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 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 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 MapObject 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, 10/16/ 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