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7/28/2019 Calculating a Map Quality Metric for DDM
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Measuring Map Quality
Material & Presentation by:
Richard Frank
Simon Fraser University
February 2004
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Presentation Overview
Motivation
Uses of Map Quality
Requirements
Assumptions
Definitions
Algorithm Details
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Motivation
Maps are generated in different ways Carefully by a human designer
Automatically by a professional program Microsoft MapPoint
Automatically by a free service www.mapquest.com
They can also be shown on a wide variety of
medium Due to resolution constraints, objects will
change or disappear.
http://www.mapquest.com/http://www.mapquest.com/7/28/2019 Calculating a Map Quality Metric for DDM
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Motivation
In printed form
(map)
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Motivation
www.MapQuest.com
through a web-
browser
http://www.mapquest.com/http://www.mapquest.com/7/28/2019 Calculating a Map Quality Metric for DDM
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Motivation
Microsoft
MapPoint(Standalone
Program)
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Motivation
Displayed on a
PDA(Mapopolis)
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Uses of Map Quality
Give the user some indication of howaccurate different aspects (location,shape, etc) of the map are
Beneficial in providing the end-user amap that is much better tailored to theirspecific wants
If the end user is interested in the structureof the maps, the computer can select thebest map out of a set of possible maps withbest possible structure
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Uses of Map Quality
Can compare qualities of two alternate maps at
same scale
Can measure quality after the generalizationoperator, or after the visualization operator
On the backside, it can be used to determine
which data-cubes to generate
Ones that can quickly produce, withoutgeneralization, on-demand maps above a certain
quality
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Comparison
compare proposed
map to original map
(the best possible
map)
To determine best
alternative, compare
measures of themaps
Map Quality Indicator
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Requirements for good
measurement
Measure must take into account
individual objects on a map
the structure between them their distribution on a map
These are enough to describe changes
on a map No such measure currently exist
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Assumptions
No symbolic representation for shapes
Shapes remain shapes
Were not concerned about changes inreadability
Objects with holes are treated as multiple
objects, i.e.: holes are treated as objectsthemselves
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Definition Voronoi Diagram
Given a map of objects
Find closest object or object edge
If the closest edges belong to two or more objects which are
equally close, then it is a Voronoi boundary
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Definition Voronoi Skeleton
If the point is inside the object and the closest edges belong to
two or more edges of the same object then it is part of the
Voronoi Skeleton
Voronoi Skeleton (in Red)
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Algorithm Components
Object Shape Similarity
Structure Similarity
Information Content Similarity
Each will generate a measure
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Shape Similarity
A map is a collection ofobjects, which aftergeneralization canchange in shape
The information lossduring the shape-change has to bemeasured
Use: Edit-Distance of
Voronoi Skeleton Idea adapted from Edit-
Distance of ShockGraphs
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Shape Similarity
Objects that contain holes are treated as multiple objects
Small perturbations do not affect the Voronoi Skeleton
Ideal for maps and bitmap objects
Calculate edit distance by assigning costs totransformations that are required to change one
structure into the other
Object from Original Map Object from Generalized Map
No Bump!
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Structure similarity
Objects will be displacedduring generalization
the position of an object willchange
relative to the mapboundaries
Relative distance to otherobjects
Procedure
Measure distances
Input distances into matrix
calculate a cosine similarity(standard way of comparingmatrices)
Objects & their Voronoi Regions
Before After
Length between neighbors
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Information Content Similarity
During generalization, several objects could bemerged/aggregated into one larger object, or can bedeleted
There is loss of information because we looseinformation about the individual objects
Loose 4 small objects Gain 1 large object
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Information Content: Entropy
Usual method: Entropy Original calculation: SUM(Pi*ln(Pi))
Should modify it by weighing objects according to
the area of their Voronoi regions If information is lost when something disappears, the
objects remaining become more important/influential
Modified method: VE=SUM(Pi*ln(Pi)*%V)
%V is the area of the Voronoi region for the objectdivided by the total map area
Where Pi = Ki/N Ki = # of objects of type i
N = total # of objects on the map
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Algorithm Components
Consolidate the 3 measures into one number (representing thequality of the map)? Q = W1 * M1 + W2 * M2+ W3 * M3
Where
Q = Map quality measure Pi= some weight for metric i
Mi= Measure of metric i
The parameters can either be pre-defined, representing an idealsituation (if there is one), or can be left up to the user to let themspecify which issue is more important to them.
OR
Display all three resulting measures independently to the userand let them interpret the results
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Future Work
Currently working on implementation
Spatio-Temporal Data mining
We can compare sub-areas of two mapsfrom different time periods to find area with
most change, with possibility of restricting to
any class
ex: Find square kilometer with most road
development
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References
Shape matching using edit-distance: an implementation (2001), Philip N.Klein, Thomas B. Sebastian, Benjamin B. Kimia, Symposium on Discrete
Algorithms
Framework for Matching shock graphs, Thomas B. Sebastian, Philip N.Klein, Benjamin B. Kimia,www.lems.brown.edu/vision/researchAreas/ShockMatching/shock-matching.html,
10/16/2003 Quantitative measures for spatial information of maps, Zhilin Li and Peizhi
Huang, Hong Kong Polytechnic University, Dec 2001
Supporting Multiple Representations with Spatial Database ViewsManagement and the concept of VUEL, Yvan Bedard and Eveline Bernier,Universite Laval
Fast computation of Generalized Voronoi Diagrams using GraphicsHardware. Kenneth E Hoff, Tim Culver, John Keyser, Ming Lin, Dinesh Manocha.
University of North Carolina Voronoi Diagrams of Polygons: A Framework for shape representation. Niranjan
Mayya & V.T. Rajan, University of Florida
Conflict Reduction in Map Generalization using Iterative Improvement, JMark Ware & Christopher B. Jones, University of Glamorgan. 1998
http://www.lems.brown.edu/vision/researchAreas/ShockMatching/shock-matching.htmlhttp://www.lems.brown.edu/vision/researchAreas/ShockMatching/shock-matching.htmlhttp://www.lems.brown.edu/vision/researchAreas/ShockMatching/shock-matching.htmlhttp://www.lems.brown.edu/vision/researchAreas/ShockMatching/shock-matching.html