Convex Geometry and Mathematical Morphology in a Generalized Structure

Mathematical Morphology and Poset Geometry

The aim of this paper is to characterize morphological convex geometries (resp., antimatroids). We define these two structures by using closure operators, and kernel operators. We show that these convex geometries are equivalent to poset geometries. 2000 Mathematics Subject Classification. 37F20, 06A07.

Convex Geometry of the Generalized

Generalized matrix-fractional (GMF) functions are a class of matrix support func4 tions introduced by Burke and Hoheisel as a tool for unifying a range of seemingly divergent matrix 5 optimization problems associated with inverse problems, regularization and learning. In this paper 6 we dramatically simplify the support function representation for GMF functions as well as the rep7 resentation o...

Digital Geometry and Mathematical Morphology Lecture

Contents: 1. Introduction 1.1. Why digital geometry? 1.2. Why mathematical morphology? 2. Morphological operations on sets and functions 2.

SIZE AND GEOMETRY OPTIMIZATION OF TRUSS STRUCTURES USING THE COMBINATION OF DNA COMPUTING ALGORITHM AND GENERALIZED CONVEX APPROXIMATION METHOD

In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelli...

Digital Geometry and Mathematical Morphology Lecture Notes , Spring Semester 2004