Differential Earth Mover's Distance with Its Applications to Visual Tracking

The Earth mover's distance (EMD) is a similarity measure that captures perceptual difference between two distributions. Its computational complexity, however, prevents a direct use in many applications. This paper proposes a novel differential EMD (DEMD) algorithm based on the sensitivity analysis of the simplex method and offers a speedup at orders of magnitude compared with its brute-force counterparts. The DEMD algorithm is discussed and empirically verified in the visual tracking context. The deformations of the distributions for objects at different time instances are accommodated well by the EMD, and the differential algorithm makes the use of EMD in real-time tracking possible. To further reduce the computation, signatures, i.e., variable-size descriptions of distributions, are employed as an object representation. The new algorithm models and estimates local background scenes as well as foreground objects to handle scale changes in a principled way. Extensive quantitative evaluation of the proposed algorithm has been carried out using benchmark sequences and the improvement over the standard mean shift tracker is demonstrated.