Deep Learning of Warping Functions for Shape Analysis.

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Rate-invariant or reparameterization-invariant matching between functions and shapes of curves, respectively, is an important problem in computer vision and medical imaging. Often, the computational cost of matching using approaches such as dynamic time warping or dynamic programming is prohibitive for large datasets. Here, we propose a deep neural-network-based approach for learning the warping functions from training data consisting of a large number of optimal matches, and use it to predict optimal diffeomorphic warping functions. Results show prediction performance on a synthetic dataset of bump functions and two-dimensional curves from the ETH-80 dataset as well as a significant reduction in computational cost.