Image Scale-Space Filtering Using Directional Local Variance Controlled Anisotropic Diffusion

The purpose of this paper is to develop an effective edge indicator and propose an image scale-space filter based on anisotropic diffusion equation for image denoising. We first develop an effective edge indicator named directional local variance (DLV) for detecting image features, which is anisotropic and robust and able to indicate the orientations of image features. We then combine two edge indicators (i.e., DLV and local spatial gradient) to formulate the desired image scale-space filter and incorporate the modulus of noise magnitude into the filter to trigger time-varying selective filtering. Moreover, we theoretically show that the proposed filter is robust to the outliers inherently. A series of experiments are conducted to demonstrate that the DLV metric is effective for detecting image features and the proposed filter yields promising results with higher quantitative indexes and better visual performance, which surpass those of some benchmark models.

Fractional-order difference curvature-driven fractional anisotropic diffusion equation for image super-resolution

Image super-resolution methods-based existing edge indicating operators — namely Gauss curvature, mean curvature and gradient — cannot effectively identify the edges, ramps and flat regions and suffer from the loss of fine textures. To address these issues, this paper presents a fractional anisotropic diffusion equation based on a new edge indicator, named fractional-order difference curvature, which can characterize the intensity variations in images. We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform, which is easy to implement numerically. The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures. Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.