Accelerating Computation of Zernike and Pseudo-Zernike Moments with a GPU Algorithm

Although Zernike and pseudo-Zernike moments have some advanced properties, the computation process is generally very time-consuming, which has limited their practical applications. To improve the computational efficiency of Zernike and pseudo-Zernike moments, in this research, we have explored the use of GPU to accelerate moments computation, and proposed a GPUaccelerated algorithm. The newly developed algorithm is implemented in Python and CUDA C++ with optimizations based on symmetric properties and k × k sub-region scheme. The experimental results are encouraging and have shown that our GPU-accelerated algorithm is able to compute Zernike moments up to order 700 for an image sized at 512 × 512 in 1.7 seconds and compute pseudo-Zernike moments in 3.1 seconds. We have also verified the accuracy of our GPU algorithm by performing image reconstructions from the higher orders of Zernike and pseudo-Zernike moments. For an image sized at 512 × 512, with the maximum order of 700 and k = 11, the PSNR (Peak Signal to Noise Ratio) values of its reconstructed versions from Zernike and pseudo-Zernike moments are 44.52 and 46.29 separately. We have performed image reconstructions from partial sets of Zernike and pseudo-Zernike moments with various order n and different repetition m. Experimental results of both Zernike and pseudo-Zernike moments show that the images reconstructed from the moments of lower and higher orders preserve the principle contents and details of the original image respectively, while moments of positive and negative m result in identical images. Lastly, we have proposed a set of feature vectors based on pseudo-Zernike moments for Chinese character recognition. Three different feature vectors are composed of different parts of four selected lower pseudo-Zernike moments. Experiments on a set of 6,762 Chinese characters show that this method performs well to recognize similar-shaped Chinese characters.Master of Science in Applied Computer Scienc

Sufficient conditions for super k-restricted edge connectivity in graphs of diameter 2

AbstractFor a connected graph G=(V,E), an edge set S⊆E is a k-restricted edge cut if G−S is disconnected and every component of G−S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G)=min{|[X,X¯]|:|X|=k,G[X]is connected}. G is λk-optimal if λk(G)=ξk(G). Moreover, G is super-λk if every minimum k-restricted edge cut of G isolates one connected subgraph of order k. In this paper, we prove that if |NG(u)∩NG(v)|≥2k−1 for all pairs u, v of nonadjacent vertices, then G is λk-optimal; and if |NG(u)∩NG(v)|≥2k for all pairs u, v of nonadjacent vertices, then G is either super-λk or in a special class of graphs. In addition, for k-isoperimetric edge connectivity, which is closely related with the concept of k-restricted edge connectivity, we show similar results

Analyzing and Improving Generative Adversarial Training for Generative Modeling and Out-of-Distribution Detection

Generative adversarial training (GAT) is a recently introduced adversarial defense method. Previous works have focused on empirical evaluations of its application to training robust predictive models. In this paper we focus on theoretical understanding of the GAT method and extending its application to generative modeling and out-of-distribution detection. We analyze the optimal solutions of the maximin formulation employed by the GAT objective, and make a comparative analysis of the minimax formulation employed by GANs. We use theoretical analysis and 2D simulations to understand the convergence property of the training algorithm. Based on these results, we develop an incremental generative training algorithm, and conduct comprehensive evaluations of the algorithm's application to image generation and adversarial out-of-distribution detection. Our results suggest that generative adversarial training is a promising new direction for the above applications

Rarefication effects on jet impingement loads

Rarefication effects on jet impingement loads are studied by comparing recent new formulas at the collisionless flow limit and numerical simulations. The jet exit size is finite, and can be either planar or round. In the simulations, the jets have different degrees of rarefication, with a Knudsen (Kn) number ranging from 0 to infinity; i.e., the jet flows can be continuum, collisional, or collisionless. The comparison results indicate that (1) the new surface load formulas are accurate at the collisionless flow limit; (2) in general, the formulas offer upper limits for the peak loads; (3) however, it is improper to assert that local loads always decrease. The new formulas can offer fast estimations of impingement loads. This may be quite helpful for applications in space engineering by significantly reducing the amount of simulations and experiment costs. Those expressions explicitly include non-dimensional parameters, and their contribution and influence on the loads can be studied in a systematic manner (e.g., with a swift parameter study)

Effect of the Steam Activation Thermal Treatment on the Microstructure of Continuous TiO 2

The continuous TiO2 fibers have been synthesized by the sol-gel method using the polymer of titanate as the precursor solution. The as-synthesized samples were characterized using XRD, SEM, and HR-TEM analysis methods. The grain growth kinetics was primarily investigated. The results demonstrated that the average diameters of the fibers were in the range of 20–30 μm, the crystal phase of the synthesized TiO2 fiber was transformed from anasate to rutile, and the crystal size became bigger with increasing the temperature using steam activation. The growth exponent and the constant of growth rate of the rutile crystal phase at 500°C were 4 and 2.55×106 nm/h, respectively. The activation energies of crystalline growth during 500°C~700°C and 700°C~800°C were 38.62 kJ/mol and 143.91 kJ/mol, respectively

Optimization of Forged 42CrMo4 Steel Piston Pin Hole Profile Using Finite Element Method

The fatigue failure of the piston pin hole is considered as a key factor affecting the service life of engines. In this work, the piston pin hole profile was designed as tapered shape following a power law. By combining finite element analysis and hydraulic pulsating fatigue tests, the pin hole profile was optimized. It has been found that the maximum contact pressure on the pin hole surface was reduced by 16,7% with appropriate increasing the radius enlarging rate of the piston pin hole, the maximum tensile stress of the piston pin seat was reduced by 13,1%, and the piston pin seat fatigue safety factor was increased by 41,4%, the piston pin hole fatigue safety factor was increased by 15,9%. The piston pin hole’s hydraulic pulsating fatigue test results were found to be consistent with the FEA results. It could be concluded that appropriate increasing the radius enlarging rate of the pin hole could significantly weaken the fatigue wear of the pin hole, further improving its fatigue resistance