基于混合t聚类的鲁棒非刚体点匹配

Improving Non-Rigid Point Matching with a New Model

针对非刚体形状控制点匹配中存在的对应性和有偏性问题,提出一个基于混合t聚类的鲁棒点匹配模型。该模型结合了混合t分布聚类和薄片样条匹配各自的优点,混合t聚类充分利用t分布的小样本和较大尾迹优势取得局部聚类的鲁棒性,并可方便地引入新的成员分布概率建模局外点,解决全局的鲁棒性;薄片样条能完全分解非刚体映射的仿射和非仿射变换。实验证明,利用确定性退火和EM(期望最大化)迭代技术,对模型中的鲁棒聚类和非刚体点匹配进行联合优化,可以有效解决非刚体点匹配的对应性和有偏性问题;通过在退火过程中应用一个模型选择准则,可以进一步提高匹配的精度,对比结果证实了该模型的鲁棒性。

In non-rigid point matching, there are, in our opinion, two difficulties： how to implement good correspondence and to suppress bias. We propose improving Ref. 5＇s robust mixture model using the t distribution and combining the improved model with Ref. 6＇s TPS （Thin Plate Splines） technique so as to deal effectively with the two above-mentioned difficulties. In the full paper, we explain in detail how to use the new method, which includes the improved Ref. 5＇s model and TPS technique; in this abstract, we just add some pertinent remarks to listing the topic of explanation： （1） robust non-rigid point matching algorithm; the four subtopics are robust mixture model using the t-distribution（subtopic 1.1）, non-rigid point matching maximum a priori estimation and EM （Expectation Maximization） algorithm （subtopic 1. 2）, non-rigid mapping based on TPS （subtopic 1. 3）, and algorithm flowchart （subtopic 1. 4）; It is worthy mentioning that , in subtopic 1.1, eq. （3） in the full paper represents mainly our improvement of Ref. 5＇s model; in subtopic 1. 3, eq. （9） in the full paper is worth being paid special attention. Test results, given in Figs. 2 and 3 in the full paper, show that the above-mentioned two difficult problems in non-rigid point matching can be solved effectively; the matching resolution can be further improved by using a model choice criterion in DA （Deterministic Annealing） process.