Heat kernels of generalized laplacians-application to color image smoothing

In this paper, we explore the theory of vector bundles over Riemannian manifolds in order to smooth multivalued images. In this framework, we consider standard PDE´s used in image processing as generalized heat equations, related to the geometries of the base manifold, given by its metric and the subsequent Levi-Cevita connection and of the vector bundle, given by a connection. As a consequence, the smoothing is made through a convolution with a 2D kernel, generalizing Gaussian, Beltrami and oriented kernel. In particular, we construct an extension of the oriented kernel, and illustrate it with an application to color image smoothing.