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

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?

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)

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

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

The Basic RCC-8 Relations (2D)

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!

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)

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

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

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

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

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

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

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

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

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

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

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

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

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)

Questions? Comments? Please contact Jennifer Leopold