Spatio-temporal Reasoning for Vague Regions

Abstract

This paper extends a mereotopological theory of spatiotemporal reasoning to vague "egg-yolk" regions. In this extension, the egg and its yolk are allowed to move and change over time. We present a classification of motion classes for vague regions as well as composition tables for reasoning about moving vague regions. We also discuss the formation of scrambled eggs when it becomes impossible to distinguish the yolk from the white and examine how to incorporate temporally and spatially dispersed observations to recover the yolk and white from a scrambled egg. Egg splitting may occur as a result of the recovery process when available information supports multiple egg recovery alternatives. Egg splitting adds another dimension of uncertainty to reasoning with vague regions.

Modeling Topological Relationships between Fuzzy Spatio-Temporal Objects

“…In order to deal with the fuzziness and imprecision of spatio-temporal objects, several efforts have been made to model fuzzy spatio-temporal objects and their topological relationships, such as fuzzy set theory-based methods [15], [16], rough set theory-based method [17], point-set topology [13], motion-based approaches [14], [18], [19], and dimensional-extended method [20], [21].…”

“…The approach in [13] focuses on a discrete change of the fuzzy region over time, but does not represent the continuous changes. In [14], a moving vague "Egg/Yolk" region is presented. The two approaches are limited to fuzzy region objects and do not take fuzzy point objects and fuzzy line objects into account.…”

“…As a result, the issue of modeling topological relationships between fuzzy spatio-temporal objects should include two problems: (i) modeling fuzzy spatio-temporal objects and (ii) modeling their topological relationships. Currently, several efforts have been made for the representation of fuzzy spatio-temporal objects such as [13], [14], [15]. The approach in [13] focuses on a discrete change of the fuzzy region over time, but does not represent the continuous changes.…”

“…Temporal changes of fuzzy line and fuzzy region are missing. At the same time, in order to model fuzzy topological relationships between fuzzy spatio-temporal objects, some efficient approaches have been proposed, mainly including fuzzy set theory-based methods [15], [16], rough set theory-based method [17], point-set topology [13], motion-based approaches [14], [18], [19], and dimensional-extended method [20], [21]. For example, in [17], the authors propose a method to model spatio-temporal topological relationships based on rough set theory.…”

An Abstract Theory and Ontology of Motion Based on the Regions Connection Calculus

“…For example [11] uses the topology-based qualitative theory of space of [1] to construct a set of six motion classes consisting of leave, reach, cross, hit, internal and external. [8] does the same but embeds vagueness in the representation of the regions under study to come up with a set of motion classes specific to vague regions.…”