Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
Close-Form Solution and Parameter Selection for Convex Minimization-Based Edge-Preserving Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
Global Total Variation Minimization
SIAM Journal on Numerical Analysis
Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
Image segmentation and edge enhancement with stabilized inverse diffusion equations
IEEE Transactions on Image Processing
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Diffusion-Inspired Shrinkage Functions and Stability Results for Wavelet Denoising
International Journal of Computer Vision
Colour, texture, and motion in level set based segmentation and tracking
Image and Vision Computing
Image and Vision Computing
A four-pixel scheme for singular differential equations
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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It has been stressed that regularisation methods and diffusion processes approximate each other. In this paper we identify a situation where both processes are even identical: the space-discrete 1-D case of total variation (TV) denoising. This equivalence is proved by deriving identical analytical solutions for both processes. The temporal evolution confirms that space-discrete TV methods implement a region merging strategy with finite extinction time. Between two merging events, only extremal segments move. Their speed is inversely proportional to their size. Our results stress the distinguished nature of TV denoising. Furthermore, they enable a mutual transfer of all theoretical and algorithmic achievements between both techniques.