Abstract
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 \(\mathfrak{so}(m)\), 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.
This work was partially supported by the ONR Grant N00014-09-1-0493, and by the ”Communauté d’Agglomération de La Rochelle”.
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Batard, T., Berthier, M. (2009). The Clifford-Hodge Flow: An Extension of the Beltrami Flow. In: Jiang, X., Petkov, N. (eds) Computer Analysis of Images and Patterns. CAIP 2009. Lecture Notes in Computer Science, vol 5702. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03767-2_48
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DOI: https://doi.org/10.1007/978-3-642-03767-2_48
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