An algorithm is proposed to determine the topology of an implicit real algebraic surface in R. The algorithm consists of three steps: surface projection, projection curve topology determination and surface patches composition. The algorithm provides a curvilinear wireframe of the surface and the surface patches of the surface determined by the curvilinear wireframe, which have the same topology...

Original scientific paper Aiming at the problems of selection parameter step-size and premature convergence that occurred when searching the local area in the optimal design of adaptive gradient projection algorithm in this paper, adaptive variable step-size mechanism strategy and adaptive variable step-size mechanism were established. They were introduced into the gradient projection algorithm...

A classical method for solving the variational inequality problem is the projection algorithm. We show that existing convergence results for this algorithm follow from one given by Gabay for a splitting algorithm for finding a zero of the sum of two maximal monotone operators. Moreover, we extend the projection algorithm to solve any monotone affine variational inequality problem. When applied ...

The iterative back-projection (IBP) algorithm for single image super-resolution (SR) can not guarantee the edge smoothness because the reconstruction error is back-projected isotropically. Furthermore, in the case that there is only one low-resolution input, the estimation of the reconstruction error is easily affected by noise. Thus, this algorithm is highly sensitive to noise. The focus of th...

The discrete-time optimal projection equations for systems with white parameters are strengthened. For the class of minimal ms (mean square) stabilizing compensators the strengthened discrete-time optimal projection equations are proved to be equivalent to first-order necessary optimality conditions for optimal reduced-order dynamic compensation of systems with white parameters. The conventiona...

The shear-warp algorithm for volume rendering is among the fastest volume rendering algorithms. It is an object-order algorithm, based on the idea of the factorization of the view matrix into a 3D shear and a 2D warp component. Thus, the compositing can be done in sheared object space, which allows the algorithm to take advantage of data locality. Although the idea of a perspective projection s...

Knowledge representation (KR) is used to store and retrieve meaningful data. This data is saved using dynamic data structures that are suitable for the style of KR being implemented. The KR allows the system to manipulate the knowledge in the data by using reasoning operations. The data structure, together with the contents of the transformed knowledge, is known as the knowledge base (KB). An a...

The shear-warp algorithm for volume rendering is among the fastest volume rendering algorithms. It is an objectorder algorithm, based on the idea of the factorization of the view matrix into a 3D shear and a 2D warp component. Thus, the compositing can be done in sheared object space, which allows the algorithm to take advantage of data locality. Although the idea of a perspective projection sh...

Abstract. We use optimal rational approximations of projection data collected in X-ray tomography to improve image resolution. Under the assumption that the object of interest is described by functions with jump discontinuities, for each projection we construct its rational approximation with a small (near optimal) number of terms for a given accuracy threshold. This allows us to augment the me...