Fixed-point iterative computation of Gaussian barycenters for some dissimilarity measures

In practical contexts like sensor fusion or computer vision, it is not unusual to deal with a large number of Gaussian densities that encode the available information. In such cases, if the computational capabilities are limited, a data compression is required, often done by finding the barycenter of the set of Gaussians. However, such computation strongly depends on the chosen loss function (dissimilarity measure) to be minimized, and most often it must be performed by means of numerical methods, since the barycenter can rarely be computed analytically. Some constraints, like the covariance matrix symmetry and positive definiteness can make non-trivial the numerical computation of the Gaussian barycenter. In this work, a set of Fixed-Point Iteration algorithms are presented in order to allow for the agile computation of Gaussian barycenters according to several dissimilarity measures.