Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
LCIS: a boundary hierarchy for detail-preserving contrast reduction
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A Natural Norm for Color Processing
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
A finite element method for surface restoration with smooth boundary conditions
Computer Aided Geometric Design
Fourth-order partial differential equations for noise removal
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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We propose a noise-removal method for vector-valued images by considering the negative gradient flow (the biharmonic map heat flow) of the intrinsic Bi-energy on Riemannian manifold of non-positive curvature. This method represents a natural generalization of both harmonic maps and minimal immersions. It is derived by finding the critical point of the variational problem associated to the integral of the squared norm of the tension-field (Bi-harmonic map) or of the mean curvature vector field (Bi-minimal immersion). In local coordinates, this method yields a fourth order non-linear system of PDE's that we, numerically, solve by an explicit finite difference method. Experiments on real color-image endowed with the Helmholtz and Stiles metrics show that the proposed method is effective, accurate and highly robust.