Transcript Class Number Class Name - Knowledge Systems Institute

A More Expressive 3D
Region Connection
Calculus
Chaman Sabharwal,
Jennifer Leopold, & Nate Eloe
Qualitative Spatial Reasoning in 3D
Set of 3D Objects
Set of Spatial Constraints
Dave is externally
connected to Phil
Jerry partially
obscures Stewart
Dave and Jerry are
disconnected with no
obscuration
…
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, DCpp, DCp, EC, ECPp, ECP,
POPp, POP, TPPP, TPPPc, EQP, NTPPP,
NTPPPc
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 AP and BP, not
possible to determine:
1) if A and B intersect in
3D space, and
2) if A is in front of B, or
B is in front of A
A
B
A
BP
A
P
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
Depth parameter
now considered
Obscuration types:
n = none
p = partial
c = complete
e = equal
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
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 + intrarelation 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 R1(A, B) and R2(B, C), can
determine set of all “possible” (i.e., composite) relations
for A and C
Computed for the VRCC3D+ 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
C
Addition of depth (i.e., VRCC-3D+)
allows conclusion that A obscures 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
([email protected])