In this paper, a new segmentation technique for multivalued images is elaborated. The technique makes use of the first fundamental form to access edge information of a multivalued image. On the obtained edge map, a watershedbased algorithm is applied. In order to remove noise or local texture, before segmentation, an anisotropic diffusion filter is applied, also making use of the first fundamen...

In this paper we develop a stability theory for broad classes of parametric generalized equations and variational inequalities in finite dimensions. These objects have a wide range of applications in optimization, nonlinear analysis, mathematical economics, etc. Our main concern is Lipschitzian stability of multivalued solution maps depending on parameters. We employ a new approach of nonsmooth...

In this paper, we introduce and study a new system of nonlinear A-monotone multivalued variational inclusions in Hilbert spaces. By using the concept and properties of A-monotone mappings, and the resolvent operator technique associated with A-monotone mappings due to Verma, we construct a new iterative algorithm for solving this system of nonlinear multivalued variational inclusions associated...

An implementation (in Maple) of the multivalued elementary inverse functions is described. The new approach addresses the difference between the single-valued inverse function defined by computer systems and the multivalued function which represents the multiple solutions of the defining equation. The implementation takes an idea from complex analysis, namely the branch of an inverse function, ...

We present a method to incrementally voxelize triangles into a volumetric dataset with pre-filtering, generating an accurate multivalued voxelization. Multivalued voxelization allows direct volume rendering of voxelized geometry as well as volumes with intermixed geometry, accurate multiresolution representations, and efficient antialiasing. Prior voxelization methods either computed only a bin...

In this paper we study nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the p...

The transformation of a relational database schema into fourth normal form, which minimizes data redundancy, relies on the correct identification of multivalued dependencies. In this work, we study the learnability of multivalued dependency formulas (MVDF), which correspond to the logical theory behind multivalued dependencies. As we explain, MVDF lies between propositional Horn and 2-Quasi-Hor...

Data tables provide a convenient means of representation of descriptive information about objects. They serve also as standard input for data analysis tools or theories. In this paper we focus our attention upon the special class of data tables, namely multivalued information systems introduced by Z. Pawlak and E. Orłowska in the early 80s. The main idea presented in the paper is to interpret m...

Object-oriented Bayesian networks (OOBNs) facilitate the design of large Bayesian networks by allowing Bayesian networks to be nested inside of one another. Weak conditional independence has been shown to be a necessary and sufficient condition for ensuring consistency in OOBNs. Since weak conditional independence plays such an important role in OOBNs, in this paper we establish two useful resu...