Abstract
We study in this paper the problem of regularization of mappings between manifolds of arbitrary dimension and codimension using variational methods. This is of interest in various applications such as diffusion tensor imaging and EEG processing on the cortex. We consider the cases where the source and target manifold are represented implicitly, using multiple level set functions, or explicitly, as functions of the spatial coordinates. We derive the general implicit differential operators, and show how they can be used to generalize previous results concerning the Beltrami flow and other similar flows.
As examples, We show how these results can be used to regularize gray level and color images on manifolds, and to regularize tangent vector fields and direction fields on manifolds.
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Shafrir, D., Sochen, N.A., Deriche, R. (2005). Regularization of Mappings Between Implicit Manifolds of Arbitrary Dimension and Codimension. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_29
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DOI: https://doi.org/10.1007/11567646_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29348-4
Online ISBN: 978-3-540-32109-5
eBook Packages: Computer ScienceComputer Science (R0)Springer Nature Proceedings Computer Science
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