Adaptive rational fractal interpolation function for image super-resolution via local fractal analysis

© 2019 Elsevier B.V. Image super-resolution aims to generate high-resolution image based on the given low-resolution image and to recover the details of the image. The common approaches include reconstruction-based methods and interpolation-based methods. However, these existing methods show difficulty in processing the regions of an image with complicated texture. To tackle such problems, fractal geometry is applied on image super-resolution, which demonstrates its advantages when describing the complicated details in an image. The common fractal-based method regards the whole image as a single fractal set. That is, it does not distinguish the complexity difference of texture across all regions of an image regardless of smooth regions or texture rich regions. Due to such strong presumption, it causes artificial errors while recovering smooth area and texture blurring at the regions with rich texture. In this paper, the proposed method produces rational fractal interpolation model with various setting at different regions to adapt to the local texture complexity. In order to facilitate such mechanism, the proposed method is able to segment the image region according to its complexity which is determined by its local fractal dimension. Thus, the image super-resolution process is cast to an optimization problem where local fractal dimension in each region is further optimized until the optimization convergence is reached. During the optimization (i.e. super-resolution), the overall image complexity (determined by local fractal dimension) is maintained. Compared with state-of-the-art method, the proposed method shows promising performance according to qualitative evaluation and quantitative evaluation

Wetting, roughness and flow boundary conditions

We discuss how the wettability and roughness of a solid impacts its hydrodynamic properties. We see in particular that hydrophobic slippage can be dramatically affected by the presence of roughness. Owing to the development of refined methods for setting very well-controlled micro- or nanotextures on a solid, these effects are being exploited to induce novel hydrodynamic properties, such as giant interfacial slip, superfluidity, mixing, and low hydrodynamic drag, that could not be achieved without roughness.Comment: 28 pages, 14 figures, 4 tables; accepted for publication in Journal of Physics: Condensed Matte

Single-image super-resolution using sparsity constraints and non-local similarities at multiple resolution scales

Traditional super-resolution methods produce a clean high-resolution image from several observed degraded low-resolution images following an acquisition or degradation model. Such a model describes how each output pixel is related to one or more input pixels and it is called data fidelity term in the regularization framework. Additionally, prior knowledge such as piecewise smoothness can be incorporated to improve the image restoration result. The impact of an observed pixel on the restored pixels is thus local according to the degradation model and the prior knowledge. Therefore, the traditional methods only exploit the spatial redundancy in a local neighborhood and are therefore referred to as local methods. Recently, non-local methods, which make use of similarities between image patches across the whole image, have gained popularity in image restoration in general. In super-resolution literature they are often referred to as exemplar-based methods. In this paper, we exploit the similarity of patches within the same scale (which is related to the class of non-local methods) and across different resolution scales of the same image (which is also related to the fractal-based methods). For patch fusion, we employ a kernel regression algorithm, which yields a blurry and noisy version of the desired high-resolution image. For the final reconstruction step, we develop a novel restoration algorithm. The joint deconvolution/denoising algorithm is based on the split Bregman iterations and, as prior knowledge, the algorithm exploits the sparsity of the image in the shearlet-transformed domain. Initial results indicate an improvement over both classical local and state-of-the art non-local super-resolution methods

A novel disparity-assisted block matching-based approach for super-resolution of light field images

Currently, available plenoptic imaging technology has limited resolution. That makes it challenging to use this technology in applications, where sharpness is essential, such as film industry. Previous attempts aimed at enhancing the spatial resolution of plenoptic light field (LF) images were based on block and patch matching inherited from classical image super-resolution, where multiple views were considered as separate frames. By contrast to these approaches, a novel super-resolution technique is proposed in this paper with a focus on exploiting estimated disparity information to reduce the matching area in the super-resolution process. We estimate the disparity information from the interpolated LR view point images (VPs). We denote our method as light field block matching super-resolution. We additionally combine our novel super-resolution method with directionally adaptive image interpolation from [1] to preserve sharpness of the high-resolution images. We prove a steady gain in the PSNR and SSIM quality of the super-resolved images for the resolution enhancement factor 8x8 as compared to the recent approaches and also to our previous work [2]

Wetting, roughness and hydrodynamic slip

The hydrodynamic slippage at a solid-liquid interface is currently at the center of our understanding of fluid mechanics. For hundreds of years this science has relied upon no-slip boundary conditions at the solid-liquid interface that has been applied successfully to model many macroscopic experiments, and the state of this interface has played a minor role in determining the flow. However, the problem is not that simple and has been revisited recently. Due to the change in the properties of the interface, such as wettability and roughness, this classical boundary condition could be violated, leading to a hydrodynamic slip. In this chapter, we review recent advances in the understanding and expectations for the hydrodynamic boundary conditions in different situations, by focussing mostly on key papers from past decade. We highlight mostly the impact of hydrophobicity, roughness, and especially their combination on the flow properties. In particular, we show that hydrophobic slippage can be dramatically affected by the presence of roughness, by inducing novel hydrodynamic phenomena, such as giant interfacial slip, superfluidity, mixing, and low hydrodynamic drag. Promising directions for further research are also discussed.Comment: 36 pages, 19 figures. This chapter would be a part of "Nanoscale liquid interfaces" boo