Artificial Intelligence
Continuous Change in Spatial Region
COSIT '97 Proceedings of the International Conference on Spatial Information Theory: A Theoretical Basis for GIS
Describing Spatial Transitions Using Mereotopological Relations Over Histories
Describing Spatial Transitions Using Mereotopological Relations Over Histories
Qualitative Spatial Reasoning with Conceptual Neighborhoods for Agent Control
Journal of Intelligent and Robotic Systems
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A natural approach to defining continuous change of shape is in terms of a metric that measures the difference between two regions. We consider four such metrics over regions: the Hausdorff distance, the dual-Hausdorff distance, the area of the symmetric difference, and the optimal-homeomorphism metric (a generalization of the Fréchet distance). Each of these gives a different criterion for continuous change. We establish qualitative properties of all of these; in particular, the continuity of basic functions such as union, intersection, set difference, area, distance, and smoothed circumference and the transition graph between RCC-8 relations. We also show that the history-based definition of continuity proposed by Muller is equivalent to continuity with respect to the Hausdorff distance.