Map Generalization of Road Networks
Jan Terje Bjørke
Norwegian Defence Research Establishement and Department of Mathematical Sciences and Technology, The Agricultural University of
Norway
decreasing amount of detail
less visual conflicts
start view Cartographic
zoom out
eliminates details
ordinaryzoom out
Zoom out
Cartographic zoomadds details
Zoom in
Generalization of road networks should consider
• The visual separation of the map symbols
• Method: solve the visual separation problem by an elimination procedure based on information theory.
• The semantics of the network like
–the connectivity of the network
–the route to travel
–the road classes
–etc.
• Method: Introduce the semantic constraints into the optimisation procedure.
Shannon entropy
)(2
log)()( ypypYHYy
The events for the entropy computation: points along the arcs
Information points
Shannon equivocation
YyXx
xypxypxpXYH )|(log)|()()|(2
where is the conditional probabilitythat map symbol x is interpreted as map symbol y.
)|( xyp
Similarity and conditional probability
,0),(
else
when ),(
xy
Ts(T-s)/Txy
Yy
xy
xyxyp
),(
),()|(
T
1.0
0 s
Shannon useful information
• R=H(Y) – H(Y|X) ; termed useful information
• R = amount of roads in the map minus the amount of visual conflicts between the roads
• The maximum value of R is termed the channel capacity.
Oslo, T=15 Oslo, T=35
Useful information
Bergen T=35Bergen T=15
Useful information
Elimination algorithm
• eliminate the most conflicting road,
• repeat the procedure until
– the R-value has reached its maximum value
– or if the topological constraints prevent any arc to being eliminated.
Generalized map, T=35. The hierarchy of the roads are considered. No topology constraints are introduced. 83% of the roads are eliminated.
Oslo road map
Main roads in red, secondary roads in black and other roads in blue.
Oslo road map
Main roads in red, secondary roads in black and other roads in blue.
Generalized map, T=35.The hierarchy and the topology of the roads are considered.49% of the roads are eliminated. .
Oslo
T=1524% eliminated
T=2543% eliminated
T=3549% eliminated20 sec.
120 sec.
350 sec.
T=1013% eliminated
T=3539% eliminated
T=2528% eliminated
Bergen
T=1027% eliminated
T=2535% eliminated
Trondheim
Running time for the algorithm
Time in seconds to generalize the Oslo road map
source, d=10source, d=20
Max R, d=20 Max R, d=10
Declutteringhouse symbols in a part of the Oslo region
d=8, from optimization
Optimize number of symbols and symbol size
Conclusions
The method presented has three application dependent parameters:
1. by tuning the similarity function we decide the visual separability of the road symbols;
2. the connectivity condition decides how important the topology of the network is;
3. the hierarchy of the roads is considered by a weight function.
Conclusions
• The method can serve as a basis for cartographic zoom since it is:
– automated;
– fast in unconditional mode;
– the implementation of the contraints in the conditional mode is critical to the time complexity of the algoritm. This step requires more experiments
Further research
• Apply the information theoretic approach to compute the optimal number of coloured depth intervals in sea floor maps.
• Speed up the algorithms to solve the optimization problem.
• Apply the method to maps composed of different information sources.
Recommended
