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Journal of Computational Physics
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IEEE Transactions on Pattern Analysis and Machine Intelligence
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SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Image processing: flows under min/max curvature and mean curvature
Graphical Models and Image Processing
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
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Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
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A Natural Norm for Color Processing
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
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IEEE Transactions on Image Processing
Modified curvature motion for image smoothing and enhancement
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Fast Evolution of Image Manifolds and Application to Filtering and Segmentation in 3D Medical Images
IEEE Transactions on Visualization and Computer Graphics
Robust Estimation of Adaptive Tensors of Curvature by Tensor Voting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tensor-based brain surface modeling and analysis
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part I
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The Beltrami flow [13,14] is one of the most effective denoising algorithms in image processing. For gray-level images, we show that the Beltrami flow equation can be arranged in a reaction-diffusion form. This reveals the edge-enhancing properties of the equation and suggests the application of additive operator split (AOS) methods [4,5] for faster convergence. As we show with numerical simulations, the AOS method results in an unconditionally stable semi-implicit linearized difference scheme in 2D and 3D. The values of the edge indicator function are used from the previous step in scale, while the pixel values of the next step are used to approximate the flow. The optimum ratio between the reaction and diffusion counterparts of the governing PDE is studied, in order to achieve a better quality of segmentation. The computational time decreases by a factor of ten, as compared to the explicit scheme. For 2D color images, the Beltrami flow equations are coupled, and do not yield readily to the AOS technique. However, in the proximity of an edge, the cross-products of color gradients nearly vanish, and the coupling becomes weak. The principal directions of the edge indicator matrix are normal and tangent to the edge. Replacing the action of the matrix on the gradient vector by an action of its eigenvalue, we reduce the color problemto the gray level case with a reasonable accuracy. The scalar edge indicator function for the color case becomes essentially the same as that for the gray level image, and the fast implicit technique is implemented.