A novel algorithm for optimal matching of elastic shapes with landmark constraints
A novel algorithm for optimal matching of elastic shapes with landmark constraints
复制标题
DOI：
10.1109/ipta.2017.8310079
复制
发表时间：
2017-11
期刊：
影响因子：
--
通讯作者：
Justin Strait;S. Kurtek
中科院分区：
文献类型：
--
作者：
Justin Strait;S. Kurtek
统计形状分析中的一个重要问题是跨形状的几何特征的匹配，称为配准。简而言之，给定两个对象，人们想知道一种形状上的点与另一种形状上的点的对应关系。无论形状的数学表示如何，都会存在具有不同复杂程度的匹配问题。最近的 n 维曲线形状分析框架将无限维函数曲线表示与编码重要曲线特征的地标信息相结合。在此设置中，形状匹配是通过最小化带有约束的目标函数来执行的，该约束尊重地标对应。目前，这种方法中的最小化器是使用分段动态规划来找到的；这不符合匹配函数的平滑要求。因此，该解决方案实际上并不是注册功能组的成员。在这项工作中，我们提出了一种地标约束梯度下降算法，该算法搜索平滑匹配函数并尊重地标位置。我们使用 MPEG-7 数据集中的示例将所提出的方法与之前使用的方法进行比较。
An important problem in statistical shape analysis is the matching of geometric features across shapes, known as registration. In short, given two objects, one wants to know the correspondence of points on one shape to points on another. Such a matching problem, with various levels of complexity, is present regardless of the shape's mathematical representation. A recent framework for shape analysis of n-dimensional curves combines an infinite-dimensional functional curve representation with landmark information encoding important curve features. In this setting, shape matching is performed by minimizing an objective function with constraints, which respect landmark correspondences. Currently, the minimizer in this approach is found using piecewise dynamic programming; this does not respect the smoothness requirement of the matching function. Thus, the solution is not really a member of the group of registration functions. In this work, we present a landmark-constrained gradient descent algorithm, which searches for a smooth matching function and respects landmark locations. We compare the proposed method to the previously used approach using examples from the MPEG-7 dataset.