GRADE: Gibbs Reaction and Diffusion Equations
Recently there have been increasing interests in using nonlinear PDEs for applications in computer vision an.d image processing, in this paper, we propose a general statistical framework for designing a new class of PDEs. For a given application, a Markov random jield model p(1) as learned according to the minimax entropy principle studied in[25][26], so that p(1) should characterize the ensemble of images in our application. p(1) 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. W e call this new class of PDEs the Gibbs Reaction And’Diffusion Equations-GRADE and we demonstrate experiments where G R A D E are used for texture pattern formation, denoising, image enhancement, and clutter removal.