A Spatial Structuration Heuristic for Integrated Automated Map

H( ) is Normalised to uniformity issues & conclusions issues & conclusions characteristic description: distribution. • optimisation minimises spatial entropy issues ...
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A Spatial Structuration Heuristic for Integrated Automated Map Generalisation with Attribute and Geometry

map generalization, classification, competing algorithm, entropy, thematic maps census population

a geometric generalisation

an attribute generalisation

clustering, spatial clustering

line simplification, amalgamation, elimination ..., line smoothing, schematisation, ...



• •

a Map

sequential approaches integrated approaches

is described by characteristics related to the objects composing the map:

integrated optimisation here we used



optimisation process = at each iteration choosing the “best” operator

, atomic transformation

among geometric and attribute families of operators [ref]

• “best”= increasing the spatial organisation or structuration = minimising the Spatial entropy [ref]

• spatial Cooccurrences at distance d of the feature types define the organisation of the objects of the map for the given characteristic description: distribution

H( ) is Normalised to uniformity

issues & conclusions • optimisation minimises spatial entropy

A

with steps i.e. choice of local (iteration level) best

d =1600m



Spatial Heuristic

operators for attribute were very simple

Transformation



40

60

80

100

Iteration

B

-1.35

20

-1.45

0

Of_geo + Of_att

attr geom

Transformation attr geom

d =1000m

0

20

40

60

Iteration

first results

80

combined optimisation makes sense only if operators introduce some interaction in the characteristics (geometry . attribute) e.g. spatial clustering based on pixel

• heuristic towards clumped feature types

-1.55

Of_geo + Of_att

-1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8

Spatial Heuristic

100

insure more homogeneity but not necessarily simplification. Solutions may be: initial simplification of some, add more characteristic descriptions for geometry)

See also the abstract with [ref]erences http://www.nottingham.ac.uk/cgs/cgs_didier_leibovici.html