Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
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
Signals & systems (2nd ed.)
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Subjective Surfaces: A Geometric Model for Boundary Completion
International Journal of Computer Vision
Geometric Level Set Methods in Imaging,Vision,and Graphics
Geometric Level Set Methods in Imaging,Vision,and Graphics
On the Foundations of Vision Modeling III. Noncommutative Monoids of Occlusive Preimages
Journal of Mathematical Imaging and Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
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In visual cognition, illusions help elucidate certain intriguing latent perceptual functions of the human vision system, and their proper mathematical modeling and computational simulation are therefore deeply beneficial to both biological and computer vision. Inspired by existent prior works, the current paper proposes a first-order energy-based model for analyzing and simulating illusory contours. The lower complexity of the proposed model facilitates rigorous mathematical analysis on the detailed geometric structures of illusory contours. After being asymptotically approximated by classical active contours, the proposed model is then robustly computed using the celebrated level-set method of Osher and Sethian [S. Osher, J.A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (12) (1988) 12-49] with a natural supervising scheme. Potential cognitive implications of the mathematical results are addressed, and generic computational examples are demonstrated and discussed.