A 3D SHAPE RETRIEVAL METHOD BASED ON CONTINUOUS SPHERICAL WAVELET TRANSFORM Zhenbao LIU, Jun MITANI, Yukio FUKUI, Seiichi NISHIHARA Department of Computer Science, University of Tsukuba, Japan Email: {liuzhenbao@npal. | mitani@ | fukui@ | nishihara@}cs.tsukuba.ac.jp ABSTRACT Recently, many efforts have concentrated on finding efficient content based retrieval methods of 3D objects. In this paper, we proposed a new retrieval method. The method is constructed on a shape descriptor based on continuous spherical wavelet transform. Continuous 2D wavelet transform has extinct advantages in content based image retrieval. The continuous wavelet transform can be extended from two dimensions to more dimensions, for example, spherical space, with the same properties. As a natural extension, continuous spherical wavelet transform can realize a spherical analysis. Therefore, we map a shape into a unit sphere by spherical parameterization, followed by continuous spherical wavelet transform of the spherical function. This method is our contribution. The result of the transform can be as a new descriptor and be used to match the dissimilarity of two shapes. We have examined our method on a small database of general objects and it is confirmed to be efficient. KEY WORDS 3D object, content based retrieval, shape descriptor, continuous spherical wavelet transform 1. Introduction With the recent rapidly increasing of 3D data in many applications, such as computer games, computer aided design, VR environments, biology, e-business, etc., 3D shape data retrieval and reutilization of them becomes more important. Accordingly, there is an increasing need for computer algorithms to help people find their interesting 3D shape data and discover relationships between them. Recently, many efforts have concentrated on researching techniques for efficient content based retrieval of 3D objects [1]. The key of a content based retrieval is to develop a descriptor capturing the main feature of 3D objects, because 3D shapes can be discriminated by measuring and comparing their features. A descriptor is a d-dimensional vector of values, and as for all the 3D shapes, the dimension d is fixed. In the d-dimensional space, if two vectors are close, two shapes are considered to be similar. Because 3D model retrieval has some similar characters with image retrieval, many 3D model retrieval methods become an extension from image retrieval methods. Wavelet theory has greatly developed in computer graphics. Continuous 2D wavelet transform plays an important role in image analysis and retrieval [21, 23]. The continuous wavelet transform can be extended from two dimensions to more dimensions, for example, spherical space, with the same properties. As a natural extension, continuous spherical wavelet transform can realize a spherical analysis. In this paper we present a 3D content based retrieval method relying on a shape descriptor based on continuous spherical wavelet transform. The shape descriptor is computed as the following: 1. Pose estimation: Translate the centroid of all the models into the origin of the coordinate system and use the Principal Component Analysis (PCA) method to get the rotation invariant dissimilarity measures. 2. Spherical parameterization: A cluster of rays are cast from the centroid of the model, and intersect with surfaces of the model. A spherical function can be defined by the distances of the farthest intersections from the centroid of the model as a function of latitude and longitude. 3. Continuous Spherical Wavelet Transform: Perform the Continuous Spherical Wavelet Transform (CSWT) of the spherical function according to CSWT theory introduced by J-P Antoine[2]. To our knowledge, this theory has not been applied to the content based retrieval of 3D objects so far. 4. Descriptor: The result of the continuous spherical wavelet transform is used as a shape descriptor. The features of models are compared with the shape descriptors. We apply our method to a small database of general objects collected from free Princeton Shape Benchmark Database [3]. This method is confirmed to be efficient. The outline of the rest of the paper is as follows: in the next section we shortly review the previous work in 3D model retrieval and relevant spherical wavelet theory. In section 3 we present a general theoretical framework for the new shape descriptor based on continuous spherical wavelet transform. We put emphasis on the analysis of the continuous spherical wavelet transform. Section 4 shows the new shape descriptor and gives a computation method of the descriptor. In Section 5 we present our experimental results and conclude in Section 6. 553-034 21