retrieving based on the obtained invariant data. .
That is, the difference is that a search step is performed instead of the above-described extraction step, and the rest is the same as the above-described three-dimensional CAD model partial search method of the present embodiment. In this embodiment, the extraction step is not allowed to be performed, which means that the search step is an essential step. By performing this search step, it is possible to perform a search accurately even when the number of component parts is large.

(Search step)
In general, an assembly model with a complex internal structure is difficult to retrieve compared to an assembly model with a simple internal structure. Therefore, a 3D assembly model retrieval method with many components is required. There are few assembly models with many of them, and there has never been such a model in our laboratory. In this paper, we used many 3D model polygon meshes from GrabCAD [2], and there were many components artificially. We propose a method for generating assembly models.
In this paper, the same or different 3D CAD models from GrabCAD [2] are combined with 2 2 2 = 8 pieces, 2 2 3 = 12 pieces, 3 3 3 = 27 pieces, and 4 4 4 = 64 pieces. Generate an assembly model with many parts.
The method of this embodiment is as follows. In the following flow, 8 assembly models are combined. Vertex data of assembly models k, l, m, n, p, q, r, and s vk, vl, vm, vn, vp, vq, vr, vs. The size of one side of the three-dimensional space is w.
(1) Obtain vk from the stl file that stores the vertex data that composes k.
(2) Calculate the center of k from vk and translate to the coordinates to be placed for each assembly model.
(3) To adjust the length of one side of the model space to w = 2, the magnification is reflected in the translated k.
(4) Perform the above for l, m, n, p, q, r, and s and sum them up.
Based on Fig. 1, the coordinates to be arranged in the case of 2 are determined as follows: K = (w / 4, w / 4, w / 4), L = (3w / 4, w / 4, w / 4), M = (w / 4, 3w / 4, w / 4), N = (3w / 4, 3w / 4, w / 4), P = (w / 4, w / 4, 3w / 4), Q = ( 3w / 4, w / 4, 3w / 4), R = (w / 4, 3w / 4, 3w / 4), S = (3w / 4, 3w / 4, 3w / 4). Table 10 shows the arrangement coordinates when 8, 12, 27, and 64 are combined.
As a result, assembly models can be combined without overlapping each other. However, since they are separated from the center of the combined model space and the coordinates of the arrangement, the model space is changed from the model space according to the posture change amount saved before the search. Since it may protrude, it is necessary to consider it.
In general, the position and orientation of 3D models are different, and there are some problems with the method of normalizing them. In order to improve such problems, feature values that are robust against translation and rotation are required. Convert the 3D CAD model into a 3D voxel model, generate a projection image for each projection point, perform 2D radon conversion on the obtained projection image (sinogramization step), and then move in the radial direction A one-dimensional Fourier transform is performed for the amplitude spectrum, and then a first-order Fourier transform is performed for the declination direction. By taking the amplitude spectrum, a robust feature against translation and rotation can be obtained. . However, if the assignment of numerical values for each material type of the component parts is not uniform between users and models, the numerical values will not be normalized unless the numerical values are normalized when calculating the similarity between the two assembly models. Influencing search results. In this case, we propose the following method.
Assume that the assembly model is m, the volume of ci that is one element of the component set of m is V (c), and the number of material types of the component of m is n. Let A be the angle of the two-dimensional Radon transform in the spherical coordinate system.
(1) Calculate the projection image of ci for each projection point (decomposition step), perform 2D radon transform, calculate all n sinograms sino (ci), and convert to sino (c ₁ , ..., c _n ) Store (sinogram step).
(2) Perform a discrete Fourier transform of sino (c ₁ , ..., c _n ) in the radial direction, take an amplitude spectrum, and store it in f (sino (c ₁ , ..., c _n )).
(3) f (sino (c 1, ..., c n)) of each of each _{A f (sino (c 1,} ..., c n)) elements e (c _n, A) of the 2 The product of the sum and the sum is stored as B (c _n , A).
(4) Set s (c _n , A) = e (c _n , A) / B (c _n , A), and reassign s (c _n , A) to e (c _n , A).
(5) Sort f (sino (c1,..., Cn)) from those with small V (c), and generate f (sino (cs1 +... + Csn)) connected in the radial direction. To do.
(6) Perform discrete Fourier transform of f (sino (cs1 + ... + csn)) in the angle direction, take the amplitude spectrum, and store it in f (f (sino (cs1 + ... + csn))) (Search step for 2-6).
As a result, f (f (sino (cs1 +... + Csn))) can obtain the feature quantity even when the volume of the component is different.

Also, the feature amount can be reduced. Since the Fourier transform is performed in the radial direction and the declination direction of the Radon transform, it is converted into a two-dimensional array with the peak at the center. The value of the feature amount decreases as the distance from the peak increases, and the influence on the search result decreases. Therefore, by reducing the high-frequency component having a small value and using only the low-frequency component as the feature amount, the data amount of the feature amount itself can be reduced, and the similarity calculation time can be reduced while maintaining the search accuracy. The number of arrays to be deleted is half the number of arrays of feature amounts, and high frequency components are removed so that the size of the two-dimensional array becomes 1/4 each time it is reduced once. In the present embodiment, the feature amount is reduced four times.
Further, the determination of the search result in the search step, that is, the determination of the similarity can be performed as follows.
The features of the assembly model are represented as a two-dimensional array. A two-dimensional array is used as a vector in the Euclidean space, the Euclidean distance between the two vectors is calculated, and this is used as the similarity. The similarity between the two assembly models can be calculated as follows.
If the numerical values assigned to the component parts are not standardized by the user or model, it is difficult to search for the common component parts by the numerical values. Therefore, in the conventional method, the similarity between the two assembly models may match. There was a need to calculate all the components. However, since the method of this embodiment generates a single sinogram for each component material for each projection point and makes it one, even if the numerical values assigned to the component are not unified by the user or model, the same feature amount is obtained. Therefore, the similarity is calculated for each projection point of the assembly model, the smallest is the similarity of that projection point, and the final similarity is the sum of the similarities generated for each projection point. And Then, it is possible to extract those having a high degree of similarity.

Claims (3)

A three-dimensional CAD model partial search method for specifying three-dimensional CAD data including a specific three-dimensional structure from a data group consisting of a plurality of three-dimensional CAD data,
An arraying step for converting the three-dimensional CAD data into a three-dimensional array;
A decomposing step of decomposing the obtained three-dimensional model for each component of the CAD data to obtain element data;
A sinogramization step of processing the obtained element data to obtain a sinogram;
Associating the obtained sinogram with the original 3D CAD data;
An extraction step of searching for each three-dimensional data using the sinogram as a landmark and collating each component data to extract matching components or extracting three-dimensional CAD data associated with the components A three-dimensional CAD model partial search method comprising: Furthermore, it has a position information acquisition step of subdividing the horizontal axis of the obtained sinogram and associating each element data to obtain a position information sinogram associated with the position information,
The association step is
The three-dimensional CAD model partial search method according to claim 1, further comprising a step of comparing the position information sinogram with the position information sinogram in the original three-dimensional CAD data.
A 3D CAD model search method for specifying 3D CAD data including a specific 3D structure from a data group consisting of a plurality of 3D CAD data,
An arraying step for converting the three-dimensional CAD data into a three-dimensional array;
A decomposing step of decomposing the obtained three-dimensional model for each component of the CAD data to obtain element data;
A sinogramization step of processing the obtained element data to obtain a sinogram;
A position information acquisition step of subdividing the horizontal axis of the obtained sinogram and associating each element data to obtain a position information sinogram associated with the position information;
An associating step for associating the obtained sinogram with the original three-dimensional CAD data and comparing the positional information sinogram with the positional information sinogram in the original three-dimensional CAD data;
And a three-dimensional CAD model retrieval method for obtaining invariant data by performing Fourier transform on each position information sinogram in the radial direction and then performing Fourier transform in the angular direction, and performing retrieval based on the obtained invariant data.