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• W1585834753 abstract "During the last decade nonlinear anisotropic diffusion models have shown to be powerful methods not only in image processing. Moreover these methodologies can be adopted to other areas in computer vision. On the level of the continuous model one can study the qualitative aspects and properties whereas approved discretization schemes are at hand for an efficient implementation. In this p aper we discuss several anisotropic diffusion methods and outline a novel technique for geometric surface processing. Moreover we will show how the solution process can be accelerated significantly by using texture hardware o f modern graphics cards, making use of the much better memory bandwidth and the built-in parallelism. AMS subject classifications. 65M60, 65Y10 1. Introduction. In the last decade PDE based models in the field of computer vis ion and image analysis became very popular. Here we outline how these techniques can be gen- eralized to surface processing and visualization purposes . Furthermore, we introduce a novel concept for fast implementation of the underlying algorithms. The nonlinear diffusion models as we know them today were firs t introduced by a work of Perona and Malik (24), who introduced a model that allows for denoising of images while retaining and enhancing edges. Analysis of the Perona Malik model showed its mathematical ill-posedness (20, 34, 19), that drove the derivation of a re gularized model by Catte et. al. (7). This still has the edge preserving property as long as th e regularization parameter is chosen appropriately. The so called scale space methods were later classified by a rigorous axiomatic theory by Alvarez et. al. (2). Recovering of lower dimensional structures was analyzed by Weickert (32). He considered an anisotropy depending on the so called structure tensor of images, that steers a nonlinear diffusion process taking care of tangential and normal directions on edges." @default.
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• W1585834753 date "2000-01-01" @default.
• W1585834753 modified "2023-09-26" @default.
• W1585834753 title "DIFFUSION MODELS AND THEIR ACCELERATED SOLUTION IN IMAGE AN D SURFACE PROCESSING" @default.
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