Adaptive rest condition potentials: first and second order edge-preserving regularization

Authors:
Mariano Rivera;Jose L. Marroquin
Affiliations:
Centro de Investigacion en Matematicas A.C. Apostado Postal 402, Guanajuato, Mexico 36020;Centro de Investigacion en Matematicas A.C. Apostado Postal 402, Guanajuato, Mexico 36020
Venue:
Computer Vision and Image Understanding
Year:
2002

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Abstract

A new regularization formulation for inverse problems in computer vision and image processing is introduced, which allows one to reconstruct second order piece-wise smooth images, that is, images consisting of an assembly of regions with almost constant value, almost constant slope, or almost constant curvature. This formulation is based on the idea of using potential functions that correspond to springs or thin plates with an adaptive rest condition. Efficient algorithms for computing the solution and examples illustrating the performance of this scheme, compared with other known regularization schemes, are presented as well.