Abstract
The problem of nonlinear alignment of functions is both fundamental and extremely important in pattern recognition. Most common approaches for alignment, including dynamic time warping (DTW), use penalized-\(\mathbb {L}^2\) minimization that has significant shortcomings, including asymmetry. A recent mathematical framework, based on an elastic Riemannian metric and square-root velocity functions, overcomes these shortcomings. The time warping problem is currently solved using a dynamic programming algorithm (DPA) which relies heavily on dense sampling of functions and can be computationally expensive. Here we present a novel theory (and algorithms) for finding the exact pairwise alignment between functions, which uses an efficient sampling of functions, restricted to their change points. In many cases, the computational cost for matching is reduced by orders of magnitude. We demonstrate the superiority of this method over the DPA using several simulated and real datasets.
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Robinson, D., Duncan, A., Srivastava, A., Klassen, E. (2017). Exact Function Alignment Under Elastic Riemannian Metric. In: Cardoso, M., et al. Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics. GRAIL MICGen MFCA 2017 2017 2017. Lecture Notes in Computer Science(), vol 10551. Springer, Cham. https://doi.org/10.1007/978-3-319-67675-3_13
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DOI: https://doi.org/10.1007/978-3-319-67675-3_13
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