Research on Shape Mapping of 3D Mesh Models based on Hidden Markov Random Field and EM Algorithm
📝 Abstract
How to establish the matching (or corresponding) between two different 3D shapes is a classical problem. This paper focused on the research on shape mapping of 3D mesh models, and proposed a shape mapping algorithm based on Hidden Markov Random Field and EM algorithm, as introducing a hidden state random variable associated with the adjacent blocks of shape matching when establishing HMRF. This algorithm provides a new theory and method to ensure the consistency of the edge data of adjacent blocks, and the experimental results show that the algorithm in this paper has a great improvement on the shape mapping of 3D mesh models.
💡 Analysis
How to establish the matching (or corresponding) between two different 3D shapes is a classical problem. This paper focused on the research on shape mapping of 3D mesh models, and proposed a shape mapping algorithm based on Hidden Markov Random Field and EM algorithm, as introducing a hidden state random variable associated with the adjacent blocks of shape matching when establishing HMRF. This algorithm provides a new theory and method to ensure the consistency of the edge data of adjacent blocks, and the experimental results show that the algorithm in this paper has a great improvement on the shape mapping of 3D mesh models.
📄 Content
This work is supported by the joint research fund for UCAS and CAS institute (Y55201TY00). Research on Shape Mapping of 3D Mesh Models based on Hidden Markov Random Field and EM Algorithm WANG Yong 1 WU Huai-yu 2 1 (University of Chinese Academy of Sciences, Beijing 100049, China) 2 (Institute of Automation, Chinese Academy of Sciences, Beijing, 100080, China) Abstract How to establish the matching (or corresponding) between two different 3D shapes is a classical problem. This paper focused on the research on shape mapping of 3D mesh models, and proposed a shape mapping algorithm based on Hidden Markov Random Field and EM algorithm, as introducing a hidden state random variable associated with the adjacent blocks of shape matching when establishing HMRF. This algorithm provides a new theory and method to ensure the consistency of the edge data of adjacent blocks, and the experimental results show that the algorithm in this paper has a great improvement on the shape mapping of 3D mesh models. Keywords Shape Mapping, 3D Mesh Model, Hidden Markov Random Field, EM Algorithm 1 Introduction Digital geometry processing of 3D mesh models has broad application prospects in the fields of industrial design, virtual reality, game entertainment, Internet, digital museum, urban planning and so on[1]. However the surface of 3D mesh models is usually bent arbitrarily, lack of continuous parameters, and has complex characterized details, as is quite different from the regular 2D image data with the uniform sampling, the data of 3D mesh models cannot be dealt with the classical orthogonal analysis tools directly. To meet the need of wide applications, researchers have proposed some processing algorithms to deal with 3D mesh models, such as surface reconstruction, mesh simplification, mesh smoothing, parametric, re-meshing, surface compression, mesh deformation and animation and so on. But these algorithms can only meet some specific requirements, the analysis and processing of 3D mesh models is still a public problem in the field of computer vision and computer graphics [2]. In intelligent analysis of 3D mesh data, how to “understand” the global and local 3D shapes is an important challenge for the analysis of 3D models, as is usually lacking in the most present methods. For example, in figure1, if the digital geometry processing framework can have global perspective and understand the shape globally, it can eliminate the interference and influence of shape analysis brought by rotation, translation, initial placement, bending deformation, different sampling rate, and different parameterization methods. (a1’/a2’, b1’/b2’) are the transformed models of (a1/a2, b1/b2) by the geometry processing framework of global perspective. It can be seen that the transformed models are much similar in their poses and shapes. So the difficulty of establishing the automatic matching between two different 3D shapes has been greatly reduced.
Figure 1 Matching between two different 3D shapes How to establish the matching (or corresponding) between two different 3D shapes is a classical problem and has always been a hot issue [3, 4]. As is the prerequisite and basis for a large number of applications. These applications include: matching the shape template to multiple 3D data sets [5], shape blending [6], statistical shape analysis (such as principal component analysis), transfer texture and surface properties, surface classification and recognition, video tracking, facial animation based on facial expression, and so on. The shape matching can be realized either globally or locally. The former is computing and mapping the surface as a whole, while the latter is dividing the whole surface into blocks equally first of all, and then establishing the mapping of each block, finally putting the results of each block together to get the complete matching (also called mapping, or cross parameterization). The typical global methods include the iterative closest point method (ICP) [7] and its variants (e.g., [8,9], as are well-known global matching methods). However, the ICP algorithm is strongly dependent on the good initial shape, and is usually not suitable for the matching when the shapes are quite different. Therefore, many methods are relying on the user to manually place the identification points to guide the matching. For example, the work of [5] and [10], as are based on the template matching technology, establishing the shape matching (such as the human body model) according to the user’s specified identification points . In addition to the direct global mapping, the global matching can also be indirectly established, which uses a temporary parameterized domain as a common domain [11,12]. For example, the shape of the disk topology can be mapped to a common plane, called the planar parameterization [11,13,14]. In addition, there is a method c
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