The application of improved block-matching method and block search method for the image motion estimation

Image block matching is one of the motion estimation methods for video inter-frame coding and digital image stabilization. The methods used for matching and searching will greatly affect the accuracy and speed of block matching. The block matching method based on the oblique vectors is suggested in this paper where matching parameters contain both horizontal and vertical vectors in the image blocks at the same time. Improved matching information can be obtained after making correlative calculations in the oblique direction. A novel search method of matching block based on the idea of simulated annealing is presented in this paper to improve the searching speed, accuracy and robustness in the fast operation of the block-matching motion estimation. The simulated annealing algorithm can easily escape from the trap of local minima effectively. With the two methods the block matching can be used for motion estimation at the real-time image processing system and high estimation accuracy can be achieved. An image stabilization system based on DSP (Digital Signal Processing) system is developed to verify this algorithm. Results show that both the matching accuracy and the search speed are improved with the methods presented.     

Ordered luminescent nanohybrid thin films of Eu(BA)3Phen nanoparticle in polystyrene matrix from diblock copolymer self-assembly

A simple route for fabricating highly ordered luminescent thin films based on hybrid material of diblock copolymer and europium complex, assisted with self-organization of polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymer upon solvent annealing, is presented. PS-b-PEO self-organized into hexagonal patterns and europium complex of Eu(BA)₃Phen was selectively embedded in PS blocks after solvent annealing in benzene or benzene/water vapor. During benzene annealing, the orientation of the PEO cylindrical domains strongly depended on the Eu(BA)₃Phen concentration. In contrast, when the hybrid thin films were annealed in mixture of benzene and water vapor, high degree of orientation of the PEO cylindrical domains is more easily obtained, which is independent of Eu(BA)₃Phen concentration. Furthermore, preferential interaction of PEO domains with water induces a generation of nanopores in the hybrid thin film. Atomic force microscopy (AFM), scanning electron microscopy (SEM), and transmission electron microscopy (TEM) were used to characterize the long-range lateral order and phase composition of the hybrid thin films. The ordered nanohybrid thin films kept the fluorescence property of Eu(BA)₃Phen and showed a strong red emission under the 254 nm light's irradiation. The fluorescence property was confirmed by photoluminescence (PL) spectra.     

On symmetric block triangular splitting iteration method for a class of complex symmetric system of linear equations

For solving a class of complex symmetric linear system, we first transform the system into a block two-by-two real formulation and construct a symmetric block triangular splitting (SBTS) iteration method based on two splittings. Then, eigenvalues of iterative matrix are calculated, convergence conditions with relaxation parameter are derived, and two optimal parameters are obtained. Besides, we present the optimal convergence factor and test two numerical examples to confirm theoretical results and to verify the high performances of SBTS iteration method compared with two classical methods.     

Covering and connectivity constraints in loop-based formulation of material flow network design in facility layout

The shortest loop covering at least one edge of each workcenter in a manufacturing facility layout is an instance of the generalized traveling salesman problem. The optimal solution to this problem is a promising design for non-vehicle-based material handling, typical of most types of conveyors and power-and-free systems, where the length of the path is the main driver of the total investment costs. The loop formulation is usually embedded within a larger problem of the concurrent design of the loop and the input/output stations for vehicle-based material handling typical of automatically guided vehicles and autonomous delivery robots. In these systems, it is not the length, but the total flow of the loaded and empty vehicles that drives the objective function. It has been shown that the shortest loop provides an effective heuristic scheme to achieve prosperous and robust solutions for the concurrent design of the loop and input/output stations. We review and compare covering constraints formulations, provide new insight into connectivity constraints, improve the model formulation and its solution procedure, and report computational results.     

The maximum girth and minimum circumference of graphs with prescribed radius and diameter

Ostrand posed the following two questions in 1973. (1) What is the maximum girth of a graph with radius $r$ and diameter $d$? (2) What is the minimum circumference of a graph with radius $r$ and diameter $d$? Question 2 has been answered by Hrn?iar who proves that if $d\le 2r?2$ the minimum circumference is $4r?2d.$ In this note we first answer Question 1 by proving that the maximum girth is $2r+1.$ This improves on the obvious upper bound $2d+1$ and implies that every Moore graph is self-centered. We then prove a property of the blocks of a graph which implies Hrn?iar’s result.     

The (2, 2, 0) group inverse problem

We characterize the existence of the group inverse of a two by two matrix with zero (2, 2) entry, over a ring by means of the existence of the inverse of a suitable function of the other three entries. Some special cases are derived.     

A characterization of block graphs

A block graph is a graph whose blocks are cliques. For each edge e=uv of a graph G, let N_e(u) denote the set of all vertices in G which are closer to u than v. In this paper we prove that a graph G is a block graph if and only if it satisfies two conditions: (a) The shortest path between any two vertices of G is unique; and (b) For each edge e=uv∈E(G), if x∈N_e(u) and y∈N_e(v), then, and only then, the shortest path between x and y contains the edge e. This confirms a conjecture of Dobrynin and Gutman [A.A. Dobrynin, I. Gutman, On a graph invariant related to the sum of all distances in a graph, Publ. Inst. Math., Beograd. 56 (1994) 18-22].     

QUANTIZATION OF LIE ALGEBRAS OF BLOCK TYPE

In this article, we use the general method of quantization by Drinfeld’s twist to quantize explicitly the Lie bialgebra structures on Lie algebras of Block type.     

A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems

The inverse-free preconditioned Krylov subspace method of Golub and Ye [G.H. Golub, Q. Ye, An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems, SIAM J. Sci. Comp. 24 (2002) 312-334] is an efficient algorithm for computing a few extreme eigenvalues of the symmetric generalized eigenvalue problem. In this paper, we first present an analysis of the preconditioning strategy based on incomplete factorizations. We then extend the method by developing a block generalization for computing multiple or severely clustered eigenvalues and develop a robust black-box implementation. Numerical examples are given to illustrate the analysis and the efficiency of the block algorithm.     

Generalized Drazin inverses of anti-triangular block matrices

In this paper we give formulae for the generalized Drazin inverse Md of an anti-triangular matrix in two different ways: one is to express Md in terms of Ad with arbitrary B and C, the other is to express Md in terms of Bd and Cd with arbitrary A. Moreover, the results are applied to obtain generalized Drazin inverses of various structured matrices and some special cases are analyzed.