Region-Based Shock-Diffusion Equation for Adaptive Image Enhancement

Abstract

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.

Shock filter coupled to curvature diffusion for image denoising and sharpening

“…It is easy to remark that Alvarez-Mazorra created homogeneous blobs, while Kornprobst and Gilboa models smoothed noise, with some blurring of geometrical objects. Fu filter has successfully eliminated noise in flat areas but as mentioned in [8], it created a strong shock due to the oscillations at big edges, which make this scheme instable. The second experiment is on Cameraman image blurred (r = 1) and noised with SNR = 11.80.…”

“…In a recent work [8], Fu developed a region-based shock-diffusion scheme. This filter is a deep study of models (12) and (13), directional diffusion and shock terms are factored by adaptive weights.…”

“…Hence, many researches using a selective smoothing operation have been developed in order to solve this problem, and some satisfactory results have been reported [3,4]. Among the existing restoration algorithms, the approach that bases a selective smoothing procedure on partial differential equations (PDEs) has attracted a lot of attentions in recent years [5][6][7][8]. In this context, a large number of techniques based on PDEs has been proposed.…”

Adaptive shock filter for image super-resolution and enhancement

“…After that, image segmentation was adopted to improve the shock filtering model [13,15], where the diffusion term and the shock filter term were separately assigned with different weights. Kornprobst and Deriche [13] proposed the improved shock filtering model in the following formula:…”

“…This method can avoid the blurring artifacts, but it also causes loss of abundant details. Fu et al [15,16] proposed a regionbased shock filtering for adaptive image enhancement. The artificial effects are decreased by use of continuous weight.…”