Department of Psychiatry, Brigham and Women’s Hospital, Harvard Medical School, Boston, MA 02115, USA.
IEEE Trans Image Process. 2012 Oct;21(10):4383-96. doi: 10.1109/TIP.2012.2206034. Epub 2012 Jun 26.
The registration of a pair of point sets as well as the estimation of their pointwise correspondences is a challenging and important task in computer vision. In this paper, we present a method to estimate the diffeomorphic deformation, together with the pointwise correspondences, between a pair of point sets. Many of the registration problems are iteratively solved by estimating the correspondence, locally optimizing certain cost functionals over the rigid or similarity or affine transformation group, then estimating the correspondence again, and so on. This type of approach, however, is well-known to be susceptible to suboptimal local solutions. In this paper, we first adopt the perspective of treating the registration as a posterior estimation optimization problem and solve it accordingly via a particle-filtering framework. Second, within such a framework, the diffeomorphic registration is performed to correct the nonlinear deformation of the points. In doing so, we provide a solution less susceptible to local minima. We provide the experimental results, which include challenging medical data sets where the two point sets differ by 180 (°) rotation as well as local deformations, to highlight the algorithm's capability of robustly finding the more globally optimal solution for the registration task.
点集对的配准以及其逐点对应关系的估计是计算机视觉中的一项具有挑战性和重要的任务。在本文中，我们提出了一种方法来估计一对点集之间的微分同胚变形以及逐点对应关系。许多配准问题通过估计对应关系来迭代解决，通过在刚体、相似或仿射变换组上局部优化某些代价函数，然后再次估计对应关系，依此类推。然而，这种方法很容易受到次优局部解的影响。在本文中，我们首先采用将配准视为后验估计优化问题的观点，并通过粒子滤波框架对其进行相应的求解。其次，在这样的框架内，进行微分同胚配准以纠正点的非线性变形。通过这种方式，我们提供了一种解决方案，该方案不太容易受到局部最小值的影响。我们提供了实验结果，其中包括具有挑战性的医学数据集，两个点集之间存在 180°（度）的旋转以及局部变形，以突出算法在找到配准任务的更全局最优解方面的稳健能力。
