Scale Invariant Technique Research Articles

WMCP-EM: An integrated dehazing framework for visibility restoration in single image

Adopting local patches for varying haze conditions is crucial for optimizing the performance in single image dehazing. We propose a novel two-fold method with a prime focus on self-adaptive prior named Weighted Median Channel Prior (WMCP) to resolve the problems introduced by using a fixed size local-patch in the dehazing process. WMCP works by leveraging the spatially changing haze statistics such as inclusion–exclusion of related pixels for estimating depth-map in varying haze conditions. It is a scale-invariant technique that retains most of the information present in the local neighbourhood of the hazy input image for estimating scene depth, which traditional methods generally fail to preserve. In addition, an unsharp-masking based technique called edge-modulation (EM) promotes hidden or missing details such as microscopic edges and textures lost due to haze, making this scheme beneficial in ensuring a visually aesthetic and realistic dehazed image. This research also includes a set of ablation tests to assess the contributions of each module engaged in the dehazing process. We performed a comparative evaluation of our method with several state-of-the-art techniques, revealing its superiority in terms of visibility improvement and edge preservation, especially when the dense haze regions are taken into consideration.

Scale-Wise Convolution for Image Restoration

While scale-invariant modeling has substantially boosted the performance of visual recognition tasks, it remains largely under-explored in deep networks based image restoration. Naively applying those scale-invariant techniques (e.g., multi-scale testing, random-scale data augmentation) to image restoration tasks usually leads to inferior performance. In this paper, we show that properly modeling scale-invariance into neural networks can bring significant benefits to image restoration performance. Inspired from spatial-wise convolution for shift-invariance, “scale-wise convolution” is proposed to convolve across multiple scales for scale-invariance. In our scale-wise convolutional network (SCN), we first map the input image to the feature space and then build a feature pyramid representation via bi-linear down-scaling progressively. The feature pyramid is then passed to a residual network with scale-wise convolutions. The proposed scale-wise convolution learns to dynamically activate and aggregate features from different input scales in each residual building block, in order to exploit contextual information on multiple scales. In experiments, we compare the restoration accuracy and parameter efficiency among our model and many different variants of multi-scale neural networks. The proposed network with scale-wise convolution achieves superior performance in multiple image restoration tasks including image super-resolution, image denoising and image compression artifacts removal. Code and models are available at: https://github.com/ychfan/scn_sr.

Study of structural and surface morphological properties of Tb doped ZnO nanoparticles using XRD, XPS and fractal analysis

A systematic study was performed on Tb3+ doped ZnO nanoparticles of different mole-fraction using Atomic Force Microscopy (AFM), X-ray Diffraction (XRD) and X-ray Photoemission Spectroscopy (XPS) measurements. XRD studies confirm that all the samples are in wurtzite phase. XRD analysis suggests a compressive lattice strain as doping concentration increases. The strain generated in the doped samples is found to be more as compared to pure nanoparticle samples. XPS result indicates the presence of several oxygen species adsorbed on the surface. Furthermore, the effect of incorporation of Tb3+ ions into ZnO nanoparticles was explored using fractal analysis approach to extract the quantitative surface parameters. The fractal dimension is a scale invariant technique for representation and understanding of surface morphology of nanostructures. Fractal dimension provides a clear distinction between vertical and horizontal properties of the surfaces and their correlation. This technique could be very useful in selecting the suitable substrate for various technological applications. The lateral correlation length was estimated by auto-correlation function. While, the roughness exponent and fractal dimension were calculated from height-height correlation function. Moreover, this study reveals that the complexity of surface increases with doping. Moreover, as doping increases, the surface becomes more and more zagged as compared to pure samples.

The polynomial approximate common divisor problem and its application to the fully homomorphic encryption

We propose and examine the approximate polynomial common divisor problem, which can be viewed as a polynomial analogue to the approximate integer common divisor problem. Since our problem is rather new, we perform extensive cryptanalysis, applying various known attacks against the structurally similar problems. Moreover, we propose a small root finding algorithm for multivariate modular equation system, and apply it to the proposed problem. Those analyses confirm that the proposed problem is difficult with appropriate parameters.Additionally, we construct a simple somewhat homomorphic encryption scheme, which can efficiently accommodate large message spaces. When the evaluation of a low degree polynomial of very large integers is required, our scheme is more efficient than the recent RLWE-based scheme, YASHE, by Bos et al. (2013). In particular, multiplication is ten times faster when evaluating degree-10 polynomial of 1638-bit integers. We convert this scheme to a leveled fully homomorphic encryption scheme by applying Brakerski’s scale invariant technique, and the resulting scheme has features similar to the variant of van Dijk et al.’s scheme by Coron et al. (2014). Our scheme, however, does not use the subset sum, which makes its design much simpler.

A rotation and scale invariant technique for ear detection in 3D

This paper presents a technique for automatic ear detection from 3D profile face range images. The proposed technique localizes ear by using inherent structural details of the ear in 3D range data and is invariant to rotation and scale. It makes use of connected components of a graph constructed using the edges of the depth map image of the range data. The main advantages of the proposed technique over other existing techniques are of two folds. First, the proposed technique does not require any registered 2D image for the detection of ear in 3D. Second, it is inherently rotation and scale invariant and can detect left and right ear simultaneously without imposing any additional computational cost. To demonstrate the effectiveness of the technique, experiments are conducted on University of Notre Dame public database, Collection J2 (UND-J2) which consists of 3D profile face range images with scale and pose variations. Experimental results are found to be encouraging and reveal the effectiveness of the proposed technique. Results are also compared with the existing 3D ear detection techniques.

Image scale determination for optimal texture classification using coordinated clusters representation

The efficiency of texture image classification is certainly influenced by image scale when a feature space or a classification method is not scale invariant. An alternative approach to the scale-invariant techniques is proposed that first estimates an effective image scale and then uses it to adjust texture features to get the best possible texture image recognition and classification. We use the correlation distance between pixels as a measure of the scale of texture images. We study the performance of classification of texture images in the coordinated cluster representation (CCR) versus an image scale and the size of the scanning window used for the coordinated cluster transform. Given the number of classes to be classified in, we find that an optimal (up to 100%) classification efficiency in the CCR feature space is obtained by changing an image scale and/or the size of the scanning window in the coordinated cluster transform.

On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance

AbstractAfter formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.