Toward a Full Probability Model of Edges in Natural Images
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
The Nonlinear Statistics of High-Contrast Patches in Natural Images
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Minimax Entropy and Learning by Diffusion
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
The Minimal Local-Asperity Hypothesis of Early Retinal Lateral Inhibition
Neural Computation
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Recently there have been increasing interest in using nonlinear PDEs for applications in computer vision and image processing, in this paper, we propose a general statistical framework for designing a new class of PDEs. For a given applications, a Markov random field model p(I) is learned according to the minimax entropy principle studied in [25] [26], so that p(I) should characterize the ensemble of images in our application. p(I) is a Gibbs distribution whose energy terms can be divided into two categories. Subsequently the partial differential equations given by gradient descent on the Gibbs potential are essentially reaction-diffusion equations, where the energy terms in one category produce anisotropic diffusion while the inverted energy terms in the second category produce reaction associated with pattern formation. We call this new class of PDEs the Gibbs Reaction And Diffusion Equations 驴 GRADE and we demonstrate experiments where GRADE are used for texture pattern formation, denoising, image enhancements, and clutter removal.