Symmetry, Volume 9, Issue 2 (February 2017) – 9 articles

In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equation, for the first time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the first time, we construct the conservation laws of the underlying equation using the multiplier method. Full article

In this paper, a symmetry particle method, the smoothed particle hydrodynamics (SPH) method, is extended to deal with non‐Newtonian fluids. First, the viscous liquid is modeled by a non‐Newtonian fluid flow and the variable viscosity under shear stress is determined by the Carreau‐Yasuda model. Then a pressure correction method is proposed, by correcting density error with individual stiffness parameters for each particle, to ensure the incompressibility of fluid. Finally, an implicit method is used to improve efficiency and stability. It is found that the nonNewtonian behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and efficient. Full article

Deformable objects have changeable shapes and they require a different method of matching algorithm compared to rigid objects. This paper proposes a fast and robust deformable object matching algorithm. First, robust feature points are selected using a statistical characteristic to obtain the feature points with the extraction method. Next, matching pairs are composed by the feature point matching of two images using the matching method. Rapid clustering is performed using the BST (Binary Search Tree) method by obtaining the geometric similarity between the matching pairs. Finally, the matching of the two images is determined after verifying the suitability of the composed cluster. An experiment with five different image sets with deformable objects confirmed the superior robustness and independence of the proposed algorithm while demonstrating up to 60 times faster matching speed compared to the conventional deformable object matching algorithms. Full article

Sparse representations are widely used tools in image super-resolution (SR) tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, the assumption may not always hold. In this paper, we propose a novel method for single image super-resolution (SISR). Unlike most prior sparsity-based SR methods, the proposed method uses non-linear sparse representation to enhance the description of the non-linear information in images, and the proposed framework does not need to assume the self-similarity of image patches. Based on the minimum reconstruction errors, support vector regression (SVR) is applied for predicting the SR image. The proposed method was evaluated on various benchmark images, and promising results were obtained. Full article

This study proposes gaze-based hand interaction, which is helpful for improving the user’s immersion in the production process of virtual reality content for the mobile platform, and analyzes efficiency through an experiment using a questionnaire. First, three-dimensional interactive content is produced for use in the proposed interaction experiment while presenting an experiential environment that gives users a high sense of immersion in the mobile virtual reality environment. This is designed to induce the tension and concentration of users in line with the immersive virtual reality environment. Additionally, a hand interaction method based on gaze—which is mainly used for the entry of mobile virtual reality content—is proposed as a design method for immersive mobile virtual reality environment. The user satisfaction level of the immersive environment provided by the proposed gaze-based hand interaction is analyzed through experiments in comparison with the general method that uses gaze only. Furthermore, detailed analysis is conducted by dividing the effects of the proposed interaction method on user’s psychology into positive factors such as immersion and interest and negative factors such as virtual reality (VR) sickness and dizziness. In this process, a new direction is proposed for improving the immersion of users in the production of mobile platform virtual reality content. Full article

The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the $2n$ -th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmetry $D_n$ or $D_{2n}$ , i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry $D_n$ or $D_{2n}$ only by iteration of substitution rules on a single tile. Full article