Clustering Techniques for Databases of CAD Models

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Clustering Techniques for Databases of CAD Models

October 15, 2001

Abstract

Computer-Aided Design data and Solid Models are of immense importance across the full spectrumof engineering disciplines. Current industrial estimates point to the existence of over 30 billion CADmodels in the world, with increasing numbers of them including 3D solid models. While the databaseand data mining communities have made great strides in management of image, audio and video media,little work exists on how to perform engineering, content-based mining of CAD data and solid models.

CAD data, and the engineering consumers of CAD data, have greatly different needs and require-ments from traditional database multimedia: large, individual database elements; multi-disciplinarycomponents (mechanical, electrical, etc.) with unique access critera; and the lack of an accepted setof readily identifiable features that can be used for model indexing and clustering.

This paper presents our approach to perform similarity-based clustering on large databases of solidmodels of mechanical CAD designs. A publicly available source of solid models is the National DesignRepository (http://www.designrepository.org), which contains over 55,000 publicly avail-able solid models from many different engineering disciplines. It is this repository which we test ourtechniques against. We create a mapping of a solid model’s boundary representation and engineeringattributes into Model Signature Graphs (MSG). From the MSG’s, we create an Invariant Topology Vec-tor (ITV) which captures shape and engineering properties of the CAD models. We use a �-clusteringalgorithm to group the models and provide some of our empirical results to illustrate the approach. Webelieve that our methodology can form the basis for adapting data mining technquies to large engineeringdatabases and building tools for handling 3D solid models as database media.

1 Introduction

Computer-Aided Design (CAD) data and Solid Models play an important role in the engineering disciplines.There are an estimated 30 billion cad models existing in the world with ever increasing numbers of thembeing 3D solid models. The database and data mining communities have made great strides in the manage-ment of image, audio and video media, but precious little work has been done on how to store, retrieve, andcompare CAD data and solid models.

Storing CAD data and solid models in multimedia databases have vastly different requirements fromthe traditional audio/visual media. The database will contain large individual elements, components from avariety of disciplines each with unique access criteria, and a general lack of consensus on what features canbe used for indexing and clustering of these models.

In this paper, we present our approach to performing clustering on large databases of solid models andmechanical CAD designs. A publicly available source of solid models is the National Design Repository(http://www.designrepository.org), which contains over 55,000 publicly available solid mod-els from many different engineering disciplines. It is this repository which we test our techniques against.

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Several models from the repository are depicted in figure 1. We describe the process by which we encodethe models into Model Signature Graphs (MSG) from which we create Invariant Topology Vectors (ITV).Finally, we show how a simple �-clustering technique can be used to group the models and provide empir-ical results to illustrate the approach. We believe our approach can form the basis for adapting data miningtechniques to large engineering databases and building tools for handling 3d solid models as database media.

This paper is organized as follows: Section 2 provides a brief overview of the relevant backgroundliterature from engineering design, modeling and databases communities. Section 3 introduces our technicalapproach to mapping solid models to MSGs, transforming the MSGs to ITVs, and �-clustering the ITVs.Section 4 presents some of our experimental results with the National Design Repository. Lastly, Section 5gives our conclusions and discusses our research contributions and areas for future work.

(a) Machined Part (83KB) (b) ANC101 BenchmarkPart (75KB)

(c) Sheet Metal Part(44KB)

(d) Cast CompressorHousing (637KB)

Figure 1: A few example 3D solid models from the Design Repository; (a), (b), and (c) are wireframerepresentations while (d) is a rendered representation.

2 Background and Related Work

The scope of our work draws together several areas of study, solid modeling and CAD, engineering databases,metric spaces, graph theory, and data clustering. Section 2.1 begins with a discussion of the types of tech-niques used to represent CAD data and solid models. In section 2.2 we describe various techniques in usefor retrieval of CAD data from databases. We define what a metric space is in Section 3.3, and finally discussdatabase clustering in Section 2.3.

2.1 Solid Modeling and Computer-Aided Design

There are three broad schemes for representation of solid models [?, ?]:

1. Decomposition approaches model a solid as collections of connected primitive objects. Data struc-tures used in this type of representation include quad-trees and oct-trees [?].

2. Constructive approaches model a solid as a combination of primitive solid objects. A commonapproach is constructive solid geometry (CSG), which represents a solid as a boolean expression on a

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BODY SHELL FACE COEDGE VERTEX

LUMP SUBSHELL LOOP EDGE WIRE

CURVE SURFACE

POINT PCURVE TRANSFORM

ELLIPSE SPHERE CONE SPLINE

STRAIGHT INTCURVE PLANE TORUS

ENTITY

Topology Geometry

Figure 2: The distinction between geometric and topological information within BRep used by the ACISSolid Modeler [?].

set of primitive solids.

3. Boundary-based approaches model a solid using a data structure that represents the geometry andtopology of its bounding faces. Recently, the boundary-representation (BRep) approach has becomethe representation of choice in solid modeling in large part due to the flexibility and power madeavailable to developers.

A BRep solid model creates a unique and unambiguous representation of the exact shape of an object.BReps have become the dominant representation schema for modern solid modelers used in mechanicaldesign. They are used for engineering analysis, simulation, collision detection, animation and manufactur-ing planning. Data formats used by other CAD industries, such as Architecture/Engineering/Construction(AEC) industries, are often surface or wireframe models—similar to BRep, but they are not required tostore a topologically bounded solid entity, and in the case of a wireframe model only the edges and theirconnectivity are stored.

On the other hand, a BRep usually consists of a graphical structure that models an entity’s topology.Connections between nodes in the BRep graph represent connections between topological components ofthe entity’s boundary. These topology nodes contain references to their underlying geometric entities; forexample, a face of a solid is a topological entity (represented as a collection of bounding edges) that has asurface associated with it. Figure 2 shows the distinction between geometric and topological informationfrom the ACIS Solid Modeling Kernel.

One of the most popular BRep structure is the winged-edge representation [?]. For more information onboundary representation data structures, interested readers are referred to [?, ?, ?, ?].

BReps and other CAD representations are distinctly different from shape models developed by the com-puter vision community in several important ways. Vision-based representations, such as super quadricsand deformable shape models, are not designed for exact modeling of shapes—rather they are employed toreconstruct shapes based on approximate data taken from sensors and cameras. These approxmiated shapescan be used for a basis of comparison among 3D objects, however such comparisons are limited to analysisof geometric moments and gross shape properties. Hence, they are not directly suitable for use in answeringthe kinds of interrogations that design and manufacturing engineers wish to pose about CAD models.

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2.2 Engineering Databases

In the 2D shape matching and image retrieval literature, the indexing and query process follows one of fourcommon approaches:

1. A Textual query based on keywords stored for each image in a database.

2. A query by example uses similarity measures derived off a set of query images provided as input.

3. Query by sketch looks for image segments matching the sketched profile.

4. Iconic queries use templates representing important aspects of the desired image to identify imageswith similar features.

Methods (2-4) employ image processing and computer vision techniques to identify relevant features(e.g., sunrises, people, trees, etc) in 2D images (i.e., GIF, JPEG, etc).

Techniques from computer vision and 2D image retrieval do not directly apply to 3D solid models forseveral reasons of which we will address the three main ones. First, when we are using solid models, weare dealing with an explicit and exact representation of the 3D objects in CAD databases, rather than anapproximate representation generated from sensor data. Shape matching approaches, for example, have hadto develop highly refined model recovery algorithms and techniques to compensate for noisy data.

Second, given a solid model �, minor perturbations in �, creating ��, model can make �� indistinguish-able from �. For example, transformations such as scaling or rotatation can introduce roundoff errors thatexacerbate the problems posed by the inexact nature of floating point arithmetic. Even a simple translationof a model in 3D space by a fixed vector can make models computationally costly to compare—requiring agraph isomorphism check to see if the BRep of � is the same as the BRep of �� with the exception of thelocation and orientation.

Finally, there is no universally acceptable set of features on which model comparisons can be based.Evaluation metrics for solid models depend on the application intent of the engineers using the database.Process engineers may need to query based on manufacturing process features but an industrial designermay need to consider shape aspects of an object. The ill-defined sematics of the engineering design andmanufacturing domain require us create a more flexible methodology for model comparisons which can becustomized to consider the criteria of required by different end users.

2.3 Database Clustering

Agrawal et al. [?] describe clustering as ”...task that seeks to identify homogeneous groups of objects basedon the values of their attributes (dimensions)...”. More formally, Given a set � of data entities, a cluster isroughly defined as a a subset, � , of � such that each of the data entities in � is “similar” or “close to” tothe other data entities in � . In a clustering, � � �� , the elements in �� are more similar toeach other than the elements in ��.

Algorithms that perform these clusterings have been studied extensively in a variety of fields such asbiology, chemistry, and sociology. There is a large taxonomy of clustering techniques that are all suited fordifferent purposes. Two of the most widely used techniques are hierarchical and partitional.

Fasulo [?] describes a popular method of partition clustering called k-clustering. �-clustering takesa set of objects, �, and an integer � and outputs a partition of � into subsets ��, ��, . . . , �� such thatobjects in a cluster are more similar to each other than to objects in different clusters. According to Jain

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et al [?], the general problem is known to be NP-Hard. Some heuristics in use are the k-means algorithmby MacQueen [?], k-medioid by Kaufman et al [?], and one algorithm by Gonzalez [?] which instead ofminimizing the sum of the partitions, minimizes the maximum inter-cluster distance.

There are a few weaknesses in these methods. They favor spherical clusters, not general shapes anddon’t deal with noise. These weaknesses have been addressed by Agrawal et al [?] and Ester et al [?]. Theseall belong to a class of clustering methods that rely on iterative partitional clustering. It is from this familyof clustering algorithms that our research will be continued and for which a general outline of the steps isdetailed below:

1. Start with initial partition of � clusters: Since � is supplied as a parameter to the algorithm, wecan set up an arbitrary partition of the data into clusters. Generally, better results can be obtained ifthe initial partition is closer to the optimal partition.

2. Updating the Partition: A method for doing this is to find a random cluster with an outlying point,and attempt to swap it into a new cluster if the criterion function is moved closer to the optimalpartition.

3. Compute the new representative objects for each of the clusters: A popular method is to computethe centroid, or mean vector, of the cluster.

4. Repeat 2 and 3 until the optimum value for the criterion function is found.

5. Merge small clusters and split large clusters and remove small, outlying clusters: This is doneto take care of excessively large clusters, empty clusters, and bad data points that may influence theclustering in a negative fashion.

3 Technical Approach

Our goal is to develop techniques to store solid models in a database and perform efficient search andretrieval of these models. In clustering the models, we accomplish two things. We show that the topologicalcharacteristics of solid models can be used as a basis for inexact similarity measures. In addition, wedemonstrate the feasibility of incorporating these techniques in a traditional database setting.

3.1 Problem Formulation

One of the main challenges in comparing solid models is finding a representation of the model in a computerusable data structure. Ideally, we would want this datastructure to approximate the overall structure of themodel as closely as possible while allowing the application of well researched and developed algorithmsto perform similarity comparison. We would further like to encode domain specific features within thisdatastructure to exploit any additional information available.

To this end, we have developed a data structure called a Model Signature Graph (MSG), the generation ofwhich is described in Section 3.2. Using the MSG allows us to view the topology of a model in abstract termsand to encode information about the model itself. It also allows the use of graph properties in clusteringthe models together. We do this by generating a fixed length vector, called an Invariant Topology Vector(ITV), containing the properties we wish to exploit, which allows us to define a metric space for the models.Finally, we cluster the MSGs based on this metric space using a simple �-clustering strategy. The overallstrategy is illustrated in Figure 3.

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Solid Model Model Signature

Graph

Invariant

Topology

Vector Clustering

Figure 3: An overall view of the transformation from solid model to an Invariant Topology Vector to be usedfor database clustering.

3.2 Model Signature Graphs

We make use of a specialized graph structure, a complex example of which is illustrated in Figure 4, inorder to represent solid models so that we can perform similarity comparisons. This structure, called aModel Signature Graph (MSG), is constructed from the BRep of a solid model in a manner similar to that byWysk et al. [?] and the Attributed Adjacency Graph (AAG) structures used to perform Feature Recognitionfrom solid models [?].

The BRep [?] essentially consists of a set of edges and a set of faces used by the solid modeler to describethe shape of the model in 3-dimensional space. A MSG for a solid model � is defined as a labeled graph, � ��, where each face � � � is represented as a vertex � , with attributes that further describethe qualities of the face in the model. For instance, we record the type of the surface (e.g., flat or curved),the relative size, and other physical attributes of the face with the vertex, including:

1. topological identifier for the face (planar, conical, etc.);

2. underlying geometric representation of the surface, i.e. the type of function describing the surface;

3. surface area, ��, for the face;

4. set of surface normals or aspects for � .

An MSG edge � �� exists whenever two faces �� adjacent—i.e., when �� and ��meet at a topological edge � in the BRep. The MSG edge � �� is attributed with features representingthe type of BRep edge, �, connection that is being used, including:

1. topological identifier for the edge � in the model � ;

2. concavity/convexity of �;

3. underlying geometric representation of the curve of �, i.e. the type of function describing the curve;

4. the length of the curve of �.

A simple example of the encoding of a solid model into a model signature graph is shown in Figure 5.As can be seen by Figure 4 and Figure 5, our representation can be used on a variety of models, regardlessof complexity. In addition, the MSG is unambiguous with respect to a model’s rotation and scale; it is onlydependent on the connection of the faces of the model.

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(a) Wireframe (b) Hidden Lines Removed

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(c) Model Signature Graph

Figure 4: Representations of a Torpedo Motor (768KB) as both a wire solid model and MSG.

3.3 Metric Spaces of Solid Models

Once the the solid models have been transformed into MSGs, we construct a metric space over the dataset.A metric space is a collection of objects with a distance function, Æ�� , known as the metric, whichcomputes the distance between any two elements in the set. The distance function Æ�� must satisfy thefollowing conditions:

Æ�� IdentityÆ�� Positivity

Æ�� Æ�� SymmetryÆ�� Æ�� Æ�� Triangle Equality

Clustering techniques such as �-means or �-medioid make use of use of metric distance functions toorganize and examine statistical distributions of data. Metric or near-metric distance functions for solid

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(c) Model Signature Graph

Figure 5: Representations of a Part from Allied Signal as both a wire solid model and MSG.

models have the potential for use in a wide range of applications.In attempting to cluster the models in the database, we must construct such a distance measure that

operates over the space defined by the MSGs and satisfies the requirements for a metric. There is a verygood chance that more than one distance function exists, leading to a number of different metric spaces thatcan be constructed over the same database of models. This will also lead to different clustering results, thequality of which must be examined experimentally.

In order to make use of distance metrics in a practical clustering system, they must be relatively easy tocompute. The algorithmic complexity in computing distance metrics for arbitrarily-formed graph structuresis an open question. We believe that an approximate solution using the ITV will be suitable for clusteringof similar models with eachother and further useful in a database setting for performing similarity basedqueries.

Proven distance metrics for graph similarity fall roughly into the category of edit distance. Given twographs, and � , edit distance is loosely defined as the number of operations needed to transform into � .

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Bunke [?] and Kubicka [?] show that different forms of edit distance satisfy the criterio for a metric distance.What this means that if �� then is isomorphic � . The catch is that neither editdistance is polynomial time computable and for large graphs, which are typically generated from solidmodels, the metric is simply unusable in a practical setting. We chose, instead, to use a euclidean distancebetween representations that we construct of the graphs based on their invariant properties and domainspecific knowledge. While there exist examples where the first criterion does not hold for a simple euclideandistance metric, ie: MSGs which have a distance of 0 by our metric are not equal, we have not found otherexamples where the other criteria fail to hold. We therefore feel this is still a usable approximation for adistance function to be used in clustering.

3.4 Invariant Topology Vectors

The eventual aim of our work is to enable indexing and quick retrieval of a large repository of CAD models.Although, a measure such as edit distance provides a proven metric for graph similarity, the cost of runningthe algorithm is much too high for a database that could potentially consist of thousands of designs. Usinggraph invariants, we can form groups, or clusters of potentially isomorphic graphs, or graphs that are closeenough in similarity to satisfy a query. To cluster graphs, we have developed the Invariant Topology Vector(ITV) which fascillitates the grouping of graphs and models by their invariant properties.

Graph Invariants Given a graph , a graph invariant is a property of G, denoted ��, such that if agraph� is isomorphic to , then �� . A complete set of invariants, �� ,determines and � up to isomorphism. So if, �� then is isomorphic to � . Nocomplete set of invariants is known.

A set of graph invariants can still be used to tell if two graphs have the potential to be isomorphic or not,but can not be used to give a definitive answer. In other words, if the invariants of two graphs are different,there is no way the graphs can be isomorphic; if the invariants are all equal, then the graphs may or maynot be isomorphic. However, by choosing to focus distance measurements and similarity assessments ononly those graphs which exhibit similar or equal values in their graph invariants, we believe an approximatesolution can be realized.

The graph invariants that we focus on are directly related to the degree sequence of a graph. The degreesequence, while not the most powerful invariant known, is easily computable, and can be exploited to recovergeneral structural properties of the graph. At this stage, we have not attempted to construct these invariantssuch that they are normalized, so that differences of scale in the number of edges or vertices might skewresults. The following graph invariants were chosen for inclusion in our system:

1. Vertex and Edge Count—Trivially computable graph invariants. Unfortunately, they reveal practi-cally no information about the graph structure, and may be weighted too strongly in the comparisonswe perform, skewing our similarity metrics.

2. Minimum and Maximum Degree—Provide a measurement of the maximum and minimum numberof adjacencies between one face and the other faces in the model.

3. Median and Mode Degree—Provides a measurement that represents statistically the most commonand “average” cardinalities of adjacencies between faces in a model.

4. Diameter – The longest path of edge/face crossings between any two faces in the model.

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5. Type Histogram – Each model BRep contains a set of faces and edges which have various types andfeatures. The analysis and statistical breakdown of these component types is used to further generatea representation of the model.

We encode a fixed set of invariants as an Invariant Topology Vector (ITV). We use the ITV to determinea “position” for a graph in the metric space relative to other graphs. Graphs with similar values for invariantswill lie in the same region of the metric space.

Using graph invariants helps prune out graphs which have no similarity to a given graph and does notdepend on the specific domain where the technique is applied. However, we would like to be able to tailor itin some fashion to a particular domain to aid in more precise measurements. The type histogram is an initialapproach to incorporating domain specific information into the ITV.

In generating the MSG from the model, we put labels on the vertices and edges. We use these valuesin our ITV to give even finer granularity in our assessment. However, since there are varying numbers ofvertices and edges in the graphs, the labels can not be used directly. The ACIS Solid Modeler from SpatialTechnologies is the modeling system used in our experiments. ACIS has 13 different surface types, and 8different curve types. We modify the definition of the ITV to include 21 additional values. In effect, wecreate a histogram of the number of times particular surface and edge types occur in the model. Thus, theITV is a point in 29 dimensions and when combined with a set of these points, will enable the clustering ofthe points in this metric space. Table 1 lists the graph invariants and type histogram used in generating theITV for the torpedo motor illustrated in Figure 4. The ITV that results from these values is simply the resultafter concatenating the numbers into a single vector:

��

Graph Invariants Surface Type Counts Edge Type CountsAttribute Value Type # Count Type # CountVertex Count 403 1 231 1 464Edge Count 939 2 0 2 246Degree Max 1 3 0 3 0Degree Min 46 4 0 4 0Degree Mode 2 5 0 5 0Degree Median 4.00 6 0 6 0Degree Std. Deviation 4.15 7 117 7 0Graph Diameter 13 8 0 8 229

9 010 1011 012 013 45

Table 1: Properties in the Invariant Topology Vector for the torpedo motor in figure 4

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3.5 Clustering Method

Since the goal of this paper is simply to show that clustering based on invariants is a useful means to anend, simple clustering methods have been chosen to illustrate feasibility. Run-time and high cluster qualityare not issues at this point, the primary interest being whether or not the clustering provides suitable resultsfor further research. The clustering method chosen is a simple version of k-means clustering introduced byMacQueen [?].

The algorithm seeks to produce a clustering, � , of � clusters such that an object in a cluster �� ismore similar to the other objects withing the cluster than it is to objects in other clusters.

Representative Vector The representative vector of a cluster, ��, is defined to be the point that residesat the middle of all the points in ��, or the mean of each of the points in the cluster. More formally, if�� is a cluster with � � �� vectors where a vector is �, then the representative vector,��, of �� is:

��

��

�

Square Error The square error, or within cluster variation, is a measure of how close the points are to therepresentative vector of the cluster. The square error is the sum of the squared euclidean distances betweeneach point in �� and its representative vector. The mathematical definition, where � � � � � � �:

��

��

� � � ��

Using the square error of a cluster, we can define a measure of the overall quality for a particularclustering, or the total square error.

Total Square Error The total square error of a clustering, � , is defined to be the sum of the square errorsfor each cluster, �� in � . In mathematical terms:

��

��

��

Given this formula, the goal of the algorithm presented is to minimize the total square error for � . Since�-clustering requires a distance function in order to group the objects, we define the distance function weuse to be the euclidean distance given by the formula:

��!� � ��!� �� !� �

Where ! and are ITVs representing models in the metric space, we call this distance an �� "��.

k-clustering algorithm The �-clustering algorithm is based on the algorithm presented by MacQueen [?].The clusters are seeded with an initial set of ITVs, next the rest of the ITVs are placed into clusters accord-ing to the euclidean distance function, finally the clustering is improved by selecting outlying points andattempting to recluster them. The algorithm is presented below in greater detail.

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1. � ITVs are generated for � MSGs.

2. � clusters are created and seeded with � ITVs.

3. Select an unclustered ITV, �.

4. Find cluster, ��, whose representative object is closest to , and insert into ��.

5. Recalculate the representative vector, ��, for ��.

6. Repeat steps 3-5 until no more uncluster ITVs remain.

7. Select two clusters, �� and �� with the largest Square Error.

8. Select two ITVs, � from �� and � from ��, furthest from the representative vector.

9. Swap � and � iff the swap will reduce the total square error of the clustering.

10. Repeat steps 6-8 for � iterations.

4 Experimental Results

Initially, we wished to see what kind of distances we could get by simply computing the distance for manydifferent pairs of models. The result of which is illustrated in Figure 6 is a matrix of the distances obtainedfrom the euclidean distances between the ITVs for a selection of the models in the repository. We include ithere to serve as an illustration of the scope of the metric distance.

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Figure 6: Distance matrices for ITV-based distance measures for selected models from the National DesignRepository.

We ran the clustering algorithm for � � �� and took various measurements dealing with thequality of the clustering. Table 2 lists the size of the clusterings alongside relevant statistical data obtained.Specifically, the things we were looking for were the size of the total square error and the standard deviation

12

k Min Size Max Size Standard Deviation Time (s) ��

1000 1 6524 351.33 36.08 5.89e72000 1 1729 52.29 79.73 1.51e73000 1 1696 38.17 126.29 1.04e74000 1 1648 31.44 175.61 4.01e65000 1 1591 26.91 220.52 2.74e66000 1 1534 23.51 268.35 2.36e67000 1 1486 20.99 303.04 1.74e68000 1 1438 18.93 336.41 1.59e69000 1 1384 17.20 375.55 1.38e610000 1 1330 15.80 403.04 1.30e611000 1 1273 14.51 427.77 1.24e612000 1 1222 13.38 449.15 1.14e613000 1 1174 12.38 468.06 9.52e514000 1 1117 11.37 484.07 8.23e515000 1 1081 10.63 501.99 7.96e516000 1 1042 9.98 512.19 7.73e517000 1 973 9.13 519.05 5.10e518000 1 940 8.54 527.31 4.69e519000 1 895 7.96 530.91 4.59e520000 1 868 7.53 532.86 4.51e5

Table 2: Results on running clustering on models in the repository for various k.

from the median cluster size. We are interested in the total square error, a graph of which is shown inFigure 7(a), since this measurement shows us how good the clustering is and can be used to improve thequality of the clustering. The standard deviation, shown in figure 7(b) of the cluster size measures theuniformity of the size of the clusters. This interests us because if our clustering is good, we should be ableto look at uniformly sized clusters. This is especially important if a clustering technique is to be used as aprecursor to performing a more detailed and refined similarity comparison in response to a query.

While quality of the clustering is important, our main interest lies in the clusters themselves. Sinceobjective similarity tests for solid models are hard to define for this type of application, we used a moresubjective testing methodology. We chose various values of � and selected random clusters from which wepulled random models to compare visually. Some of the results are shown in figure 8.

One model we focused particularly on is the Torpedo Motor shown in Figure 4. This model is complexand unique enough to make finding a similar model a daunting task to do manually. We were interestedin what models might be clustered with it and how closely they looked to eachother visually. We chose� � �� since for that number of clusters on a relatively small dataset of 40,000 models, the models willtend to find their own clusters. As can be seen from Figure 8(c), the model the Torpedo Motor was eventuallyclustered with is a model of a Compressor and is not too different topologically. In this particular clustering,this cluster had only two parts. The other parts shown in Figure 8 are also very similar to eachother, but arevery simple compared to the two other models.

Visualizing the clustering is a non-trivial task, we decided to represent the clusters as a graph; Fig-

13

(a) Total Square Error. (b) Standard Deviation.

Figure 7: Plots of measures taken from several clustering runs.

ure 9 shows an example of the representation and continues the running example with the Torpedo Motorclustering with the Compressor. The cluster in which the Torpedo Motor appears with the Compressor ishighlighted in Figure 9(c) in red. Each cluster is represented by a connected component in the graph, wherea connected node represents a model in that cluster. The graph does not show the clusters’ relative positionsin the metric space, but rather the graph does help illustrate the relative distribution of the models in theclustering.

5 Conclusions

This paper presented out techniques for clustering solid models to be use in a modern relation database man-agement system. Our contributions are the development of a technique for grouping similar solid modelstogether. Our Model Signature Graph approach can be an effective formalism for topological similarity as-sessment of solid models and enable clustering for data mining of large Design Repositories. Our empiricalresults show that our distance measurement technique, Invariant Topology Vectors, can be used to createsemantically meaningful metric spaces in which solid models can be clustered. We believe this work willbegin to bridge the solid modeling and database communities, enabling new paradigms for interrogation ofsolid models.

Future Work. Currently, we are considering plain solid models. In future, we believe that additionaldomain knowledge can be used to refine our techniques. Information about engineering tolerances, surfacefinishes, constraints and parametrics, etc. all can be used to augment the basic techniques presented here.

Information about the feature locations, dimensions, and orientations have to be exploited fully. Byleveraging some earlier work [?], we hope to incorporate additional feature attribute information into ourdata structures for clustering and eventual comparison and indexing of the solid models in relational databases.

While there is no canonical set of CAD features, numerous feature recognition algorithms have beencreated and systems deployed for indexing models. Most often, current feature recognizers for solid models

14

(a) Two members ofcluster 1000-cluster�-clustering on theDesign Repository.

(b) Two members of the same clus-ter, after performing a 3000-cluster�-clustering on the Design Reposi-tory.

(c) Members of the cluster containing the Torpedo Mo-tor model, after performing a 20000-cluster �-clusteringon the Design Repository.

Figure 8: Examples of figures clustered together.

translate the BRep information into features that are sematically relevant to a particular engineering domain:machining, casting, injection molding, finite element analysis, etc. Our approach can be expanded to includefeature data from an arbitrary set of recognizers—alowing us to store this information in the database anduse it to refine our indexing and clustering methods.

As we noted earlier, techniques from model-based vision and 2D image retrieval are not directly suitablefor use with 3D models, however they may prove useful if combined with the approach we presented in thispaper. For example, gross shape properties or geometric moments may prove to be valuable discriminatingcriteria when examining large datasets of solid models.

With respect to further development of the �� "�� metric, we believe that the attribute lists thatare used in the ITVs may be further refined to eliminate interdependence of attributes, identify discrimi-nating attributes, and allow for more refined clustering. Other graph invariants may also be developed orexploited. Also very important will be the development of a weighting of ITV attributes to optimize similar-ity calculations over particular collections of models, and to minimize the effects of attributes which containlittle information.

Furthermore, we believe that our approach is applicable to other 3D media domains: solid free-form(SFF) fabrication techniques often use Stereolithography (STL) format files; VRML is a common modelingformat for web data; video games, such as Doom and Quake, employ discrete 3D world models. In eachof these cases, there are geometry, topology, shape and sematics which we believe can be used to createdatabase access methods that can store these file formats in a manner to enable meaningful queries.

Finally, we plan to apply our similarity metrics to databases of solid models collected from the NationalDesign Repository [?]. We believe that the metrics will prove to be extremely useful in performing databaseindexing and clustering of the models for knowledge-discovery and data mining (KDD).

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(a) View of the whole Cluster Graph.

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(b) Graph Representation of a smallsubset of the clusters.

Figure 9: Graph Representations of clustering for � � ��.

Acknowledgements. This work was supported in part by National Science Foundation (NSF) Knowledgeand Distributed Intelligence in the Information Age (KDI) Initiative Grant CISE/IIS-9873005; CAREERAward CISE/IIS-9733545 and Grant ENG/DMI-9713718.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of theauthor(s) and do not necessarily reflect the views of the National Science Foundation or the other supportinggovernment and corporate organizations.

References

[1] National design repository. http://www.designrepository.org., 2000.

[2] Rakesh Agrawal, Johannes Gehrke, Dimitrios Gunopulos, and Prabhakar Raghavan. Automatic sub-space clustering of high dimensional data for data mining applications. In Proceedings of 1998ACM-SIGMOD International Conference on Management of Data. ACM, June 1998. file-name: sig-mod98 clique.pdf.

[3] Horst Bunke and Kim Shearer. On a relation between graph edit distance and maximum commonsubgraph. Pattern Recognition Letters, pages 689–694, 1997.

[4] Alexei Elinson, Dana S. Nau, and William C. Regli. Feature-based similarity assessment of solidmodels. In Christoph Hoffman and Wim Bronsvoort, editors, Fourth Symposium on Solid Modelingand Applications, pages 297–310, New York, NY, USA, May 14-16 1997. ACM, ACM Press. Atlanta,GA.

[5] M. Ester, H.P. Kriegel, J. Sander, and X. Xu. A density-based algorithm for discovering clusters in largespatial databases with noise. In Proceedings 2nd International Conference on Knowledge Discoveryand Data Mining (KDD’96), pages 226–231, 1996.

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[6] Daniel Fasulo. An analysis of recent work on clustering algorithms. Web??, April 1999.http://citeseer.nj.nec.com/fasulo99analysi.html.

[7] Teofilo F. Gonzalez. Clustering to minimize the maximum intercluster distance. Theoretical ComputerScience, 38:293–306, 1985.

[8] Christopher M. Hoffmann. Geometric and Solid Modeling: An Introduction. Morgan KaufmannPublishers, Inc., California, USA, 1989.

[9] Anil K. Jain and Richard C. Dubes. Algorithms for Clustering Data. Prentice Hall, Englewood Cliffs,New Jersey 07632, 1988.

[10] S. Joshi and T. C. Chang. Graph-based heuristics for recognition of machined features from a 3D solidmodel. Computer-Aided Design, 20(2):58–66, March 1988.

[11] Leonard Kaufman and Peter J. Rousseeuw. Finding Groups in Data: An Introduction to ClusterAnalysis. John Wiley and Sons, Inc., 1990.

[12] Ewa Kubicka, Grzegorz Kubicki, and Ignatios Vakalis. Using graph distance in object recognition. InProceedings of the 1990 ACM annual conference on Cooperation, pages 43–48, February 1990.

[13] J. MacQueen. Some methods for classification and analysis of multivariate observations. In Proceed-ings of 5th Berkeley Symposium, pages 281–297, 1967.

[14] Martti Mantyla. An Introduction to Solid Modeling. Computer Science Press, College Park, MD, 1988.

[15] Aristides A. G. Requicha. Representation for rigid solids: Theory, methods, and systems. ComputingSurveys, 12(4):437–464, December 1980.

[16] H. Samet. The quadtree and related hierarchical data structures. ACM Computing Surveys, 16(3):287–260, 1984.

[17] Spatial Technology Inc., Three-Space Ltd., and Applied Geometry Corp., 2425 55th Street, BuildingA, Boulder, CO 80301. ACIS c� Geometric Modeler Application Guide, v1.6 edition, November 1994.

[18] Tien-Lung Sun, Chuan-Jun Su, Richard J. Mayer, and Richard A. Wysk. Shape similarity assessmentof mechanical parts based on solid models. In Rajit Gadh, editor, ASME Design for ManufacturingConference, Symposium on Computer Integrated Concurrent Design, pages 953–962. ASME, Boston,MA. September 17-21. 1995.

[19] Kevin Weiler. Edge-based data structures for solid modeling in curved-surface environments. IEEEComputer Graphics and Applications, 5(1):21–40, January 1985.

[20] Tony C. Woo. A combinatorial analysis of boundary data structure schemata. IEEE Computer Graphicsand Applications, pages 19–27, March 1985.

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Clustering Techniques for Databases of CAD Models

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