The Clifford-Hodge Flow: An Extension of the Beltrami Flow

摘要

In this paper, we make use of the theory of Clifford algebras for anisotropic smoothing of vector-valued data. It provides a common framework to smooth functions, tangent vector fields and mappings taking values in so(m), the Lie algebra of SO(m), defined on surfaces and more generally on Riemannian manifolds. Smoothing process arises from a convolution with a kernel associated to a second order differential operator: the Hodge Laplacian. It generalizes the Beltrami flow in the sense that the Laplace-Beltrami operator is the restriction to functions of minus the Hodge operator. We obtain a common framework for anisotropic smoothing of images, vector fields and oriented orthonormal frame fields defined on the charts.