论文标题
数据驱动的，使用形状和地标对功能数据的软对准
Data-Driven, Soft Alignment of Functional Data Using Shapes and Landmarks
论文作者
论文摘要
功能的一致性或注册是功能和形状统计分析中的基本问题。尽管有几种可用的方法，但基于Fisher-Rao公制和方形速度函数（SRVF）的最新方法已显示出良好的性能。但是，该SRVF方法具有两个局限性：（1）它容易对过度对齐，即噪声和信号对齐，以及（2）如果有地标的其他信息，则原始公式不会规定一种合并该信息的方式。在本文中，我们提出了一个扩展名，该扩展可以纳入地标信息，以寻求匹配曲线和地标之间的妥协。这导致了一个柔软的地标对准，使地标将地标靠近，而无需确切的叠加层以发现功能和地标之间的贡献之间的妥协。在某些实际情况下，提出的方法被证明是优越的。
Alignment or registration of functions is a fundamental problem in statistical analysis of functions and shapes. While there are several approaches available, a more recent approach based on Fisher-Rao metric and square-root velocity functions (SRVFs) has been shown to have good performance. However, this SRVF method has two limitations: (1) it is susceptible to over alignment, i.e., alignment of noise as well as the signal, and (2) in case there is additional information in form of landmarks, the original formulation does not prescribe a way to incorporate that information. In this paper we propose an extension that allows for incorporation of landmark information to seek a compromise between matching curves and landmarks. This results in a soft landmark alignment that pushes landmarks closer, without requiring their exact overlays to finds a compromise between contributions from functions and landmarks. The proposed method is demonstrated to be superior in certain practical scenarios.
