Roussos-Maragos Tensor-Driven Diffusion for Image Interpolation

Roussos and Maragos proposed a method for image interpolation in "Reversible interpolation of vectorial images by an anisotropic diffusion-projection PDE." An earlier version was also published in conference paper (Roussos and Maragos, "Vector-Valued Image Interpolation by an Anisotropic Diffusion-Projection PDE," 2007). Given a discretely sampled image v, the method finds an image u such that v(n) = (h * u)(n), for all n in Z2, where h is the (assumed known) point spread function and * denotes convolution. The method is inspired by tensor-driven diffusion works of Tschumperlé and Weickert. Roussos and Maragos propose interpolation by evolving a diffusion equation to steady state, dt u = P0(div(T gradient(u)), where T is a tensor determined from image structure tensor and the diffusion is orthogonally projected to agree with the observed data. This diffusion is based on the general anisotropic diffusion model proposed by Weickert. The method can be applied to grayscale, color, or general vector-valued images.

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