NORTHWESTERN UNIVERSITY Collaborative Multiple Kernel Tracking: Theory and Algorithms

To make the kernel-based tracking algorithms more reliable, in this work, we mainly deal with two major singular cases in kernel-based tracking, concerned with kernel observability and tracking stability. Singular kernel observability indicates that the motions of interest cannot be uniquely recovered by the kernel. We present a novel multiple collaborative kernel approach, in which a complex motion is represented by a set of inter-correlated simpler motions. With this formulation, we present a rigorous analysis on a critical issue of kernel observability and obtain a criterion, based on which we propose a new method using collaborative kernels that has the theoretical guarantee of enhanced observability. This new method has been shown to be computationally efficient in both theory and practice, which can be readily applied to complex motions such as articulated motions. Another singular case, unstableness in tracking, is caused by inappropriate kernel placement, which requires research on optimal kernel placement. The theoretical analysis presented in this work indicates that the optimal kernel placement can be evaluated based on a closed-form criterion, and achieved efficiently by a novel gradient-based algorithm. Based on that, new methods for temporal-stable 2 multiple kernel placement and scale-invariant kernel placement are also proposed. These new theoretical results and new algorithms greatly advance the study of kernel-based tracking in both theory and practice. Extensive experimental results demonstrate the improved tracking reliability.