Recently, a unifying framework was introduced for shape matching that uses mixture-models and the Fisher-Rao metric to couple both the shape representation and deformation. A fundamental drawback of the Fisher-Rao metric is that it is NOT available in closed-form for the mixture models making shape comparisons computationally very expensive. Here, we propose a new Riemannian metric based on generalized Á- entropy measures. In sharp contrast to the Fisher-Rao metric, our new metric is available in closed-form.