Title :
Meshless Harmonic Volumetric Mapping Using Fundamental Solution Methods
Author :
Li, Xin ; Guo, Xiaohu ; Wang, Hongyu ; He, Ying ; Gu, Xianfeng ; Qin, Hong
Author_Institution :
Dept. of Electr. & Comput. Eng., Louisiana State Univ., Baton Rouge, LA, USA
fDate :
7/1/2009 12:00:00 AM
Abstract :
Harmonic volumetric mapping aims to establish a smooth bijective correspondence between two solid shapes with the same topology. In this paper, we develop an automatic meshless method for creating such a mapping between two given objects. With the shell surface mapping as the boundary condition, we first solve a linear system constructed by a boundary method called the method of fundamental solution, and then represent the mapping using a set of points with different weights in the vicinity of the shell of the given model. Our algorithm is a true meshless method (without the need of any specific meshing structure within the solid interior) and the behavior of the interior region is directly determined by the boundary, which can improve the computational efficiency and robustness significantly. Therefore, our algorithm can be applied to massive volume data sets with various geometric primitives and topological types. We demonstrate the utility and efficacy of our algorithm in information transfer, shape registration, deformation sequence analysis, tetrahedral remeshing, and solid texture synthesis.
Keywords :
computational geometry; mesh generation; automatic meshless method; deformation sequence analysis; fundamental solution methods; geometric primitives; information transfer; linear system; meshless harmonic volumetric mapping; method of fundamental solution; shape registration; shell surface mapping; solid texture synthesis; tetrahedral remeshing; topological types; Computational geometry and object modeling; computer graphics; computing methodologies; geometric algorithms;
Journal_Title :
Automation Science and Engineering, IEEE Transactions on
DOI :
10.1109/TASE.2009.2014735