Lie-Struck: Affine Tracking on Lie Groups Using Structured SVM

Abstract

This paper presents a novel and reliable tracking-by detection method for image regions that undergo affine transformations such as translation, rotation, scale, dilatation and shear deformations, which span the six degrees of freedom of motion. Our method takes advantage of the intrinsic Lie group structure of the 2D affine motion matrices and imposes this motion structure on a kernelized structured output SVM classifier that provides an appearance based prediction function to directly estimate the object transformation between frames using geodesic distances on manifolds unlike the existing methods proceeding by linearizing the motion. We demonstrate that these combined motion and appearance model structures greatly improve the tracking performance while an incorporated particle filter on the motion hypothesis space keeps the computational load feasible. Experimentally, we show that our algorithm is able to outperform state-of-the-art affine trackers in various scenarios.