High-dimensional statistical distance for region-of-interest tracking: Application to combining a soft geometric constraint with radiometry

This paper deals with region-of-interest (ROI) tracking in video sequences. The goal is to determine in successive frames the region which best matches, in terms of a similarity measure, an ROI defined in a reference frame. Two aspects of a similarity measure between a reference region and a candidate region can be distinguished: radiometry which checks if the regions have similar colors and geometry which checks if these colors appear at the same location in the regions. Measures based solely on radiometry include distances between probability density functions (PDF) of color. The absence of geometric constraint increases the number of potential matches. A soft geometric constraint can be added to a PDF-based measure by enriching the color information with location, thus increasing the dimension of the domain of definition of the PDFs. However, high-dimensional PDF estimation is not trivial. Instead, we propose to compute the Kullback-Leibler distance between high-dimensional PDFs without explicitly estimating the PDFs. The distance is expressed directly from the samples using the k-th nearest neighbor framework. Tracking experiments were performed on several standard sequences.