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![Page 1: FORSVARETS FORSKNINGSINSTITUTT Transformation of geographical information into linguistic sentences: Two case studies Jan Terje Bjørke.](https://reader035.fdocuments.in/reader035/viewer/2022062409/56649f525503460f94c76e6b/html5/thumbnails/1.jpg)
FORSVARETS FORSKNINGSINSTITUTT
Transformation of geographical information into linguistic sentences: Two case studies
Jan Terje Bjørke
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FORSVARETS FORSKNINGSINSTITUTT
Overview
• Levels of communication
• Information reduction, the application of BLOBs
• Fuzzy BLOBs
• The description of topological relations between fuzzy BLOBs
• A travel: The sea floor seen from a submarine
• The design of navigation instruments based on risk factor computation
• The description of the risk factor in natural language
• Conclusions
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FORSVARETS FORSKNINGSINSTITUTT
Communication levels
• Syntactic level: low level information, i.e., the map symbols or the words,
• Semantic level: the meaning of the map symbols,
• Pragmatic level: the application of the map information, i.e., the meaning of the map symbols related to a certain application.
• e.g.: S=1000m.
• e.g.: the distance from A to B is one thousand meters.
• e.g.: the distance from A to B is rather short.
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FORSVARETS FORSKNINGSINSTITUTT
CASE 1: Fuzzy BLOBs and fuzzy regions
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FORSVARETS FORSKNINGSINSTITUTT
Channel capacity
Useful information = Entropy – Equivocation
The channel capacity C is defined as:
C=max(R) where R= H(y)-H(Y|X)
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Entropy
)(2
log)())(/1(2
log)()( ypypypypYHYyYy
where is a measure of the amount of information. )(/1 yp
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Equivocation
YyXx
xypxypxpXYH )|(log)|()()|(2
where is the conditional probabilitythat symbol x is interpreted as symbol y.
)|( xyp
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Dot size r=5Dot size r=10
Max R, when r=10 Max R, when r=5
Max R when r=optimal symbol size
Optimize the communication at the syntactic level
by eliminating conflicting
map elements
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FORSVARETS FORSKNINGSINSTITUTT
Group elements, i.e., create BLOBs (Wright and Kapler):Move the information to a higher level of abstraction
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FORSVARETS FORSKNINGSINSTITUTT
Crisp or fuzzy BLOBs
Fuzzy BLOB
Fuzzy BLOB
Crisp BLOB
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How to visualize the topological relation between fuzzy regions
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FORSVARETS FORSKNINGSINSTITUTT
How to talk about topological relations between fuzzy BLOBs?
• Disjoint
• Disjoint touch
• Touch disjoint
• Touch
• Touch overlap
• Overlap touch
• Overlap
• Overlap inside
• Inside overlap
• Inside
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FORSVARETS FORSKNINGSINSTITUTT
Computation of topological relations between fuzzy regions
• The computation is based on the similarity to the crisp 4-intersection
• This requires a definition of:
1. fuzzy interior
2. fuzzy boundary
3. concept for the similarity computation. This concept can be based on union and intersection operators for fuzzy sets.
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A fuzzy region and its boundary
A fuzzy region
Its boundary
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FORSVARETS FORSKNINGSINSTITUTT
The fuzzy 4-intersection
The crisp 4-intersection
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FORSVARETS FORSKNINGSINSTITUTT
Definition of topological properties of fuzzy regions
• Fuzzy region A is defined by its membership function as:
• The interior of A is defined as:
• The boundary of A is defined so it has its maximum membership value for points wich are midway between the exterior, i.e. the complement, and the interior of A.
),( yxuA
),(),(0 yxuyxu AA
),(2),( yxuyxu AA
)),(1(2),( yxuyxu AA
if
else
end
5.0),( yxuA
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FORSVARETS FORSKNINGSINSTITUTT
Demonstration oflinguistic descriptionsof topological relationsbetween fuzy regions
Inclusion index
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CASE 2: Navigation of a submarine
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Perspective view
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Risk factor
• Apply natural language sentences as:
• the risk is low;
• the risk is high;
• the risk is very high.
• Natural language has many dialects, multiple representation;
• Goal: find an iconic representation which is close to the natural language statements considered.
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Perception of distance
• The perception of distance is investigated among 40 subjects. Each of them was asked to evaluate the propositions:
• the distance is large
• the distance is small
• Several maps were designed. The maps were presented on a 20 inc. screen in a window of two kinds of size.
• Size of window 1: 30 x 20 cm.
• Size of window 2: 40 x 30 cm.
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The test plates
One point symbol in each window
The subjects were asked to evaluatethe distance from a certain circle to the shore line
Several point symbols in each window
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FORSVARETS FORSKNINGSINSTITUTT
normalized window size
Me
mb
ers
hip
va
lue
Distance is small
Distance is large
The two propositions distance is large / short
come out as complementary statements
0.4
0.4 1.0
1.0
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The scale effect
• The effect that the interpretation of the distance between the map symbols depends on a relation between the bounding frame and the map scale, is termed the scale effect.
• The scale effect can be utilized in the design of instruments.
small
large
very large
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The navigation intruments
6 axis:
port starboard ahead backwards up down
Metrical information can be turned on
100m
0m
500m
50m
0m
200m
highrisk
very highrisk
lowrisk
When the metrical information isturned on, the instrument showsboth the degree of risk and the distanceto the terrain surface. The scale isselected so that the yellow barhas a length 40% of its maximal length when the risk is on theboarder between high and low.
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FORSVARETS FORSKNINGSINSTITUTT
The navigation intruments
starboardport
up
down
ahead
backward
Research questions:how is this instrument perceived?is it too complex?
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The navigation intruments: Design 2
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The navigation intruments: Complement design
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Simulation of a travel in the terrain model
• The next views simulate a travel in the terrain model.
• They illustrate the problem of visualizing how safe the vessel rout is.
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FORSVARETS FORSKNINGSINSTITUTT
degree of risk
-1 0 1 2 3
x 104
-1000
-500
0
500
1000
degree of risk
profile
route map
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FORSVARETS FORSKNINGSINSTITUTT
degree of risk
-1 0 1 2 3
x 104
-1000
-500
0
500
1000
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-1 0 1 2 3
x 104
-1000
-500
0
500
1000
degree of risk
risk
profile
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FORSVARETS FORSKNINGSINSTITUTT
degree of risk
-1 0 1 2 3
x 104
-1000
-500
0
500
1000
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degree of risk
-1 0 1 2 3
x 104
-1000
-500
0
500
1000
risk
profile
route
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Conclusion 1: don’t overload the user with information
• Due to the users limited perceptual properties, he/she must not be overloaded with information. This calls for generalization of the information.
• Transformation of information to higher level of communication, i.e., pragmatic level, can reduce the amount of information to be processed by the user, e.g., the application of BLOBs and natural language sentences.
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M ap in itiator
Cartographicknow ledgeD1
D2Dom ainknow ledge
Geodata baseD3
Selectgeodata
1.2
1.1
1.3
1.4
Evaluate
Genera lizegeodata
Presenttheinform ation
M ap user
M apD4
Conclusion 2:the perceptual domain has several channels
The map can be any perceptual representation of geographical data as (1) visual image, (2) iconicrepresentation, (3) sound image,(4) natural language expression etc.etc.
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Conclusion 3: the need for soft map
design
• Most of the features of the real world have fuzzy boundaries and not well defined interiors. This calls for the application of soft map tools.
• Natural language sentences and iconic representations can be applied in soft map design.
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Conclusion 4: Iconic representations as alternative to linguistic sentences
• Sentences like: close to, huge, large, small, meet, intersects etc. etc. can be expressed in all natural languages., i.e., we have multiple representations.
• In some cases iconic representations can solve the problem of multiple linguistic representations, i.e., the language barrier.