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A More Expressive 3D Region Connection Calculus Chaman Sabharwal, Jennifer Leopold, & Nate Eloe

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Qualitative Spatial Reasoning in 3D Dave is externally connected to Phil Jerry partially obscures Stewart Dave and Jerry are disconnected with no obscuration … Set of 3D ObjectsSet of Spatial Constraints Can you pick out Dave, Phil, Jerry, and Stewart?

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Hasn’t This Already Been Solved? In game theory, all computations are quantitative and precise Whereas here computations are qualitative and predictive (allow discovery of relations)

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Hasn’t This Already Been Solved? Also, animation can “cheat” because many frames (i.e., configurations of objects) displayed in quick succession

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Region Connection Calculus (RCC) Formal, mathematical model for doing Qualitative Spatial Reasoning (QSR) RCC fundamentals: - JEPD set of relations (i.e., for any 2 objects, there is exactly 1 relationship from the set) - Specific definitions of parthood & connectivity

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The Basic RCC-8 Relations (2D)

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Related Work RCC-23: handles concave regions in 2D LOS-14, ROC-20: qualify 2D relations in terms of obscuration Others… But only with respect to a particular 2D viewpoint; potentially ambiguous and/or incomplete analyses!

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Our Previous Solution: RCC-3D RCC-3D: spatial relation computed in 3D + obscuration computed for particular 2D projection 13 relations: DC, DC p p, DC p, EC, EC P p, EC P, PO P p, PO P, TPP P, TPP P c, EQ P, NTPP P, NTPP P c subscript P = which 2D projection plane p at end of relation name = partial obscuration (vs. complete obscuration)

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Our Previous Solution: RCC-3D VRCC-3D: RCC-3D + Visual UI States = sequence of configurations of objects Reasoner checks relation consistency between states

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VRCC-3D: Some Knowledge Lacking… From intersection of 2D projections A P and B P, not possible to determine: 1) 1)if A and B intersect in 3D space, and 2) 2)if A is in front of B, or B is in front of A APAP A A B BPBP

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VRCC-3D+ Characterization of Base Relations in 3D Int = Interior, Bnd = Boundary, Ext = Exterior (all 3D) ∅ = non-empty intersection, ∅ = empty intersection

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VRCC-3D+ Characterization of Obscuration in 2D Int = Interior, Ext = Exterior (in 2D) ∅ = non-empty intersection, ∅ = empty intersection Y = A is in front of B, N = B is in front of A, E = even Depth parameter now considered Obscuration types: n = none p = partial c = complete e = equal

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VRCC-3D+ Possible Obscurations for Base Relations Because not every type of obscuration is applicable to every base relation

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VRCC-3D+ Allows for finer distinction between various possible spatial configurations Base relation between A and B is partial overlap (PO) in each figure

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Conceptual Neighborhood Useful to identify transitions that can occur when geometry of one object in a pair is changed gradually Topological distance between relations computed as the number of intersections that change from empty to not empty (or vice versa) Distance expressed as inter-relation distance + intra- relation distance

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Conceptual Neighborhood inter-relation distance(R1, R2) = # intersections that differ between base spatial relations R1 and R2 Same as for VRCC-3D because characterization still in terms of an 8-intersection model

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Conceptual Neighborhood intra-relation distance(O1, O2) = # predicates that differ between obscuration type O1 and O2 (see paper for detailed discussion of how this is computed) Different from VRCC-3D because we now have more expressive obscuration types

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Conceptual Neighborhood Graph Nodes grouped vertically by closeness (distance) of base relations, and horizontally by closeness of obscuration relations

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Composition Table Another way we can “reason” with spatial relation info: Given VRCC-3D+ relations R 1 (A, B) and R 2 (B, C), can determine set of all “possible” (i.e., composite) relations for A and C Computed for the VRCC- 3D+ model using a Prolog program; stored as a table for lookup as needed

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Relation Composition Simple example of something we can do with VRCC-3D+ (and couldn’t do before with VRCC-3D)… 3 planes of equal size From controller’s 2D screen (hence VRCC-3D), know that A occludes B and B occludes C Addition of depth (i.e., VRCC-3D+) allows conclusion that A obscures C C B A

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Future Work Test implementation on a variety of datasets from different domains (e.g., anatomy, mechanical design, etc.); analyze usefulness, accuracy, and scalability Consider additional dimensions of information (e.g., transparency, translucency, and repulsion of objects)

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Questions? Comments? Please contact Jennifer Leopold

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