The computation of the Bhattacharyya distance between histograms without histograms

In this paper we present a new method for fast histogram computing and its extension to bin to bin histogram distance computing. The idea consists in using the information of spatial differences between images, or between regions of images (a current and a reference one), and encoding it into a specific data structure: a tree. The Bhattacharyya distance between two histograms is then computed using an incremental approach that avoid histogram: we just need histograms of the reference image, and spatial differences between the reference and the current image to compute this distance using an updating process. We compare our approach with the well-known Integral Histogram one, and obtain better results in terms of processing time while reducing the memory footprint. We show theoretically and with experimental results the superiority of our approach in many cases. Finally, we demonstrate the advantages of our approach on a real visual tracking application using a particle filter framework by improving its correction step computation time.