Department of Science and Engineering, School of Medicine, Oregon Health and Science University, Beaverton, OR 97006, USA.
IEEE Trans Pattern Anal Mach Intell. 2010 Dec;32(12):2262-75. doi: 10.1109/TPAMI.2010.46.
Point set registration is a key component in many computer vision tasks. The goal of point set registration is to assign correspondences between two sets of points and to recover the transformation that maps one point set to the other. Multiple factors, including an unknown nonrigid spatial transformation, large dimensionality of point set, noise, and outliers, make the point set registration a challenging problem. We introduce a probabilistic method, called the Coherent Point Drift (CPD) algorithm, for both rigid and nonrigid point set registration. We consider the alignment of two point sets as a probability density estimation problem. We fit the Gaussian mixture model (GMM) centroids (representing the first point set) to the data (the second point set) by maximizing the likelihood. We force the GMM centroids to move coherently as a group to preserve the topological structure of the point sets. In the rigid case, we impose the coherence constraint by reparameterization of GMM centroid locations with rigid parameters and derive a closed form solution of the maximization step of the EM algorithm in arbitrary dimensions. In the nonrigid case, we impose the coherence constraint by regularizing the displacement field and using the variational calculus to derive the optimal transformation. We also introduce a fast algorithm that reduces the method computation complexity to linear. We test the CPD algorithm for both rigid and nonrigid transformations in the presence of noise, outliers, and missing points, where CPD shows accurate results and outperforms current state-of-the-art methods.
点集配准是许多计算机视觉任务的关键组成部分。点集配准的目标是为两组点分配对应关系，并恢复将一个点集映射到另一个点集的变换。多种因素，包括未知的非刚性空间变换、点集的大维数、噪声和离群点，使得点集配准成为一个具有挑战性的问题。我们引入了一种概率方法，称为连贯点漂移（CPD）算法，用于刚性和非刚性点集配准。我们将两个点集的对齐视为概率密度估计问题。我们通过最大化似然来拟合高斯混合模型（GMM）质心（表示第一组点）到数据（第二组点）。我们强制 GMM 质心作为一个整体一致移动，以保持点集的拓扑结构。在刚性情况下，我们通过使用刚性参数重新参数化 GMM 质心位置来施加一致性约束，并推导出任意维度的 EM 算法最大化步骤的闭式解。在非刚性情况下，我们通过正则化位移场并使用变分微积分来推导出最优变换来施加一致性约束。我们还引入了一种快速算法，将方法的计算复杂度降低到线性。我们在存在噪声、离群点和缺失点的情况下对点集进行刚性和非刚性变换的 CPD 算法进行了测试，CPD 算法表现出准确的结果，并优于当前最先进的方法。
