Extended Shape of Gaussian: Feature descriptor based on element set of matrix Lie group

In this paper, we extend the feature descriptor known as Shape of Gaussian (SOG) and we call the new descriptor Extended Shape of Gaussian (ESOG). SOG has a matrix Lie group structure, it use the geodesic distance to measure the difference between two features. First, we decompose geodesic distance on the Lie algebra into two orthogonal components. By adjusting the weights of components, we get a distance sequence. Then we identify that every element in the sequence corresponds to an element of the original Lie group, a matrix. All these matrices form ESOG. Thus the new descriptor utilizes a matrix set rather than one matrix to describe feature. In this view, SOG and region covariance are both special element of ESOG. So we can choose different element from it for different application. Noting that different elements in the ESOG describe a signal in a different view, we propose an adaptive method to select appropriate ESOG element for visual tracking. The element selected by this method is called Adaptive SOG (ASOG). ASOG keeps the advantages of both SOG and region covariance and has better accuracy and robustness under different conditions. Experiments show the tracking results compared with SOG.