Study On Geometry Driven Image Enhancement Based On Self-similarity Filtering

In image acquisition and transmission process, blur and noise are in-evitable due to imaging devices and imaging conditions, so image is often degraded. Eliminating these factors of image degradation and enhancing im-age features, in order to be convenient for people to interpret and for machine to further processing, are an important research field in digital image pro-cessing. Therefore, researchers have proposed many methods, for example, variational and partial differential equation method, the sparse representation method and statistical method etc.. However, eliminating the interference and maintaining and enhancing image features as a key problem have not been completely solved.The local and nonlocal filtering methods based on self-similarity and re-dundant information have a huge impact on image enhancement, especially for texture images. In this paper, based on differential geometric features, and taking comprehensively advantage of self-similarity and limited flux technique, we achieve good results for enhancing different noise and blurred images with adaptive methods.Specifically, we carry out the following innovative works for the filed of image enhancement.For the image that is lightly blurred and polluted by noise, a ge-ometry driven image enhancement based on self-similarity filtering. The bilateral filter structures the weight function for the pixels’proximity and the gray values’similarity, through the normalized weighted average arith-metic, in order to de-noise and enhance image. But for the blurred image, this algorithm does not work on feature sharpening. We use the step edge of one-dimensional blurred model, observe and study the one order and two order derivative properties, then structure the selective offset component, embedded it into the gray-similarity terms of the bilateral filtering, so that the values of the pixels on edge will adjusted up or down, which reduce the width of edge, then we can get good effect on the enhancement of the edge sharpness.For the image that is lightly blurred and moderately polluted by noise, a self-similarity filtering with flux limit. The flux limiting tech-nology in computational fluid dynamics, which is based on the total variation diminishing of the fluid data, will get high resolution for fluid characteristic. For the edge of the image whose noise is larger, we use the flux limiting tech-nology to control the degree of edge sharpness’enhancement, to eliminate the overshoot and zigzag trace, then enhance the robustness of the edge sharpness. In addition, we use the non local averaging algorithm which is an efficient filter-ing for noisy image, combined with non sharpening template which is efficient for enhancement, adapt adjustment by the smoothing parameter, then we can obtain better image results.Detection of image features and adaptive processing are the key to the success of the algorithm. As a frontier research involves mathematics and information, this paper deepens the application of the differential geometry analysis and self-similarity processing in image enhancement, and has the im-portant theory and application value.