IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection
Image and Vision Computing - Special issue on the first ECCV 1990
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
Nonlinear multiscale representations for image segmentation
Computer Vision and Image Understanding
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Gaussian Scale-Space Theory
Parallel Implementations of AOS Schemes: A Fast Way of Nonlinear Diffusion Filtering
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 3 - Volume 3
Information measures in scale-spaces
IEEE Transactions on Information Theory
Nonlinear image recovery with half-quadratic regularization
IEEE Transactions on Image Processing
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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We show that regularization methods can be regarded as scale-spaces where the regularization parameter serves as scale. In analogy to nonlinear diffusion filtering we establish continuity with respect to scale, causality in terms of a maximum-minimum principle, simplification properties by means of Lyapunov functionals and convergence to a constant steady-state. We identify nonlinear regularization with a single implicit time step of a diffusion process. This implies that iterated regularization with small regularization parameters is a numerical realization of a diffusion filter. Numerical experiments in two and three space dimensions illustrate the scale-space behaviour of regularization methods.