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Abstract:
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Alignment or registration of signals and functions is a fundamental problem in statistical analysis of functions and shapes. While there are many approaches in the literature for such registration, including the famous dynamic time warping, 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 can be 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, to help with the registration, the original formulation does not prescribe a way to incorporate that information. In this paper we propose a modification that allows for incorporation of landmark information, in addition to the original elastic matching term, to seek a compromise between matching curves and matching landmarks. This results in soft landmark alignment that bring landmarks closer, without insisting on them being matched exactly, and thus often avoids over alignment. The proposed method is demonstrated to be superior in certain practical scenarios using both simulated and real datasets.
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