Learning Invariant Riemannian Geometric Representations Using Deep Nets

Suhas Lohit, Pavan Turaga; Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017, pp. 1329-1338

Abstract


Non-Euclidean constraints are inherent in many kinds of data in computer vision, often expressed in the language of Riemannian geometry. The central question this paper deals with is: How does one train deep neural nets whose final outputs are elements on a Riemannian manifold? To answer this, we propose a general framework for manifold-aware training of deep neural networks -- we utilize tangent spaces and exponential maps in order to convert the proposed problem into a form that allows us to bring current advances in deep learning to bear upon this problem. We describe two specific applications to demonstrate this approach: prediction of probability distributions for multi-class image classification, and prediction of illumination-invariant subspaces from a single face-image via regression on the Grassmannian. These applications show the generality of the proposed framework, and result in improved performance over baselines that ignore the geometry of the output space.

Related Material


[pdf] [supp][arXiv]
[bibtex]
@InProceedings{Lohit_2017_ICCV,
author = {Lohit, Suhas and Turaga, Pavan},
title = {Learning Invariant Riemannian Geometric Representations Using Deep Nets},
booktitle = {Proceedings of the IEEE International Conference on Computer Vision (ICCV) Workshops},
month = {Oct},
year = {2017}
}