Abstract
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.
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Zéraï, M. (2009). Image Denoising by Harmonic Mean Curvature Flow. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_47
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DOI: https://doi.org/10.1007/978-3-642-02256-2_47
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