SrvfRegNet: Elastic Function Registration Using Deep Neural Networks

Chao Chen, Anuj Srivastava; Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2021, pp. 4462-4471

Registering functions (curves) using time warpings (reparameterizations) is central to many computer vision and shape analysis solutions. While traditional registration methods minimize penalized-L2 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 L2 norm between SRVFs of given functions. However, the computational cost of this elastic dynamic programming framework - O(nT2k) - where T is the number of time samples along a curve, 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 super-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. It achieves close to the state-of-the-art alignment performance but at much reduced computational cost. We demonstrate the efficiency and efficacy of this framework using several standard curve datasets