The document presents Christian Freksa's 1992 approach to qualitative spatial reasoning using orientation information. It motivates the use of qualitative rather than quantitative representations, discusses previous approaches, and argues that qualitative orientation is directly available through perception. It then introduces the concept of directional orientation in 2D spaces, how qualitative relations can be augmented with front-back information, the idea of conceptual neighborhoods, and provides examples of how an orientation-based framework can be used for spatial reasoning and inferences.

1. Using Orientation Information
for Qualitative Spatial Reasoning
Christian Freksa, 1992
presented by Amenity Applewhite
23.5.2008
1

2. Outline
• Introduction
• Motivation
• Previous approaches
• Argument for qualitative orientation
• Directional orientation in 2D
• Augmenting qualitative relations
• Conceptual neighborhood theory
• Using the orientation-based framework
• Applications
• Further work
2

3. Introduction
An approach to represent spatial knowledge
using qualitative, neighborhood-oriented
spatial information.
3

4. Motivation: Why qualitative?
Quantitative knowledge obtained by measuring:
4

5. Motivation: Why qualitative?
Quantitative knowledge obtained by measuring:
“thirteen centimeters”
5

6. Motivation: Why qualitative?
Quantitative knowledge obtained by measuring:
“thirteen centimeters”
• Requires mapping between object domain and scale domain
• Mapping can produce distortions
6

7. Motivation: Why qualitative?
Qualitative knowledge obtained by comparison
rather than measuring:
7

8. Motivation: Why qualitative?
Qualitative knowledge obtained by comparison
rather than measuring:
“longer”
8

9. Motivation: Why qualitative?
Qualitative knowledge obtained by comparison
rather than measuring:
“longer”
• Direct evaluation entirely within object domain
• Focuses knowledge processing on information relevant to
decision making 9

10. Motivation: Why spatial?
• Spatial reasoning is essential to numerous
actions and decisions
• Arguably, physical space is more fundamental
than logical reason:
– Spatial reasoning more “primitive” in nature
– Logic as an abstraction of spatial reasoning
10

11. Previous approaches to qualitative
spatial reasoning
Cartesian framework Güsgen, 1989
11

12. Previous approaches to qualitative
spatial reasoning
Cartesian framework Güsgen, 1989
String representations Chang & Jungert, 1986
12

13. Previous approaches to qualitative
spatial reasoning
Cartesian framework Güsgen, 1989
String representations Chang & Jungert, 1986
Object-boundary and interior intersections
Egenhofer & Franzosa, 1991
13

14. Previous approaches to qualitative
spatial reasoning
Cartesian framework Güsgen, 1989
String representations Chang & Jungert, 1986
Object-boundary and interior intersections
Egenhofer & Franzosa, 1991
Cardinal direction grids Frank, 1991
14

15. Why qualitative orientation?
Availability of spatial information:
• Qualitative orientation is available through pure
perception
• Other representations, such as Cartesian
coordinates or cardinal orientation, refer to
extra-perceptual information
15

16. Directional orientation in 2D
Directional orientation a 1D feature determined by an
oriented line
Oriented line specified by an ordered set of two points
A B
orientation ab
16

17. Directional orientation in 2D
Directional orientation a 1D feature determined by an
oriented line
Oriented line specified by an ordered set of two points
A B
orientation ba
17

18. Directional orientation in 2D
Relative Orientation specified by two oriented
lines
Orientation of line bc
relative to line ab
18

19. Properties of qualitative orientation
wrt. location b and orientation ab
19

20. Properties of qualitative orientation
wrt. location b and orientation ab
20

21. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
wrt. location b and orientation ab
21

22. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
wrt. location b and orientation ab
22

23. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
wrt. location b and orientation ab
23

24. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
wrt. location b and orientation ab
24

25. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
Opposite periodic
wrt. location b and orientation ab
25

26. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
Opposite periodic
opposite ∞ left yields right
wrt. location b and orientation ab
26

27. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
Opposite periodic
opposite ∞ left yields right
wrt. location b and orientation ab
27

28. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
Opposite periodic
opposite ∞ left yields right
opposite ∞ opposite ∞ left yields
left
wrt. location b and orientation ab
28

29. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
Opposite periodic
opposite ∞ left yields right
opposite ∞ opposite ∞ left yields
left
opposite ∞ opposite ∞ opposite ∞
wrt. location b and orientation ab
left yields right
29

30. Properties of qualitative orientation
Same transitive
if ab=bc and bc=cd then ab=cd
Opposite periodic
opposite ∞ left yields right
opposite ∞ opposite ∞ left yields
left
opposite ∞ opposite ∞ opposite ∞
wrt. location b and orientation ab
left yields right
Orientation is a circular dimension
30

31. Augmenting qualitative relations
Front-back segmentation
• cognitively meaningful to people and animals
• most objects have this implicit dichotomy
8 disjoint orientation relations
0 straight-front
straight-back
4
1 right-front
5 left-back
2 right-neutral
6 left-neutral
3 right- back
7 left-front
31

32. Orientation-based qualitative location
+ =
front-back dichotomy wrt. front-back dichotomy wrt.
ab in b ba in a
32

33. Orientation-based qualitative location
c
+ =
front-back dichotomy wrt. front-back dichotomy wrt.
ab in b ba in a
33

34. Conceptual neighborhood
Conceptual neighbor a relation that represents a
direct transition in the object domain from
the initial relation
• Based on studies of temporal cognition
• Cognitive & computational advantages
34

35. Conceptual neighborhood
• Conceptual neighbor a relation that represents
a direct transition in the object domain from
the initial relation
35

36. Conceptual neighborhood
• Conceptual neighbor a relation that represents
a direct transition in the object domain from
the initial relation
36

37. Conceptual neighborhood
• Conceptual neighbor a relation that represents
a direct transition in the object domain from
the initial relation
Conceptual neighbors:
i and 6
i and 7
i and 0
6 and 7
7 and 0
37

38. Conceptual neighborhood
• Conceptual neighbor a relation that represents
a direct transition in the object domain from
the initial relation
Conceptual neighbors:
i and 6
i and 7
i and 0
6 and 7
7 and 0
Not conceptual neighbors:
Require intermediate relations
6 and 0
38

39. Conceptual neigborhood in represented domain
39

40. Conceptual neigborhood in represented domain
40

41. Conceptual neigborhood in represented domain
• 15 qualitative relations
• 105 (unordered) pairs
• 30 conceptual neighbors
41

42. Conceptual neigborhood in represented domain
Utility
• Reflects represented world
• Reasoning strategies entirely
within the represented domain
• Assist domain visualization
• Computationally restrict
problem space to feasible
operations
42

43. Orientation-based qualitative distance
• Finer spatial resolution
conveys distance
• Does not increase
orientation precision
43

44. Represented entities
Most approaches
• spatially extended objects
• convex or rectangular shapes
Points as basic entities, fundamental approach
• Properties & relations hold for entire spatial domain
• Shapes can be described as points with various levels of abstraction
and precision; flexible
0D point
city on wide area map
1D extension
length of a road
2D projection
area of a lake
3D constellation
shape or group of objects
44

45. Qualitative spatial reasoning
Using the orientation-based framework for
inferences
• Describe one spatial
vector with relation to
another
• Infer unknown vector
relations based on known
relations
45

46. Qualitative spatial reasoning
Using the orientation-based framework for
inferences
Given
• relation of vector bc to
vector ab
• relation of vector cd to
vector bc
Infer
location of d to vector ab
46

47. Qualitative spatial reasoning
Using the orientation-based framework for
inferences
• Consider front-back
dichotomies for known
vectors
47

48. Qualitative spatial reasoning
Using the orientation-based framework for
inferences
• Consider front-back
dichotomies for known
vectors
• c right-front (1) ab
48

49. Qualitative spatial reasoning
Using the orientation-based framework for
inferences
• Consider front-back
dichotomies for known
vectors
• c right-front (1) ab
• d right-back (3) cb
49

50. Qualitative spatial reasoning
Using the orientation-based framework for
inferences
• Consider front-back
dichotomies for known
vectors
• c right-front (1) ab
• d right-back (3) cb
Wrt. to original vector
ab, vector bd is either
right-front (1), front
(0), or left front (2)
50

51. Composition table
• Organize qualitative
orientation-based
inferences
• Neighboring rows
and columns show
conceptual
neighbors
51

52. Composition table
• Initial conditions
52

53. Composition table
• Possible locations
of c
53

54. Composition table
• Possible locations
of d
54

55. Composition table
• Orientation-less
c=d
d=b
55

56. Composition table
56

57. Composition table
57

58. Composition table
25% of all cases hold uncertainty
• neighboring possibilities increase
orientation angle up to 180˚
• degree of uncertainty is precisely
known
58

59. Composition table
r orientation of c wrt. ab
s the orientation of d wrt. bc
t orientation of d wrt. ab
59

60. 4
Composition table 3 5
2 6
1 0 7
r orientation of c wrt. ab
s the orientation of d wrt. bc
t orientation of d wrt. ab
7 0 1
6 2
5 3
4 60

61. 4
Composition table 3 5
2 6
1 0 7
r orientation of c wrt. ab s
s the orientation of d wrt. bc 3
t orientation of d wrt. ab
7 0 1
6 2 r
1
5 3
4 61

62. Composition table
r orientation of c wrt. ab s
s the orientation of d wrt. bc 3
t orientation wrt. ab
r and s are odd: t
r
t ={(r+s-1)…(r+s+1)} mod 8 1 7,0,1
t ={(1+ 3 -1)…(1+ 3+ 1)} mod 8
t = {3 … 5} mod 8
62

63. Fine grain composition table
• Higher resolution
• 2 front-back
dichotomies
• Produced by
producing sub-rows
and sub-columns
from previous table
63

64. Applications
• Determine an unknown location in space
based on own location and known location
• Wayfinding & route descriptions
64

65. Referencing work
257 citations in Google Scholar
A few examples:
– Computational methods for representing
geographical concepts (Egenhofer, Glasgow, et al)
– Schematic maps for robot navigation (Freksa, et al)
– Pictorial language for retrieval of spatial relations
from image databases (Papadias, et al)
65

66. Questions?
66