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。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.
高阶变分方程在有效抑制TV模型去噪中的阶梯效应方面表现出色,但其求解过程往往较为复杂。本文针对单位法向量梯度的L1范数做正则项的高阶变分模型求解问题,提出利用法向光滑和曲面拟合两步将其转化为两个低阶变分模型来求解。对这两个低阶变分模型构造了有效的数值方法,实验结果表明本文提出的方法在峰值信噪比、结构相似性以及计算时间上均优于传统的TV模型。峰值信噪比与结构相似性比TV模型分别高0.3 dB、0.02 dB,在时间上也表现出了较大的差别。Higher-order variational equations are excellent in effectively suppressing the step effect in denoising TV models, but their solution process is often complicated. In this paper, for the problem of solving the higher-order variational model with the L1-parameter of the unit normal vector gradient as a regular term, it is proposed to use two steps of normal smoothing and surface fitting to transform it into two lower-order variational models to solve it. An effective numerical method is constructed for these two low-order variational models, and the experimental results show that the method proposed in this paper outperforms the traditional TV model in terms of peak signal-to-noise ratio, structural similarity, and computation time. The peak signal-to-noise ratio and structural similarity are 0.3 dB and 0.02 dB higher than the TV model, respectively, and also show a large difference in time.
