Enforcing non-positive weights for stable support vector tracking

In this paper we demonstrate that the support vector tracking (SVT) framework first proposed by Avidan is equivalent to the canonical Lucas-Kanade (LK) algorithm with a weighted Euclidean norm. From this equivalence we empirically demonstrate that in many circumstances the canonical SVT approach is unstable, and characterize these circumstances theoretically. We then propose a novel ldquononpositive support kernel machinerdquo (NSKM) to circumvent this limitation and allow the effective use of discriminative classification within the weighted LK framework. This approach ensures that the pseudo-Hessian realized within the weighted LK algorithm is positive semidefinite which allows for fast convergence and accurate alignment/tracking. A further benefit of our proposed method is that the NSKM solution results in a much sparser kernel machine than the canonical SVM leading to sizeable computational savings and much improved alignment performance.