SrvfRegNet: Elastic Function Registration Using Deep Neural Networks

Abstract

Registering functions (curves) using time warpings (re-parameterizations) is central to many computer vision and shape analysis solutions. While traditional registration methods minimize penalized-${\mathbb{L}^2}$ norm, the elastic Riemannian metric and square-root velocity functions (SRVFs) have resulted in significant improvements in terms of theory and practical performance. This solution uses the dynamic programming algorithm to minimize the ${\mathbb{L}^2}$ norm between SRVFs of given functions. However, the computational cost of this elastic dynamic programming framework – O(nT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> k) – where T is the number of time samples along curves, n is the number of curves, and k < T is a parameter – limits its use in applications involving big data. This paper introduces a deep-learning approach, named SRVF Registration Net or SrvfRegNet to overcome these limitations. SrvfRegNet architecture trains by optimizing the elastic metric-based objective function on the training data and then applies this trained network to the test data to perform fast registration. In case the training and the test data are from different classes, it generalizes to the test data using transfer learning, i.e., retraining of only the last few layers of the network. It achieves the state-of-the-art alignment performance albeit at much reduced computational cost. We demonstrate the efficiency and efficacy of this framework using several standard curve datasets.