Wang Fei, Vemuri Baba C, Rangarajan Anand, Eisenschenk Stephan J
IBM Almaden Research Center, G1-003, 650 Harry Road, San Jose, CA 95120, USA.
IEEE Trans Pattern Anal Mach Intell. 2008 Nov;30(11):2011-22. doi: 10.1109/TPAMI.2007.70829.
Groupwise registration of a set of shapes represented by unlabeled point sets is a challenging problem since, usually, this involves solving for point correspondence in a nonrigid motion setting. In this paper, we propose a novel and robust algorithm that is capable of simultaneously computing the mean shape, represented by a probability density function, from multiple unlabeled point sets(represented by finite-mixture models), and registering them nonrigidly to this emerging mean shape. This algorithm avoids the correspondence problem by minimizing the Jensen-Shannon (JS) divergence between the point sets represented as finite mixtures of Gaussian densities. We motivate the use of the JS divergence by pointing out its close relationship to hypothesis testing. Essentially,minimizing the JS divergence is asymptotically equivalent to maximizing the likelihood ratio formed from a probability density of the pooled point sets and the product of the probability densities of the individual point sets. We derive the analytic gradient of the cost function, namely, the JS-divergence, in order to efficiently achieve the optimal solution. The cost function is fully symmetric, with no bias toward any of the given shapes to be registered and whose mean is being sought. A by-product of the registration process is a probabilistic atlas, which is defined as the convex combination of the probability densities of the input point sets being aligned. Our algorithm can be especially useful for creating atlases of various shapes present in images and for simultaneously (rigidly or nonrigidly)registering 3D range data sets (in vision and graphics applications), without having to establish any correspondence. We present experimental results on nonrigidly registering 2D and 3D real and synthetic data (point sets).
对由未标记点集表示的一组形状进行逐组配准是一个具有挑战性的问题，因为通常这涉及在非刚性运动设置中求解点对应关系。在本文中，我们提出了一种新颖且稳健的算法，该算法能够从多个未标记点集（由有限混合模型表示）中同时计算由概率密度函数表示的平均形状，并将它们非刚性地配准到这个新出现的平均形状上。该算法通过最小化表示为高斯密度有限混合的点集之间的詹森 - 香农（JS）散度来避免对应问题。我们通过指出其与假设检验的密切关系来激发对JS散度的使用。本质上，最小化JS散度渐近等同于最大化由合并点集的概率密度与各个点集的概率密度之积形成的似然比。我们推导了成本函数（即JS散度）的解析梯度，以便有效地获得最优解。成本函数是完全对称的，对任何要配准的给定形状以及正在寻求其均值的形状都没有偏差。配准过程的一个副产品是概率图谱，它被定义为正在对齐的输入点集的概率密度的凸组合。我们的算法对于创建图像中存在的各种形状的图谱以及同时（刚性或非刚性）配准3D距离数据集（在视觉和图形应用中）特别有用，而无需建立任何对应关系。我们展示了对2D和3D真实及合成数据（点集）进行非刚性配准的实验结果。
