Particle Filter with Mode Tracker(PF-MT) for Visual Tracking Across Illumination Change

In recent work, the authors introduced a multiplicative, low dimensional model of illumination that is computed as a linear combination of a set of simple-to-compute Legendre basis functions. The basis coefficients describing illumination change, are can be combined with the "shape" vector to define a joint "shape"-illumination space for tracking. The increased dimensionality of the state vector necessitates an increase in the number of particles required to maintain tracking accuracy. In this paper, we utilize the recently proposed PF-MT algorithm to estimate the illumination vector. This is motivated by the fact that, except in case of occlusions, multimodality of the state posterior is usually due to multimodality in the "shape" vector (e.g. there may be multiple objects in the scene that roughly match the template). In other words, given the "shape" vector at time t, the posterior of the illumination (probability distribution of illumination conditioned on the "shape" and illumination at previous time) is unimodal. In addition, it is also true that this posterior is usually quite narrow since illumination changes over time are slow. The choice of the illumination model permits the illumination coefficients to be solved in closed form as a solution of a regularized least squares problem. We demonstrate the use of our method for the problem of face tracking under variable lighting conditions existing in the scene.