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.

Motivation

In printed form

(map)

Motivation

www.MapQuest.com through a web-browser

Motivation

Microsoft

MapPoint(Standalone

Program)

Motivation

Displayed on a PDA

(Mapopolis)

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