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Managing the Granularity of a Spatial Configuration

Managing the Granularity of a Spatial Configuration. Matthew P. Dube and Max J. Egenhofer QuaCon 2009 – Stuttgart, Germany. The Importance of Context. Every situation in our world provides a unique context This context determines human reaction to a phenomena or display

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Managing the Granularity of a Spatial Configuration

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  1. Managing the Granularity of a Spatial Configuration Matthew P. Dube and Max J. Egenhofer QuaCon 2009 – Stuttgart, Germany

  2. The Importance of Context Every situation in our world provides a unique context This context determines human reaction to a phenomena or display This context also determines the interpretation

  3. Spatial Context • You own this piece of land • You are looking to build on this land, but you do not have the money • So you go to the bank

  4. What can I do for you today, Mr. Johnson? Do you have the deed to the property, Mr. Johnson? And you are building this facility completely on this property? Okay, just sign here and it is all set! Spatial Context Jim, I am looking to build a facility to house some of my farm equipment. Yessir, just as long as you can front me the money! Yes I do. It’s right here in my jacket pocket!

  5. Does the size or the location of the building matter? You don’t get the loan: not on your property! You don’t get the loan: you don’t own all the property you are building on! You get the loan and everything is normal! You get the loan, but you may need an easement to clean parts of it. You get the loan, but you will certainly need a rite of way or an easement. Depends on the context!

  6. An Analogous Picture Object 1 Object 2 Both Objects Object 1 inside Object 2 Object 1 equals Object 2 Object 1 coveredBy Object 2 Consider two objects like this:

  7. Why does this matter? • We make decisions based on contexts • I give you a vague spatial detail (inside) • It might suffice (bank only needed ownership) • But it might not (law needs proximal information) • How do you make your decision properly if I cannot change the message?

  8. Outline Classification Methods Formalisms for Spatial Reasoning Using Psychology to Enable Mathematics A New Configuration Space

  9. Classification Methods • Prototype Theory • We have an image in our minds of an archetype • Exemplar Theory • We have a class of images in our minds that we base judgment off of • Graded Sets • We have a class of images in our minds which we assign a hierarchical rating upon

  10. For the Birds... American Robin .45 Ruby-Throated Hummingbird .25 Emperor Penguin .10 Mallard Duck .20

  11. Back to Jim and Mr. Johnson Failure in Communication! Object 1 coveredBy Object 2 Object 1 equals Object 2 Object 1 inside Object 2 Jim sees inside as a prototype relation Mr. Johnson sees inside as an exemplar set of relations

  12. Formalisms for Spatial Reasoning Two really important formalisms: Region Connection Calculus 9-Intersection Matrix For two simple regions, RCC-8 ≈ 9-INT RCC-5 represents disjunctions of these relations

  13. Two Spatial Reasoning Sets Region Connection Calculus 8 (RCC-8) Region Connection Calculus 5 (RCC-5) D Aggregation of Relations O M Equivalent Relations OV OV IN-1 IN CV CB How can we fit these together? E CN E I

  14. O D O M OV CV CB CN E I C I C I

  15. Merge Psychology and Math Topological Comparisons (Topology) Category Assignment (Psychology) Mathematical Averaging (Calculus)

  16. Establish a Bounding Set Exemplar Theory Which relations in RCC-8 bound the RCC–5 relations topologically? Example: in is bounded by inside, coveredBy, and equal

  17. On the Conceptual Neighborhood Graphs D O M OV OV IN-1 IN CV CB E CN E I The node for IN should be placed somewhere inside this box to account for exemplar theory

  18. Refining the Box 1st Update OV 1 Naïve Position CB 1 1 ½ ½ E I

  19. Collapsing the Line Prototype Theory Which relation is the prototypical configuration of IN? Recall Jim’s response to Mr. Johnson inside

  20. 2nd Update OV CB E I

  21. Identifying the Node 3rd Update OV CB E I .975 .454

  22. Creating a Graded Set We have created a graded set inside is .454 away coveredBy is 2/3 away equal is .975 away Through symmetry, all of the other nodes in the graph can be placed (and also on the sphere) OV CB E I .975 .454

  23. OV OV OV OV CV M M CB E E E E C I D D Final Configuration EX O EM D A EN M OV CV CB IN-1 IN

  24. Conclusions Distances less than 1 found for aggregated concepts 82% of pre-alignment distances unchanged Smaller differences produced than the 50% model Resulting space is metric as it satisfies the triangle inequality

  25. Questions

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