Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
An introduction to wavelets
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image processing: flows under min/max curvature and mean curvature
Graphical Models and Image Processing
A New Interpretation and improvement of the Nonlinear Anisotropic Diffusion for Image Enhancement
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
A Review of Nonlinear Diffusion Filtering
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Formation of Step Images During Anisotropic Diffusion
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 3 - Volume 3
Behavioral analysis of anisotropic diffusion in image processing
IEEE Transactions on Image Processing
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
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Any image filtering operator designed for automatic shape restoration should satisfy robustness (whatever the nature and degree of noise is) as well as non-trivial smooth asymptotic behavior. Moreover, a stopping criterion should be determined by characteristics of the evolved image rather than dependent on the number of iterations. Among the several PDE based techniques, curvature flows appear to be highly reliable for strongly noisy images compared to image diffusion processes.In the present paper, we introduce a regularized curvature flow (RCF) that admits non-trivial steady states. It is based on a measure of the local curve smoothness that takes into account regularity of the curve curvature and serves as stopping term in the mean curvature flow. We prove that this measure decreases over the orbits of RCF, which endows the method with a natural stop criterion in terms of the magnitude of this measure. Further, in its discrete version it produces steady states consisting of piece-wise regular curves. Numerical experiments made on synthetic shapes corrupted with different kinds of noise show the abilities and limitations of each of the current geometric flows and the benefits of RCF. Finally, we present results on real images that illustrate the usefulness of the present approach in practical applications.