Abstract
In this paper we investigate a family of partial differential equations (PDEs) for image processing which can be regarded as isotropic nonlinear diffusion with an additional factor on the right-hand side. The one-dimensional analogues to this filter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent examples of this family of PDEs. Other representatives of the filter class combine properties of curvature motion with the enhanced edge preservation of Perona-Malik diffusion. It becomes appearent that these PDEs require a careful discretisation. Numerical experiments display the differences between Perona-Malik diffusion, classical mean curvature motion and the proposed extensions. We consider, for example, enhanced edge sharpness, the question of morphological invariance, and the behaviour with respect to noise.
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Didas, S., Weickert, J. (2007). Combining Curvature Motion and Edge-Preserving Denoising. In: Sgallari, F., Murli, A., Paragios, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72823-8_49
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DOI: https://doi.org/10.1007/978-3-540-72823-8_49
Publisher Name: Springer, Berlin, Heidelberg
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