Target Recognition Based on a Novel Riemannian Map

The geometric warps of a rigid planar object can be represented by a projective Lie group The Riemannian map and its inverse map play an important role in designing an efficient algorithm to compute the Riemannian mean on special linear group. This mean is the key to constructing the Lie group normal distribution which is an important prior when using the Bayes statistical reference rule in the planar target recognition. In order to solve the problem that the inverse map of Riemannian map on special linear map based on Cartan decomposition has not a closed formula, we define a new Riemannian map and get its inverse map in terms of the polar decomposition theorem. Then we propose a stable algorithm to compute the mean on special linear group and give a simple target recognition experiment to show that it is helpful to improve success recognition rate if utilizing the transformation group prior.