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Measuring Map Quality
Material & Presentation by:
Richard Frank
Simon Fraser University
February 2004
Presentation Overview
Motivation Uses of Map Quality Requirements Assumptions Definitions Algorithm Details
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.
Uses of Map Quality
Give the user some indication of how accurate different aspects (location, shape, etc) of the map are
Beneficial in providing the end-user a map that is much better tailored to their specific wants If the end user is interested in the structure
of the maps, the computer can select the best map out of a set of possible maps with best possible structure
Uses of Map Quality
Can compare qualities of two alternate maps at same scale
Can measure quality after the generalization operator, or after the visualization operator
On the backside, it can be used to determine which data-cubes to generate Ones that can quickly produce, without
generalization, on-demand maps above a certain quality
Comparison
compare proposed map to original map (the best possible map)
To determine best alternative, compare measures of the maps
Map Quality Indicator
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
Assumptions
No symbolic representation for shapes Shapes remain shapes
We’re not concerned about changes in readability
Objects with holes are treated as multiple objects, i.e.: holes are treated as objects themselves
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
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)
Algorithm Components
Object Shape Similarity Structure Similarity Information Content Similarity
Each will generate a measure
Shape Similarity A map is a collection of
objects, which after generalization can change in shape
The information loss during the shape-change has to be measured
Use: Edit-Distance of Voronoi Skeleton
Idea adapted from ‘Edit-Distance of Shock Graphs’
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 to transformations that are required to change one structure into the other
Object from Original Map Object from Generalized Map
No Bump!
Structure similarity Objects will be displaced
during generalization the position of an object will
change relative to the map
boundaries Relative distance to other
objects Procedure
Measure distances Input distances into matrix calculate a cosine similarity
(standard way of comparing matrices)
Objects & their Voronoi Regions
Before After
Length between neighbors
Information Content Similarity
During generalization, several objects could be merged/aggregated into one larger object, or can be deleted
There is loss of information because we loose information about the individual objects
Loose 4 small objects Gain 1 large object
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 object
divided by the total map area Where Pi = Ki/N
Ki = # of objects of type i N = total # of objects on the map
Algorithm Components
Consolidate the 3 measures into one number (representing the quality 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 ‘ideal’ situation (if there is one), or can be left up to the user to let them specify which issue is more important to them.
OR
Display all three resulting measures independently to the user and let them interpret the results
Future Work
Currently working on implementation Spatio-Temporal Data mining
We can compare sub-areas of two maps from different time periods to find area with most change, with possibility of restricting to any class ex: Find square kilometer with most road
development
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 Views Management and the concept of VUEL, Yvan Bedard and Eveline Bernier, Universite Laval
Fast computation of Generalized Voronoi Diagrams using Graphics Hardware. 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, J Mark Ware & Christopher B. Jones, University of Glamorgan. 1998