Image Processing Based on Partial Differential Equations: by Xue-Cheng Tai, Knut-Andreas Lie, Tony F. Chan, Stanley Osher
By Xue-Cheng Tai, Knut-Andreas Lie, Tony F. Chan, Stanley Osher
This publication publishes a set of unique medical examine articles that deal with the state-of-art in utilizing partial differential equations for snapshot and sign processing. insurance comprises: point set equipment for photograph segmentation and development, denoising thoughts, electronic photo inpainting, photograph dejittering, photo registration, and speedy numerical algorithms for fixing those difficulties.
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Extra resources for Image Processing Based on Partial Differential Equations: Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse ... 8-12, 2005 (Mathematics and Visualization)
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Most of the existing analysis is related to the existence and non-uniqueness of the minimizers. And it does not provide quantitative understandings on why the models work well. In this paper, we investigate the error estimate for the missing information recovery and hope to explain the observations being made in these applications. 3 Recovery Bound for the H 1 Model In this paper, we focus on the H 1 variational wavelet interpolation model, which uses (8) F (α) = |∇x u(x, α)|2 dx, in the wavelet interpolation model (7).
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13) Definition 4 (Dejittering). The dejittering problem is the inverse problem of restoring the original image u(z) from its jittered observation uJ (z) (see Fig. 1). 2 Linear slicing moments and Bayesian inference Definition 5 (Linear Slicing Moments). Let the codimension d linear moments md (y|u) for u ∈ BVc+ (Rn ) be the vectorial function md (y|u) = md (y|u, e1 ), · · · , md (y|u, en−d ) , (14) where ei = (0, · · · , 0, 1ith , 0, · · · , 0), i = 1, . . , n − d. Equivalently, it is given by md (y|u) = Rn−d xu(x, y)dx, x = (z1 , · · · , zn−d ).