Geodesic
Quad-tree Based Finite Volume Method for Diffusion Equations with Application to SAR Imaged Filtering
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 2, pp. 41-61.

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In this paper we present a method to remove the noise by applying the Perona Malik algorithm working on an irregular computational grid. This grid is obtained with a quad-tree technique and is adapted to the image intensities—pixels with similar intensities can form large elements. We apply this algorithm to remove the speckle noise present in SAR images, i.e., images obtained by radars with a synthetic aperture enabling to increase their resolution in an electronic way. The presence of the speckle in an image degrades the quality of the image and makes interpretation of features more difficult. Our purpose is to remove this noise to such a degree that the edge detection or landscape elements detection can be performed with relatively simple tools. The progress of smoothing leads to grids with significantly less number of elements than the original number of pixels. The results are compared with measurements performed on an inspected area of interest. At the end we show the possibility to modify the scheme to the adaptive mean curvature flow filter which can be used to smooth the boundaries.
Classification : 65M50, 65M60, 68U10
Keywords: Image processing; linear heat equation; finite volume method; adaptivity; SAR image; speckle noise 
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     author = {Kriv\'a, Zuzana and Pap\v{c}o, Juraj and VANKO, Jakub},
     title = {Quad-tree {Based} {Finite} {Volume} {Method} for {Diffusion} {Equations} with {Application} to {SAR} {Imaged} {Filtering}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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Krivá, Zuzana; Papčo, Juraj; VANKO, Jakub. Quad-tree Based Finite Volume Method for Diffusion Equations with Application to SAR Imaged Filtering. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 54 (2015) no. 2, pp. 41-61. http://geodesic.mathdoc.fr/item/AUPO_2015__54_2_a2/