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Abstract. In this paper, a region-based shock-diffusion equation is presented for image denoising and edge sharpening. An image is divided into three-type different regions according to image features: edges, textures and details, and flat areas. For edges, a shock-type backward diffusion is performed in the gradient direction to the isophote line (edge), incorporating a forward diffusion in the isophote line direction; while for textures and details, a soft backward diffusion is done to enhance image features preserving a natural transition. Moreover, an isotropic diffusion is used to smooth flat areas simultaneously. Finally, a shock capturing scheme with a special limiter function is developed to speed the process with numerical stability. Experiments on real images show that this method produces better visual results of the enhanced images than some related equations.

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Most image interpolation algorithms currently used suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This letter presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the isophote lines (edges), while a normal diffusion is done to remove artifacts ("jaggies") along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first order and the second order directional derivatives of the image. Experimental results on the Lena image demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

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