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Department of Geography Assessing the Cartographic Performance of Real-Time Quadtree-based Generalisation of Point Data Pia Bereuter & Robert Weibel Department of Geography, University of Zurich (UZH) {pia.bereuter |

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Department of Geography

Assessing the Cartographic Performance of Real-Time Quadtree-based Generalisation of Point Data

Pia Bereuter & Robert Weibel Department of Geography, University of Zurich (UZH) {pia.bereuter | robert.weibel}@geo.uzh.ch

25 Aug 2013 ICA Workshop on Generalisation and Map Production, Dresden, 2013 1

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Department of Geography

ICA Workshop on Generalisation and Map Production, Dresden, 2013

Motivation: Web & mobile maps today

25 Aug 2013

Source: http://www.openstreetmap.org http://www.myswitzerland.com http://www.google.com/publicdata http://map.search.ch/

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Too Clustered Too generalised Too cluttered

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Department of Geography

Objective

Provide a set of algorithms for on-the-fly generalisation of foreground point data

  • points of interest (POIs)
  • point collections (animal observations, Flickr points etc.)

Proposed approach, contributions

  • exploit properties of quadtrees as an auxiliary data structure for

generalisation

  • develop the major generalisation operators on point sets:

selection, simplification, aggregation and displacement

  • real-time performance
  • Assessing the cartographic performance of the algorithms

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Content

  • 1. Background
  • 2. Quadtree-based algorithms for point data generalisation
  • 3. Assessing the cartographic performance
  • 4. Conclusions & outlook

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Background

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Real-time point data generalisation

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Focus today is on real-time generalisation algorithms and the assessment of their cartographic performance. Existing algorithms: Initial solution for real-time aggregation based on the quadtree data structure: Burghardt et al. (2004) and Edwardes et al. (2005) Pre- computation & hierarchical data structures Simple algorithms using heuristics to achieve real- time performance Efficiency Flexibility

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Quadtree-based algorithms for point data generalisation

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Useful properties of quadtree for point data generalisation

Property Use Spatial Index Speed up spatial search Hierarchy Progressive subdivision = scale progression Quad coverage Estimates of densities and distribution Topology Quad neighbourhood

25 Aug 2013 ICA Workshop on Generalisation and Map Production, Dresden, 2013

Key idea: The quadtree data structure lends itself to a number of simple, yet efficient and effective algorithms. See: Bereuter P and Weibel R, 2013. Real-time generalization of point data in mobile and web mapping using quadtrees. Cartography and Geographic Information Science, 40 (4), 1–11.

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Method: Three main steps

25 Aug 2013

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Apply generalisation algorithm

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Create quadtree

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Storage (optional)

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Target LOD Target LOD

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Object Directed Operators – Point Reduction

  • Selection: Based on attribute

values; no geometric criteria used.

  • Simplification: Centrality

based – use geometric criteria to select subset of points — as in line simplification.

  • Aggregation: Various

principles: midpoint, cluster- based, collocation

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Object directed operators – Displacement

25 Aug 2013

4 1 3

A B C

Direction Capacity Total C 1 3 3 B 2 4,3 7 A 1 1 1

M

2 3

C B

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Storage

25 Aug 2013

Quadnode Occupied leaf Empty leaf Stored generalization result Algorithm search range Level 2 3 1 4 Storage structure for generalisation results for interactive zooming

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Assessing the cartographic perfomance

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Implementation

Java Processing http://www.processing.org Open source programming language and IDE (1991 - now)

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Data

Swiss Lichens of the Nationales Daten- und Informationszentrum der Schweizer Flechten – WSL, Birmensdorf.

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Species & Collection attribute Species name, Genus, Ecotype, observation date Locality Coordinate (randomised < 1km max), XY precision, Habitat, Substrate Population characteristics Size and vitality Ecology and conservation Red list status, Conservational priority, Ecological indicator (Eutrophication, Humidity, Continentality, Light, Temperatur

Lichen

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Performance

25 Aug 2013 ICA Workshop on Generalisation and Map Production, Dresden, 2013800 ms 16

Small data set Medium data set Large data set

  • ca. 290 points ca. 2800 points
  • ca. 86000 points

Quadtree creation 0.8 ms 8 ms 460 ms Average computation time to move between two different zoom levels Selection 0.13 ms 3 ms 150 ms Median Selection 0.06 ms 2 ms 110 ms Aggregation 0.05 ms 1.6 ms 90 ms Displacement 0.98 ms 13 ms 800 ms

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SwissLichens Dataset: Displacement Selection, Simplification, Aggregation

Data Reduction

What is the data reduction rate in relation to the zoom level?

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Clustered Point Pattern: 20 clusters, stdev. 0.1 Displacement Selection, Simplification, Aggregation Clustered Point Pattern: 10 clusters, stdev. 0.05 Displacement Selection, Simplification, Aggregation Regular Point Pattern: All generalisation operators Random Point Pattern: Displacement Selection, Simplification, Aggregation Radical law

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Data Reduction

What is the data reduction rate in relation to the zoom level?

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SwissLichens Dataset: Displacement Selection, Simplification, Aggregation Radical law with base zoom level 15 Radical law with various base zoom levels Area of positive difference Selection, Simplification, Aggregation Displacement Area of negative difference Selection, Simplification, Aggregation Displacement

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Conflict reduction

How many overlaps between points symbols are resolved? Quadtree selection operator

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Conflict reduction

How many overlaps between points symbols are resolved? Quadtree selection operator

  • including horizontal and

vertical neighbour check

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Conflict reduction

How many overlaps between points symbols are resolved? Quadtree selection operator

  • including horizontal and

vertical neighbour check

  • including diagonal neighbour

check

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Conflict reduction

How many overlaps between points symbols are resolved? Quadtree selection operator

  • including horizontal and

vertical neighbour check

  • including diagonal neighbour

check

  • Debug view

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Conflict reduction

How many overlaps between points symbols are resolved?

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Selection with no conflict reduction Selection with horizontal & vertical conflict reduction Selection with diagonal conflict reduction ~ 200ms ~ 450ms ~ 700ms

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Data Enhancement

How are important point attributes retained?

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Map zoom level 10

Least concern Near threatened Endangered species Critically endangered

Red list status (IUCN)

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Data Enhancement

How are important point attributes retained?

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Map zoom level 9

Least concern Near threatened Endangered species Critically endangered

Red list status (IUCN)

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Data Enhancement

How are important point attributes retained?

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Map zoom level 8

Least concern Near threatened Endangered species Critically endangered

Red list status (IUCN)

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Data Enhancement

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Global selection (Radical Law) Local selection (Quadtree) zoom level 8

Map zoom level 8

Global selection (global hotspots) versus local selection (retaining local context)

Map zoom level 8

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Displacement Measures

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Centrality-based simplification 647 points How is displacement achieved?

Map zoom level 11

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Displacement Measures

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Displacement 788 points How is displacement achieved?

Map zoom level 11

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Displacement Measures

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Displacement 788 points How is displacement achieved?

Map zoom level 11

Cumulative displacement vectors

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Maintenance of spatial patterns

Is the overall point distribution maintained?

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Kernel Density Estimation Difference between Kernel Density Estimation between two consecutive zoom levels (9 and 10)

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Conclusions & outlook

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Discussion

  • Data reduction reflects the underlying spatial distribution of the point data.
  • Conflict resolution reveals where “action-rich” zoom levels are.
  • Data Enhancement shows how the algorithm keeps the local context.
  • Displacement measures highlights displacement and directionality
  • Maintenance of spatial distribution, highlights where most changes

happen.

  • Quadtrees are: sufficiently fast and modular, can be used for storage of pre-

computed states and allow implementing the major generalization

  • perators on points: selection, simplification, aggregation and displacement

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Thank you for your attention!

Pia Bereuter pia.bereuter@geo.uzh.ch Robert Weibel robert.weibel@geo.uzh.ch

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Department of Geography

Stofer, S., Scheidegger, C., Clerc, P., Dietrich, M., Frei, M., Groner, U., Jakob, P., Keller,C., Roth, I., Vust, M., and Zimmermann, E. (2012). Nationales Daten- und Informationszentrum der Schweizer Flechten -

  • SwissLichens. Birmensdorf, Schweiz. Eidgenossische

Forschungsanstalt WSL, Datenbankauszug vom 25. September 2012 (SST 201209).

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Midpoint tile-based aggregation

Raw distribution of eating places in the City of Zurich

Aggregation of points inside a quadnode to the tile center Graduated circles: Weighting the point symbols by number of

  • riginal points they

represent.

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Selection

25 Aug 2013 14 13 12

Rank-based selection for LOD 14, 13, 12 — for each quadnode, retain the point with the highest observation count.

LOD Scale Points Radical law

14 ~1:36000 ~130 130 13 ~1:72000 ~50 32 12 ~1:144000 ~20 8

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Ibex Chamois Red deer

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Simplification

Centrality-based simplification algorithm applied to POIs.

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Simplification

Centrality-based simplification algorithm applied to animal

  • bservations (point collection).

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Aggregation

Overlay for LOD 13:

  • Blue points:

Midpoint-based aggregation, with symbol size weighted by number

  • f aggregated points
  • Red points:

Ranking-based selection

  • Purple points:

Overlapping symbols

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Aggregation by co-location filtering

Aggregation by co-location Symbol size weighted by number of co-

  • ccurrences for restaurant and parking.

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Displacement

Centrality-based simplification

25 Aug 2013

Displacement applied after centrality-based simplification  allows retaining more points Alpine ibex Chamois Red deer

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Process

25 Aug 2013

  • 1. Raw data
  • 2. Centrality-based

generalization

  • 3. Displacement
  • 4. Content Zooming

a) increased LOD b) decreased LOD

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“Content Zooming”: see Bereuter & Weibel (2012, AGILE)

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