Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visual reconstruction
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
Parallel and Deterministic Algorithms from MRFs: Surface Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Journal on Applied Mathematics
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
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The Perona---Malik equation (PM), in the continuum limit, is interpreted as the gradient flow for a functional, corresponding to the reconstruction of an image with edges with non-zero thickness. This result is based on an image model (u,Γ) where Γ is an edge set, and u is a slowly-varying function. PM simplifies the image by reducing the jump across each component of Γ, resulting in an automatic edge pruning procedure. The initial-value problem thus defined is well-posed, but practically stable only for small times: it leads to a semi-group with exponential growth. The rigorous analysis gives a mathematical basis for empirical observations, including edge localization and the need to use a small number of iterations. The variational formulation enables an easy comparison with earlier methods.