基于高斯混合模型的非刚性点集配准

Non-Rigid Point Set Registration Based on Gaussian Mixture Model

摘要: 点集配准的目的是获取对应关系和估计模型点集到目标点集的变换。非刚性点集配准的求解难度大，且点集可能含有噪声、遮挡等失真使其求解更加复杂。概率点集配准方法因其对变形、噪声和遮挡具有鲁棒性，本文将点集配准视为概率密度估计问题，通过极大似然估计，并用EM算法求解对应关系及变换。在再生核希尔伯特空间中指定了两点集之间的变换，并对核函数(即高斯分布)中的高斯滤波器的宽度在迭代过程中逐渐缩小。在合成数据的实验表明，本文方法在变形、噪声等各种类型的畸变下具有鲁棒性，与CPD算法比较，本文方法比它的配准误差更小。

Abstract: The purpose of point set alignment is to obtain correspondences and estimate the transformation from the model point set to the target point set. Non-rigid point set alignment is difficult to solve, and the point set may contain distortions such as noise and occlusion to complicate its solution. Probabilistic point set alignment methods are robust to distortions, noise and occlusion, and in this paper, point set alignment is considered as a probability density estimation problem, which is estimated by great likelihood and solved by EM algorithms for the correspondences and transformations. The transformation between the two point sets is specified in the regenerated kernel Hilbert space, and the width of the Gaussian filter in the kernel function (i.e., the Gaussian distribution) is gradually narrowed down during the iteration process. Experiments on synthesized data show that the method of this paper is robust under various types of distortions such as deformation and noise, and compared with the CPD algorithm, the method of this paper has less alignment error than it.