A 3D Object Retrieval System Based on Multi-Resolution Reeb Graph

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1 A 3D Object Retrieval System Based on Multi-Resolution Reeb Graph Ding-Yun Chen and Ming Ouhyoung Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan {dynamic, Abstract This paper proposes a 3D model retrieval system which extended the work of Hilaga in 001. We apply the pre-processing stage to 3D models in practical use. The demo system with over 450 3D models from the Net is on the web page: and can also be used in PocketPC with wireless LAN card. There are 445 various models in our database. 1. Introduction In this decade, multimedia data, which usually doesn t need any text to represent, grow rapidly. Content-based retrieval for multimedia data becomes more and more important. In order to communicate with people s information, the MPEG group aims to create MPEG-7 international standard, also known as Multimedia Content Description Interface, for the description of the multimedia data, including image, video, audio, D shape and 3D object [8]. 3D object retrieval research is active now, because the technique of 3D modeling and digitizing tools is on a progressive improvement. In the last few years, several articles have been devoted to the study of 3D object retrieval. Cyr and Kimia [5] proposed an aspect-graph approach. They generate a set of D silhouette for each 3D object, and then measure the similarity between two views by D shape similarity metrics. Kolonias et al. [3] proposed aspect ratio, a binary 3D shape mask and set of paths outlining the shape of the 3D object for matching. Paquet and Rioux [7] presented an approach for 3D models retrieval using the distribution of moment, normal, cord, color, material and texture. Zhang and Chen [] propose a 3D model retrieval system using volume-surface ratio, aspect ratio, moment invariants and Fourier transformation coefficients. Elad et al. [6] apply relevant feedback to 3D object retrieval, which uses moments as features. Osada et al. [4] propose and analyze a method for computing shape signatures for arbitrary 3D polygonal models. Hilaga et al. [1] propose a technique in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing the skeletal and topological structure. The structure decomposes 3D model to a one-dimensional graph structure. The graph is invariant to translation, rotation and scaling, robust against connectivity changes, and resistant against noise, certain changes due to deformation. Our system is based on the research of Hilaga, which is one of the best ideas among the previous works. Fig. 1 shows the flow chart of our system when querying by a 3D object. The last two stages are the same with Hilaga, please refer to [1]. Chapter details the pre-processing stage in our system.. Pre-Processing of 3D Object This stage is designed for accurately and fast getting the search key. There are four steps in this stage: merging vertices, merging parts, re-sampling and adding short-cut edges. The first two steps solve practical problems when many models are used. The last two steps are modified from the approach of Hilaga [1].

2 Input a 3D model Merge vertices Merge different parts Re-sample 3D model Add short-cut edges Geodesic distance Create MRG Compare models Show results Fig. 1 The flow chart of our system. The same vertices may be shared in duplicate at adjacent triangles for 3D models. The first step is to merge these vertices. The way we used is to sort the vertices according to the coordinate, and then check the adjacent vertices. The time complexity is O(nlgn), since we use the heapsort algorithm. Stage 1: Pre-processing is used for accurately and fast calculating the search key (Chapter ) Stage : Calculate the search key MRG for the 3D model Stage 3: Compare the MRG to all models in the database 3D models are saved as different parts in many cases for easy editing and animation. The approach we used is to construct the search key by the whole model rather than some separated parts. Therefore, we add edges to connect different parts. The approach is similar to the first step. The coordinate of each vertex is quantized first, and an edge is created to connect the same quantized value for the separated parts. The time complexity is also O(nlgn). For more accurate calculation of the search key, each triangle has to be re-sampled. Each triangle splits into smaller triangles until all edges are less than a threshold. To speedup re-sampling time in all cases, each triangle is split at once. There are three cases for all triangles. In the first case, there is only one edge in triangle larger than threshold, just split into two triangles. In the second case, if two edges in a triangle are larger than threshold, the two edges are averagely split into many segments. Re-sample by connecting the new vertices from the two edges. In the third case, if all three edges in triangle are larger than threshold, select the two largest edges and split into many triangles first, then each triangle recursively is split using the second case. The fourth step is adding some edges called "short-cut edges" to models. The purpose of short-cut edges is used for accurately calculating the search key. The short-cut edges make the distance of two vertices in adjacent triangles to be straightforward through the 3D surface, as shown in Fig. (a). There are two cases of triangles. In the first case, if a triangle have two same vertices with other triangle. Take Fig. (b) as an example, triangle 1 and share vertex c and d, and then get the angle ace, which is sum of acd and ecd. If the angle is less than 180 degree, add a short-cut edge between vertex a and e. Alternative can start from the angle ade. The angle is less than 180 degree means that edge ae will inside the polygon aced. The distance of short-cut edge ae can be calculated by the following formula. Given the length of two edges (x, y) and their angle (w), then the length of third edge is: x + y x y cos( w). e (a) (b) Fig. The short-cut edges make the distance of two vertices in adjacent triangles to be straightforward through the 3D surface. In the second case, if some triangle have only one the same vertex with this triangle, and if there is a triangle adjacent to the two triangles. For example, triangle 1 and 3 share vertex d, and triangle adjacent to them. Then get the angle c 1 a 3 d b edb, which is

3 sum of edc, cda and adb. As similar to case one, if the angle is less than 180 degree, add a short-cut edge between vertex b and e. 3. Experimental Results The system is implemented in C language, and is compiled using gcc in Linux. The system is on the World Wide Web by using a simple php code. The web page is The user can upload a 3D model and the system will calculate the MRG for the model, and then compare it with all models in the database. Alternatively, the user can select one model in the database. The system compares it with all other models and the results show thumb pictures of top similar models. There are 445 various models, downloaded from [10] and [11], in the database. The average time of comparing two models is about 0.08 second in a PC with Pentium III 800MHz CPU. Fig. 3 shows results of 3D object retrieval in our system. In addition, our retrieval system can be used in PocketPC with wireless LAN card, as shown in Fig Discussion and Future Works While the system can work well in many cases, there exist considerable improvements as to the following problems: sub-graph matching, partial matching, MRG doesn't always represent the skeletal structure, different density of vertices, some vertices inside the 3D object. To overcome the problems, we plan to use the hierarchical medial axis to match the 3D models. The 3D medial axis algorithm based on radial basis function (RBF) is proposed in our group [9]. 5. Conclusion A 3D object retrieval system, which improves the practical use of Hilaga s research [1], is proposed. The pre-processing stage is applied for accurately and fast getting the search key. Reference [1] M. Hilaga, Y. Shinagawa, T. Kohmura and T. L. Kunii, Topology Matching for Fully Automatic Similarity Estimation of 3D Shapes, ACM SIGGRAPH, pp. 03-1, Aug [] C. Zhang and T. Chen, Efficient Feature Extraction for D/3D Objects in Mesh Representation, IEEE International Conference on Image Processing, Oct [3] I. Kolonias, D. Tzovaras, S. Malassiotis and M. G. Strintzis, Fast Content-Based Search of VRML Models Based on Shape Descriptors, IEEE International Conference on Image Processing, Oct [4] R. Osada, T. Funkhouser, B. Chazelle and D. Dobkin Matching 3D Models with Shape Distributions, Workshop on Shape-Based Retrieval and Analysis of 3D Models, Oct [5] C. M. Cyr and B. B. Kimia, 3D Object Recognition Using Shape Similiarity-Based Aspect Graph, International Conference on Computer Vision, 001. [6] M. Elad, A. Tal and S. Ar, Content Based Retrieval of VRML Objects A Iterative and Interactive Approach, 001. [7] E. Paquet and M. Rioux, Content-Based Access of VRML Libraries, Lecture Notes in Computer Sciences, Vol.1464, pp. 0-3, [8] S. Jeannin, L. Cieplinski, J. R. Ohm and M. Kim, MPEG-7 Visual part of experimentation Model Version 7.0, ISO/IECJTC1/SC9/WG11 /N351, July 000. [9] F.C. Wu, W.C. Ma and M. Ouhyoung, Skeleton Extraction of 3D Objects with Radial Basis Function, Technical Report NTUCSIE 0-01, Dept. of CSIE, National Taiwan University, Taipei, Taiwan, Apr. 00. [10] [11]

4 Fig. 3 Some results of 3D object retrieval in our system.

5 (continue) Fig. 4 Our retrieval system can be used in PocketPC with wireless LAN card.

A 3D Model Alignment and Retrieval System

A 3D Model Alignment and Retrieval System Ding-Yun Chen and Ming Ouhyoung Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan dynamic@cmlab.csie.ntu.edu.tw,