Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stochastic Motion and the Level Set Method in Computer Vision: Stochastic Active Contours
International Journal of Computer Vision
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Stochastic differential equations and geometric flows
IEEE Transactions on Image Processing
Euler's approximations to image reconstruction
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
Application of backward stochastic differential equations to reconstruction of vector-valued images
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
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In this paper we propose a novel approach for reconstruction of images with additive Gaussian noise. In order to solve this inverse problem we use backward stochastic differential equations. Model of the image reconstruction is driven by two stochastic processes. One process has values in domain of the image, and second one in codomain. Appropriate construction of these processes leads to smoothing (anisotropic diffusion) and enhancing filters. Our numerical experiments show that the new algorithm gives very good results and compares favourably with classical Perona-Malik method.