Robust point matching via vector field consensus.
Robust point matching via vector field consensus.
复制标题
通过矢量场一致性进行稳健的点匹配
DOI：
10.1109/tip.2014.2307478
复制
发表时间：
2014-04
期刊：
影响因子：
--
通讯作者：
Zhuowen Tu
中科院分区：
文献类型：
--
作者：
Jiayi Ma;Ji Zhao;Jinwen Tian;Yuille AL;Zhuowen Tu
在本文中，我们提出了一个有效的算法，称为向量场共识，建立两组点之间的强大的点对应。我们的算法首先创建一组假定的对应关系，除了有限数量的真实对应关系（内点）之外，还可以包含大量的假对应关系或离群值。接下来，我们通过在两个点集之间插入一个向量场来解决对应关系，这涉及到估计其匹配遵循非参数几何约束的内点的一致性。我们制定这一最大后验概率（MAP）估计的贝叶斯模型与隐/潜变量表明是否匹配在假定的集合是离群值或内点。我们施加非参数几何约束的对应关系，作为一个先验分布，使用Tikhonov正则化再生核希尔伯特空间。MAP估计由EM算法执行，EM算法还通过估计先验模型的方差（初始化为大值）能够非常快速地获得良好的估计（例如，避免了该公式中固有的许多局部最小值）。我们在2D和3D数据集上说明了这种方法，并证明了它对大量离群值（甚至高达90%）具有鲁棒性。我们还表明，在特殊情况下，有一个基本的参数几何模型（例如，核线约束），如果存在大量离群值，则我们获得比标准替代方案（如RANSAC）更好的结果。这表明了一个两阶段的策略，我们使用我们的非参数模型来减少假定集的大小，然后应用我们的方法的参数变体来估计几何参数。我们的算法是计算效率高，我们提供的代码供他人使用。此外，我们的方法是通用的，可以应用于其他问题，如学习与严重损坏的训练数据集。
In this paper, we propose an efficient algorithm, called vector field consensus, for establishing robust point correspondences between two sets of points. Our algorithm starts by creating a set of putative correspondences which can contain a very large number of false correspondences, or outliers, in addition to a limited number of true correspondences (inliers). Next, we solve for correspondence by interpolating a vector field between the two point sets, which involves estimating a consensus of inlier points whose matching follows a nonparametric geometrical constraint. We formulate this a maximum a posteriori (MAP) estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. We impose nonparametric geometrical constraints on the correspondence, as a prior distribution, using Tikhonov regularizers in a reproducing kernel Hilbert space. MAP estimation is performed by the EM algorithm which by also estimating the variance of the prior model (initialized to a large value) is able to obtain good estimates very quickly (e.g., avoiding many of the local minima inherent in this formulation). We illustrate this method on data sets in 2D and 3D and demonstrate that it is robust to a very large number of outliers (even up to 90%). We also show that in the special case where there is an underlying parametric geometrical model (e.g., the epipolar line constraint) that we obtain better results than standard alternatives like RANSAC if a large number of outliers are present. This suggests a two-stage strategy, where we use our nonparametric model to reduce the size of the putative set and then apply a parametric variant of our approach to estimate the geometric parameters. Our algorithm is computationally efficient and we provide code for others to use it. In addition, our approach is general and can be applied to other problems, such as learning with a badly corrupted training data set.