Abstract
Singular diffusion equations such as total variation (TV) and balanced forward–backward (BFB) diffusion are appealing: They have a finite extinction time, and experiments show that piecewise constant structures evolve. Unfortunately, their implementation is awkward. The goal of this paper is to introduce a novel class of numerical methods for these equations in the 2D case. They are simple to implement, absolutely stable and do not require any regularisation in order to make the diffusivity bounded. Our schemes are based on analytical solutions for 2×2-pixel images which are combined by means of an additive operator splitting (AOS). We show that they may also be regarded as iterated 2D Haar wavelet shrinkage. Experiments demonstrate the favourable performance of our numerical algorithm.
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Welk, M., Weickert, J., Steidl, G. (2005). A Four-Pixel Scheme for Singular Differential Equations. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds) Scale Space and PDE Methods in Computer Vision. Scale-Space 2005. Lecture Notes in Computer Science, vol 3459. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11408031_52
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DOI: https://doi.org/10.1007/11408031_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25547-5
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