A 3D Object Retrieval System Based on Multi-Resolution ... - CMLab

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 E-mail: {dynamic, ming}@cmlab.csie.ntu.edu.tw Abstract

models retrieval using the distribution of moment,

This paper proposes a 3D model retrieval

normal, cord, color, material and texture. Zhang and

system which extended the work of Hilaga in 2001.

Chen [2] propose a 3D model retrieval system using

We apply the pre-processing stage to 3D models in

volume-surface ratio, aspect ratio, moment invariants

practical use. The demo system with over 450 3D

and Fourier transformation coefficients. Elad et al. [6]

models from the Net is on the web page:

apply relevant feedback to 3D object retrieval, which

http://3dsite.dhs.org/~dynamic, and can also be used

uses moments as features. Osada et al. [4] propose and

in PocketPC with wireless LAN card. There are 445

analyze a method for computing shape signatures for

various models in our database.

arbitrary 3D polygonal models. Hilaga et al. [1] propose a technique in which similarity between

1.

Introduction In this decade, multimedia data, which usually

polyhedral models is quickly, accurately, and automatically calculated by comparing the skeletal and

doesn’t need any text to represent, grow rapidly. Content-based retrieval for multimedia data becomes

topological structure. The structure decomposes 3D model to a one-dimensional graph structure. The graph

more and more important. In order to communicate with people’s information, the MPEG group aims to

is invariant to translation, rotation and scaling, robust against connectivity changes, and resistant against

create MPEG-7 international standard, also known as “Multimedia Content Description Interface”, for the

noise, certain changes due to deformation. Our system is based on the research of Hilaga,

description of the multimedia data, including image, video, audio, 2D shape and 3D object [8]. 3D object

which is one of the best ideas among the previous works. Fig. 1 shows the flow chart of our system

retrieval research is active now, because the technique of 3D modeling and digitizing tools is on a

when querying by a 3D object. The last two stages are the same with Hilaga, please refer to [1]. Chapter

progressive improvement. In the last few years, several articles have been devoted to the study of 3D object retrieval. Cyr and

2 details the pre-processing stage in our system.

2.

Pre-Processing of 3D Object

Kimia [5] proposed an aspect-graph approach. They

This stage is designed for accurately and fast

generate a set of 2D silhouette for each 3D object, and

getting the search key. There are four steps in this

then measure the similarity between two views by 2D

stage: merging vertices, merging parts, re-sampling

shape similarity metrics. Kolonias et al. [3] proposed

and adding short-cut edges. The first two steps solve

aspect ratio, a binary 3D shape mask and set of paths

practical problems when many models are used. The

outlining the shape of the 3D object for matching.

last two steps are modified from the approach of

Paquet and Rioux [7] presented an approach for 3D

Hilaga [1].

averagely split into many segments. Re-sample by

Input a 3D model

connecting the new vertices from the two edges. In Merge vertices Merge different parts Re-sample 3D model

Stage 1: Pre-processing is used for accurately and fast calculating the search key (Chapter 2)

Add short-cut edges Geodesic distance Create MRG Compare models Show results

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

Stage 2: Calculate the search key MRG for the 3D model Stage 3: Compare the MRG to all models in the database

Fig. 1 The flow chart of our system. The same vertices may be shared in duplicate at

"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. 2 (a). There are two cases of triangles. In the first case, if a triangle have two same vertices with other triangle. Take Fig. 2 (b) as an example, triangle 1 and 2 share ace, which

adjacent triangles for 3D models. The first step is to

vertex c and d, and then get the angle

merge these vertices. The way we used is to sort the

is sum of

vertices according to the coordinate, and then check

180 degree, add a short-cut edge between vertex a

the adjacent vertices. The time complexity is O(nlgn),

and e. Alternative can start from the angle

since we use the heapsort algorithm.

The angle is less than 180 degree means that edge ae

acd and

ecd. If the angle is less than

ade.

3D models are saved as different parts in many

will inside the polygon aced. The distance of

cases for easy editing and animation. The approach

short-cut edge ae can be calculated by the following

we used is to construct the search key by the whole

formula. Given the length of two edges (x, y) and

model rather than some separated parts. Therefore,

their angle (w), then the length of third edge is:

we add edges to connect different parts. The

x 2 + y 2 − 2 ⋅ x ⋅ y ⋅ cos( w) .

approach is similar to the first step. The coordinate of

to connect the same quantized value for the separated parts. The time complexity is also O(nlgn).

b

a

each vertex is quantized first, and an edge is created

3 2

c

1

d

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

e (a) (b) Fig. 2 The short-cut edges make the distance of two vertices in adjacent triangles to be straightforward through the 3D surface.

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

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 2 adjacent to them. Then get the angle

edb, which is

sum of

edc,

cda and

adb. As similar to case

[1]

M. Hilaga, Y. Shinagawa, T. Kohmura and T. L.

one, if the angle is less than 180 degree, add a

Kunii, “Topology Matching for Fully Automatic

short-cut edge between vertex b and e.

Similarity Estimation of 3D Shapes”, ACM SIGGRAPH, pp. 203-212, Aug. 2001.

3.

Experimental Results

[2]

The system is implemented in C language, and

C. Zhang and T. Chen, “Efficient Feature Extraction for 2D/3D Objects in Mesh

is compiled using gcc in Linux. The system is on the Representation”, IEEE International World Wide Web by using a simple php code. The

Conference on Image Processing, Oct. 2001.

web page is http://3dsite.dhs.org/~dynamic. The user [3] can upload a 3D model and the system will calculate

I. Kolonias, D. Tzovaras, S. Malassiotis and M. G. Strintzis, “Fast Content-Based Search of

the MRG for the model, and then compare it with all VRML Models Based on Shape Descriptors”, models in the database. Alternatively, the user can

IEEE International Conference on Image

select one model in the database. The system Processing, Oct. 2001. compares it with all other models and the results

[4]

R. Osada, T. Funkhouser, B. Chazelle and D.

show thumb pictures of top similar models. There are Dobkin “Matching 3D Models with Shape 445 various models, downloaded from [10] and [11],

Distributions”, Workshop on Shape-Based

in the database. The average time of comparing two Retrieval and Analysis of 3D Models, Oct. 2001. models is about 0.08 second in a PC with Pentium III

[5]

C. M. Cyr and B. B. Kimia, “3D Object

800MHz CPU. Fig. 3 shows results of 3D object Recognition Using Shape Similiarity-Based retrieval in our system. In addition, our retrieval

Aspect Graph”, International Conference on

system can be used in PocketPC with wireless LAN Computer Vision, 2001. card, as shown in Fig. 4.

4.

[6]

Retrieval of VRML Objects – A Iterative and

Discussion and Future Works While the system can work well in many cases,

there exist considerable improvements as to the following problems:

Interactive Approach”, 2001. [7]

sub-graph matching, partial

E. Paquet and M. Rioux, “Content-Based Access of VRML Libraries”, Lecture Notes in

matching, MRG doesn't always represent the skeletal structure, different density of vertices, some vertices

M. Elad, A. Tal and S. Ar, “Content Based

Computer Sciences, Vol.1464, pp. 20-32, 1998. [8]

S. Jeannin, L. Cieplinski, J. R. Ohm and M.

inside the 3D object. To overcome the problems, we

Kim, MPEG-7 Visual part of eXperimentation

plan to use the hierarchical medial axis to match the 3D

Model Version 7.0, ISO/IECJTC1/SC29/WG11

models. The 3D medial axis algorithm based on radial

/N3521, July 2000.

basis function (RBF) is proposed in our group [9].

[9]

F.C. Wu, W.C. Ma and M. Ouhyoung, “Skeleton Extraction of 3D Objects with

5.

Conclusion

Radial Basis Function”, Technical Report

A 3D object retrieval system, which improves NTUCSIE 02-01, Dept. of CSIE, National the practical use of Hilaga’s research [1], is proposed.

Taiwan University, Taipei, Taiwan, Apr. 2002.

The pre-processing stage is applied for accurately [10] http://www.3dcafe.com and fast getting the search key.

Reference

[11] http://www.3dm-mc.com

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

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Fig. 4 Our retrieval system can be used in PocketPC with wireless LAN card.