  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.

Methodology;Computer Vision and Pattern Recognition;Applications