Mathematical Morphology and Poset Geometry

Spacetime topology from causality

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. This provides an abstract mathematical setting in which one can study causality independent of geometry and differentiable structure.

Traditional Signal Processing Seen From the Morphological Poset- Theoretical Point of View

Mathematical Morphology, partially ordered sets, complete semilattices, signal processing, image processing In this paper, we prove that several key signal processing tasks (linear filtering, quantization, decimation, JPEG coding, and others) are particular cases of morphological operators. This is obtained as a consequence of the recent extension of MM's framework, from complete lattices to co...

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.

Digital Geometry and Mathematical Morphology Lecture Notes , Spring Semester 2004

A domain of spacetime intervals in general relativity

We prove that a globally hyperbolic spacetime with its causality relation is a bicontinuous poset whose interval topology is the manifold topology. From this one can show that from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbo...