Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
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
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Constrained Restoration and the Recovery of Discontinuities
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
Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
International Journal of Computer Vision
Prior Learning and Gibbs Reaction-Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Interpretation and improvement of the Nonlinear Anisotropic Diffusion for Image Enhancement
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Relaxation: Restoration and Feature Extraction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized Spatio-Chromatic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A stochastic diffusion approach to signal denoising
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 04
Bridging scale-space to multiscale frame analyses
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 03
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way
Behavioral analysis of anisotropic diffusion in image processing
IEEE Transactions on Image Processing
Automatic target recognition organized via jump-diffusion algorithms
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image segmentation and edge enhancement with stabilized inverse diffusion equations
IEEE Transactions on Image Processing
Center-of-mass variation under projective transformation
Pattern Recognition Letters
Graph spectral image smoothing using the heat kernel
Pattern Recognition
Building Blocks for Computer Vision with Stochastic Partial Differential Equations
International Journal of Computer Vision
A smart stochastic approach for manifolds smoothing
SGP '08 Proceedings of the Symposium on Geometry Processing
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Abstract--In this paper, a stochastic interpretation of nonlinear diffusion equations used for image filtering is proposed. This is achieved by relating the problem of evolving/smoothing images to that of tracking the transition probability density functions of an underlying random process. We show that such an interpretation of, e.g., Perona-Malik equation, in turn allows additional insight and sufficient flexibility to further investigate some outstanding problems of nonlinear diffusion techniques. In particular, upon unraveling the limitations as well as the advantages of such an equation, we are able to propose a new approach which is demonstrated to improve performance over existing approaches and, more importantly, to lift the longstanding problem of a stopping criterion for a nonlinear evolution equation with no data term constraint. Substantiating examples in image enhancement and segmentation are provided.