TY - GEN
T1 - Regularization of mappings between implicit manifolds of arbitrary dimension and codimension
AU - Shafrir, David
AU - Sochen, Nir A.
AU - Deriche, Rachid
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33646546056&partnerID=8YFLogxK
U2 - 10.1007/11567646_29
DO - 10.1007/11567646_29
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AN - SCOPUS:33646546056
SN - 3540293485
SN - 9783540293484
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 344
EP - 355
BT - Variational, Geometric, and Level Set Methods in Computer Vision - Third International Workshop, VLSM 2005, Proceedings
T2 - 3rd International Workshop on Variational, Geometric, and Level Set Methods in Computer Vision, VLSM 2005
Y2 - 16 October 2005 through 16 October 2005
ER -