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 Spatio-Temporal Continuity
COSIT 2001 Proceedings of the International Conference on Spatial Information Theory: Foundations of Geographic Information Science
Pouring liquids: A study in commonsense physical reasoning
Artificial Intelligence
Temporalizing spatial calculi: on generalized neighborhood graphs
KI'05 Proceedings of the 28th annual German conference on Advances in Artificial Intelligence
Preserving geometric properties in reconstructing regions from internal and nearby points
Computational Geometry: Theory and Applications
Exploiting qualitative spatial neighborhoods in the situation calculus
SC'04 Proceedings of the 4th international conference on Spatial Cognition: reasoning, Action, Interaction
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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.