Chinese Journal of Computers   Full Text
Title	Metamorphosis Based on the Level-Set Methods
Authors	PAN Qing1) XU Guo-Liang2)
Address	1)(College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081) 2)(Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190)
Year	2009
Issue	No.2(213—220)
Abstract &   Background	Abstract This paper presents a new approach for metamorphosis. First, it introduces a first-order energy functional, then minimizes it to derive a second-order geometric partial differential equation (GPDE) in the level-set formulation. The surface deformation process is transferred into an evolution process of an implicit model in a 3-dimensional volume. The sequence of deformed surfaces generated from the model evolution is represented as a level-set function on the 3-dimensional densely sampled volume. The experiment result shows that the big shape change and the change of topology can be desirably achieved. The C2 smooth B-spline function is used as the level-set function, which improves the quality of surface. At the same time, the algorithm has some other advantages, such as the simplicity of user input, the flexibility of mathematical model, and the robustness of numerical algorithm. Keywords metamorphosis; level-set method; distance function; geometric partial differential equation Background In simplicity, morphing makes a smooth and continuous transition from the source object to the target object through producing a series of intermediate objects between the two objects. Morphing is a special technique in computer art, motion pictures and computer animation, etc., where it brings some magic and fantastic effects. With the rapid development of computer, morphing creates more and more natural and realistic vision effect. There are many methods to realize the morphing effect. We represent an algorithm based on the geometric partial differential equations in the level-set formation, which has its own advantages. At the same time, our algorithm possesses several attractive features, such as the simplicity of user input, the flexibility of mathematical model, and the robustness of numerical algorithm. This research is supported by the National Natural Science Foundation of China (No.60773165 and No.10701071) and the National Key Basic Research Development Plan of China (No.2004CB318000). The group already achieved some research work in the area of using the geometric partial differential equations to solve several surface modeling problems, which was published in the international journal, such as Computer-Aided Geometric Design, Computer Aided Design. As for the geometric partial differential equations method, there are still a lot of things warrant studying not only in theory, but also in application. Currently, the authors are conducting intensive research in this area to get more and better results.