A Lie group based spatiogram similarity measure

Spatiograms were generalization of histograms, which can harvest spatial information of images. The similarity measure is important when applying spatiograms to various computer vision problems such as tracking and image retrieval. The original proposed measures use Mahalanobis distance of coordinate mean to measure spatial information in spatiograms. However, spatial information which is described by spatiograms does not lie on vector space. Measures for vector space such as Mahalanobis distance are not effective measures for them. In this paper, We model spatial information as Gaussian approximation of coordinate distributions. Then we parameterize them as a Lie group. Based on Lie group theory, we analyze function space structure of Gaussian pdfs (probability density function) and propose an effective spatiogram similarity measure. We test our measure in object tracking scenarios. Experiments show better tracking results compared with previously proposed measures.