Research On 3d Mesh Segmentation Algorithms Using Markov Random Filed

Scientific and technological advances in the fields of digital image processing, computer graphics, computer storage technology, and internet during the last decade have contributed to the emergence of new multimedia, especially three-dimensional (3D) digital data. For processing the 3D digital data, researchers had proposed Digital Geometric Processsing, in which 3D mesh segmentation has become an active research hotpot, and is a key problem of mesh parameterization,mesh texture mapping, mesh geometry morph etc.A Markov random field, also known as a Markov network or an undirected graphical model, provides a convenient and consistent way of modeling context-dependent entities such as image pixels and correlated features, and has been widely used in the field of digital image processing.This thesis summarized the latest achievements and applications in the field of 3D mesh segmentation, gave the definition of 3D mesh segmentation, and proposed two 3D mesh segmentation algorithms using markov random filed and graph cuts.The first algorithm use hierarchical Gibbs random filed to model the values of Shape Diameter Function (SDF) of faces and the spatial dependency between faces in the mesh. The higher-level distribution models the spatial dependency between faces in the mesh by using Gibbs distribution; the lower-level distribution classfies the values of SDF through Gaussian Mixture Model (GMM), decibles the degrees of every value match different cluters. This algorithm can integrate both geometric information and topology information of 3D mesh, so can remove over-segments effectively and makes the boundary of segments more smooth.The second algorithm construct the Reeb graph of 3D mesh by calculating the protrusion of faces in the mesh. Based on the Reeb graph, the algorithm can extract the prominent faces of the mesh fast and effectively. Then we use Markov Random Field to model the ditance between faces in the mesh and prominent faces or center of the mesh and the spatial dependency between faces in the mesh, according to the minima rule. Finally, we slove the model using graph cuts. The experiment results show that this algorithm can obtain semantic mesh segments.