Learning on Lie Groups for Invariant Detection and Tracking

Abstract

This paper presents a novel learning based tracking model combined with object detection. The existing techniques proceed by linearizing the motion, which makes an implicit Euclidean space assumption. Most of the transformations used in computer vision have matrix Lie group structure. We learn the motion model on the Lie algebra and show that the formulation minimizes a first order approximation to the geodesic error. The learning model is extended to train a class specific tracking function, which is then integrated to an existing pose dependent object detector to build a pose invariant object detection algorithm. The proposed model can accurately detect objects in various poses, where the size of the search space is only a fraction compared to the existing object detection methods. The detection rate of the original detector is improved by more than 90% for large transformations.