The Research For 3D Model Geometry Shape Similarity Matching

With the recent increase in the number of three-dimensional (3D) geometric models, 3D model retrieval system is widely used in people's live, CAD/CAM, and computer animation. The techniques and tools for shape representation and matching has been developed in the context of MPEG-7 standard. Although text-based search engines are widely used today for multimedia data, such as 3D models, however, they usually lack in meaningful description for 3D models. Development of the technology for effective content-based search and retrieval of 3D models has become an important issue. It is thus necessary to have such a system that is based on the features intrinsic to the 3D models, most important of which is the 3D shape. Compared to text-based search system, the content-based search and retrieval of 3D models has more advantage for its objectivity, content-based retrieval, and fast retrieval.The method for geometrical shape similarity matching among 3D models is one of main research problems of 3D model retrieval system. So far many methods have been presented, and can be broadly classified into three categories: outline-based matching, visual-based matching, and topology-based matching. The outline-based approaches utilize the distribution of vertices or polygons to judge the similarity between 3D models. The topology-based approaches utilize the topological structures of 3D models to measure the similarity between them. The visual-based approaches get similarity among 3D models via matching the similarity among their visual projections. For a good 3D models retrieval system, the geometrical similarity matching method should be suited to calculate the geometry characteristic of all kinds 3D models (robust calculation), and be robust to rotation, noise, model degeneracy etc.One of the challenges in 3D shape matching arises from the fact that in many applications, the modes should be considered to be the same even if they differ by a rotation. In the related works, many researchers normalize the coordinate rotation via K-L transform before computing the descriptor of 3D models, and K-L transform is named as principle cell analysis (PCA) too. In this paper, we utilize the principle of K-L transform to testify that the normalization of coordinate rotation via K-L transform is not robust, and is sensitive to the noise, model degeneracy. The experimental results show the validity of our deduction. If two models have different anisotropic scales, it is difficult to establish correct correspondences between them. Thus, matching methods that depend on correspondences for evaluating similarity will be inaccurate in this case. In contrast, when the models are transformed so that each is isotropic, the correspondences are more accurate and the measure of shape similarity is more discriminating. In this way, the anisotropic transform can be successfullyapplied to 3D model retrieval system. In this paper, we detailed analyze the anisotropic transform and give an improved anisotropic transform.Visual-based shape matching of 3D models is based on such idea that comes from the following statement, "If two 3D models are similar, they also look similar from all viewing angles." Some visual-based shape matching methods have been proposed. In this paper, we present a novel visual-based shape similarity for 3D models; we first calculate the depth perspective projection of 3D models from viewpoints, and then extract the topology characteristic and light distribution characteristic of the perspective projection, finally we obtain shape similarity among 3D models via matching the similarity of the characteristics of perspective projection. In our algorithm, we express the topology of projection with Reeb graph, and adopt multi-scale generic Fourier descriptor to express the light distribution of projection. We choose the best view angle and efficient distribution fashion via the retrieval experiments. Experimental results show that our visual-base search key is robust to rotation, noise and changes caused by mesh simplification or subdivision, and it provides better performance (in sense of precision-recall evaluation diagram) than some other competing approaches.The outline-based shape approach uses the distribution of vertices or polygons to judge the similarity between two 3D models. A novel outline- based shape similarity matching algorithm is presented. We construct a new Feature Binary Tree of 3D model based on spherical harmonic descriptor, and consider it as a search key for 3D shape data sets. Experimental results show that our outline-base search key is robust to rotation, noise and changes caused by mesh simplification or subdivision, and it provides better performance (in sense of precision-recall evaluation diagram) than some other competing approaches.In this paper, we present a content-based image similarity matching approach based on spherical harmonic descriptor. Experimental results show that this descriptor provides better performance (in sense of precision-recall evaluation diagram) than some other descriptors, and it is invariant to rotation and invariant to roll back.