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
Variational methods in image segmentation
Variational methods in image segmentation
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
From High Energy Physics to Low Level Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
A Natural Norm for Color Processing
ACCV '98 Proceedings of the Third Asian Conference on Computer Vision-Volume I - Volume I
Images as embedding maps and minimal surfaces: movies, color, and volumetric medical images
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A general framework for low level vision
IEEE Transactions on Image Processing
Modified curvature motion for image smoothing and enhancement
IEEE Transactions on Image Processing
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Geometry Motivated Variational Segmentation for Color Images
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Deep structure from a geometric point of view
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
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We merge techniques developed in the Beltrami framework to deal with multi-channel, i.e. color images, and the Mumford-Shah functional for segmentation. The result is a color image enhancement and segmentation algorithm. The generalization of the Mumford-Shah idea includes a higher dimension and codimension and a novel smoothing measure for the color components and for the segmenting function which is introduced via the Γ-convergence approach. We use the Γ-convergence technique to derive, through the gradient descent method, a system of coupled PDEs for the color coordinates and for the segmenting function.