calculating a map quality metric for ddm

7/28/2019 Calculating a Map Quality Metric for DDM

1/23

Measuring Map Quality

Material & Presentation by:

Richard Frank

Simon Fraser University

February 2004


2/23

Presentation Overview

Motivation

Uses of Map Quality

Requirements

Assumptions

Definitions

Algorithm Details


3/23

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/


4/23

Motivation

In printed form

(map)


5/23

Motivation

www.MapQuest.com

through a web-

browser
http://www.mapquest.com/http://www.mapquest.com/


6/23

Motivation

Microsoft

MapPoint(Standalone

Program)


7/23

Motivation

Displayed on a

PDA(Mapopolis)


8/23

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


9/23

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


10/23

Comparison

compare proposed

map to original map

(the best possible

map)

To determine best

alternative, compare

measures of themaps

Map Quality Indicator


11/23

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


12/23

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


13/23

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


14/23

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)


15/23

Algorithm Components

Object Shape Similarity

Structure Similarity

Information Content Similarity

Each will generate a measure


16/23

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


17/23

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!


18/23

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


19/23

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


20/23

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


21/23

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


22/23

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


23/23

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

calculating a map quality metric for ddm

Documents