Münster GI-Days 2004 – 1-2 july – Germany 1 Description, Definition and Proof of a Qualitative State Change of Moving Objects along a Road Network Peter Bogaert, Nico Van de Weghe, Philippe De Maeyer Ghent University

Münster GI-Days 2004 – 1-2 july – Germany 2 Spatial Reasoning spatial reasoning lot of work has been done in stating the topological dyadic relations between objects Two approaches artificial intelligence → GI Science 1992 Randell, Cui, Cohn Region Connection Calculus databases → GI Systems 1991 Egenhofer, Franzosa 4-Intersections model

Münster GI-Days 2004 – 1-2 july – Germany 3 RCC - diagram Assuming continuous motion Constraints upon the way the base relations can change

Münster GI-Days 2004 – 1-2 july – Germany 4 Conceptual Neighborhood Diagram Freksa (1992 ) Conceptual Neighbors ‘Two relations between pairs of events are conceptual neighbors, if they can be directly transformed into one another by continuously deforming (i.e. shortening, lengthening, and moving) the events in a topological sense’ Conceptual Neighborhood Diagram Graphical representation of the conceptual neighbors

Münster GI-Days 2004 – 1-2 july – Germany 5 QTC Problem : How to describe disjoint objects Van de Weghe et al. (2004) QTC = Qualitative Trajectory Calculus studies the changes in qualitative relations between two disconnected continuously moving objects. based on direction of movement movement speed resulting in transition-codes

Münster GI-Days 2004 – 1-2 july – Germany 6 QTC – simplification to 1D space

Münster GI-Days 2004 – 1-2 july – Germany 7 QTC - labeling 3. speed of K and L: D(Kt2,Kt1) > D(Lt2,Lt1) : + D(Kt2,Kt1) < D(Lt2,Lt1) : - D(Kt2,Kt1) = D(Lt2,KL1) : 0 1.movement of K relative to original position of L: D(Kt2,Lt1) > D(Kt1,Lt1) : + D(Kt2,Lt1) < D(Kt1,Lt1) : - D(Kt2,Lt1) = D(Kt1,Lt1) : 0 2. movement of L relative to original position of K: D(Lt2,Kt1) > D(Lt1,Kt1) : + D(Lt2,Kt1) < D(Lt1,Kt1) : - D(Lt2,Kt1) = D(Lt1,Kt1) : 0 Kt1Kt2Lt1Lt

Münster GI-Days 2004 – 1-2 july – Germany 8 Conceptual Neighborhood Diagram Results in 3³ = 27 possible trajectories CND can be represented by a cube character character 1

Münster GI-Days 2004 – 1-2 july – Germany 9 QTC – 1D space In 1D space : Only 17 real-life trajectories

Münster GI-Days 2004 – 1-2 july – Germany 10 QTC – diagram (1D) Conceptual neighbourhood diagram

Münster GI-Days 2004 – 1-2 july – Germany 11 QTC-N Moreira et al. (1999): In real-life there are two kinds of moving objects those having a free trajectory (e.g. a bird flying through the sky) those with a constrained trajectory (e.g. a vehicle driving through a city along a road network). QTC-N deals with object that have a constraint trajectory due to a network

Münster GI-Days 2004 – 1-2 july – Germany 12 QTC-N both objects are inserted as nodes in the graph representing the network. the cost (e.g. Euclidian distance, time, etc.) between those two objects is measured along the shortest path an object can only approach the other object, if and only if it moves along the shortest path between these two objects.

Münster GI-Days 2004 – 1-2 july – Germany 13 New definition of QTC - labeling 3. speed of K and L: D(Kt2,Kt1) > D(Lt2,Lt1) : + D(Kt2,Kt1) < D(Lt2,Lt1) : - D(Kt2,Kt1) = D(Lt2,KL1) : 0 1.movement of K relative to original position of L: k does not move along the shortest path: + k moves along the shortest path : - k stable : 0 2. movement of L relative to original position of K: l does not move along the shortest path : + l moves along the shortest path : - l stable : 0 Kt1Kt2Lt1Lt

Münster GI-Days 2004 – 1-2 july – Germany 14 QTC-N If two objects on a network change their speed, they can reach each label in the QTC-1D

Münster GI-Days 2004 – 1-2 july – Germany 15 If speed is constant there can still be a transition Passing a node change node with a degree of minimum 3 only an object with label ‘–‘ Degree less than 3 can only choose to follow the shortest path Label ‘+’ impossible because it can’t choose to follow an arc that belongs to the Shortest path QTC-N

Münster GI-Days 2004 – 1-2 july – Germany 16 QTC-N If speed is constant there can still be a transition Change in the shortest path between the objects Only if one or both objects have label ‘+‘ Both Labels ‘-’ Impossible because this way there can’t be a change in the shortest path

Münster GI-Days 2004 – 1-2 july – Germany 17 CND of the QTC-N character character 1

Münster GI-Days 2004 – 1-2 july – Germany 18 CONCLUSION AND FUTURE WORK CONCLUSION QTC can be used to describe moving objects on a network objects moving on a network can’t be treated as objects moving in 1D space. 17 vs. 27 possible trajectories FUTURE WORK QTC-N from 2 moving objects to n moving objects Composition table Calculating quatlitative trajectory using Shortest Path calulation tables

Münster GI-Days 2004 – 1-2 july – Germany 19 Description, Definition and Proof of a Qualitative State Change of Moving Objects along a Road Network Geography Department – Ghent University Krijgslaan 281 S8 B-9000 Gent Peter Bogaert + 32 (0)