Contour tracking using weighted structure tensor based variational level set

A novel contour tracking method using weighted structure tensor based variational level set is proposed in this paper.The image is first converted to weighted structure tensor field by extracting apositive definite symmetric covariance matrix for each pixel.Then,a level set method is employed to represent object contour implicitly which separates the image domain into two areas each modeled by tensor field based Gaussian mixture model separately.By solving agradient flow equation of energy functional with respect to the level set,the object contour will converge to its real profile in the newly arrived frame.Experimental results on several video sequences demonstrate the better performance of our method than the other two contour tracking algorithms.

Function S-Rough sets and its applications

Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one direction S-rough sets （function one direction singular rough sets） and function two direction S-rough sets （function two direction singular rough sets）. This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.

Function S-rough sets and mining-discovery of rough law in systems

Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.

FIXED POINTS OF NONEXPANSIVE MAPPINGS ON STAR-SHAPED SUBSETS OF A CONVEX METRIC SPACE

In this paper, we give some characteristic properties of star-shaped sets which include a subset of a convex metric space. Using the characteristic properties, we discuss the existence problems of fixed points of nonexpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an example which shows that our generalizations are essential.

Parameter Ecology for Feedback Vertex Set

This paper deals with the FEEDBACK VERTEX SET problem on undirected graphs, which asks for the existence of a vertex set of bounded size that intersects all cycles. Due it is theoretical and practical importance,the problem has been the subject of intensive study. Motivated by the parameter ecology program we attempt to classify the parameterized and kernelization complexity of FEEDBACK VERTEX SET for a wide range of parameters.We survey known results and present several new complexity classifications. For example, we prove that FEEDBACK VERTEX SET is fixed-parameter tractable parameterized by the vertex-deletion distance to a chordal graph. We also prove that the problem admits a polynomial kernel when parameterized by the vertex-deletion distance to a pseudo forest, a graph in which every connected component has at most one cycle. In contrast, we prove that a slightly smaller parameterization does not allow for a polynomial kernel unless NP coNP=poly and the polynomial-time hierarchy collapses.