Point Set Registration: Coherent Point Drift
Point Set Registration: Coherent Point Drift
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DOI：
10.1109/tpami.2010.46
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发表时间：
2010-12-01
影响因子：
23.6
通讯作者：
Song, Xubo
中科院分区：
文献类型：
--
作者：
Myronenko, Andriy;Song, Xubo
点集配准是许多计算机视觉任务的关键组成部分。点集配准的目标是分配两组点之间的对应关系并恢复将一个点集映射到另一点集的变换。多种因素，包括未知的非刚性空间变换、点集的大维数、噪声和异常值，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，称为相干点漂移（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将高斯混合模型 (GMM) 质心（代表第一个点集）拟合到数据（第二个点集）。我们迫使 GMM 质心作为一个组一致移动，以保留点集的拓扑结构。在刚性情况下，我们通过使用刚性参数对 GMM 质心位置进行重新参数化来施加相干约束，并导出任意维度 EM 算法最大化步骤的封闭形式解。在非刚性情况下，我们通过正则化位移场并使用变分演算来导出最佳变换来施加相干约束。我们还引入了一种快速算法，可将方法计算复杂度降低为线性。我们在存在噪声、异常值和缺失点的情况下测试了 CPD 算法的刚性和非刚性变换，其中 CPD 显示了准确的结果，并且优于当前最先进的方法。
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.