Multiseeded Segmentation Using Fuzzy Connectedness
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Variational Approach to Maximum a Posteriori Estimation for Image Denoising
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Low Bit Rate Image Coding in the Scale Space
DCC '02 Proceedings of the Data Compression Conference
Smart Nonlinear Diffusion: A Probabilistic Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric Analysis of Particle Motion in a Vector Image Field
Journal of Mathematical Imaging and Vision
Theoretical foundations for spatially discrete 1-D shock filtering
Image and Vision Computing
Staircasing in semidiscrete stabilised inverse linear diffusion algorithms
Journal of Computational and Applied Mathematics
A nonlinear entropic variational model for image filtering
EURASIP Journal on Applied Signal Processing
Theoretical Foundations for Discrete Forward-and-Backward Diffusion Filtering
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
The dynamics of image processing viewed as deformation of elastic sheet
DSP'09 Proceedings of the 16th international conference on Digital Signal Processing
Equivalence results for TV diffusion and TV regularisation
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Anti-diffusion method for interface steepening in two-phase incompressible flow
Journal of Computational Physics
Approximate methods for constrained total variation minimization
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Stabilised nonlinear inverse diffusion for approximating hyperbolic PDEs
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Novel schemes for hyperbolic PDEs using osmosis filters from visual computing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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We introduce a family of first-order multidimensional ordinary differential equations (ODEs) with discontinuous right-hand sides and demonstrate their applicability in image processing. An equation belonging to this family is an inverse diffusion everywhere except at local extrema, where some stabilization is introduced. For this reason, we call these equations “stabilized inverse diffusion equations” (SIDEs). Existence and uniqueness of solutions, as well as stability, are proven for SIDEs. A SIDE in one spatial dimension may be interpreted as a limiting case of a semi-discretized Perona-Malik equation (1990, 19994). In an experiment, SIDE's are shown to suppress noise while sharpening edges present in the input signal. Their application to image segmentation is also demonstrated