A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Image Deblurring in the Presence of Impulsive Noise
International Journal of Computer Vision
Image deblurring in the presence of salt-and-pepper noise
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Variational approach for edge-preserving regularization using coupled PDEs
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Variational denoising of partly textured images
Journal of Visual Communication and Image Representation
Mumford-Shah regularizer with contextual feedback
Journal of Mathematical Imaging and Vision
Ambrosio-tortorelli segmentation of stochastic images
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
From a modified ambrosio-tortorelli to a randomized part hierarchy tree
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
International Journal of Computer Vision
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
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As recently discussed by Bar, Kiryati, and Sochen in [3], the Ambrosio-Tortorelli approximation of the Mumford-Shah functional defines an extended line process regularization where the regularizer has an additional constraint introduced by the term ρ|∇υ|2. This term mildly forces some spatial organization by demanding that the edges are smooth. However, it does not force spatial coherence such as edge direction compatibility or edge connectivity, as in the traditional edge detectors such as Canny. Using the connection between regularization and diffusion filters, we incorporate further spatial structure into the regularization process of the Mumford-Shah model. The new model combines smoothing, edge detection and edge linking steps of the traditional approach to boundary detection. Importance of spatial coherence is best observed if the image noise is salt and pepper like. Proposed approach is able to deal with difficult noise cases without using non-smooth cost functions such as L1 in the data fidelity or regularizer.