### Abstract

Cartograms are used to visualize geographically distributed data by scaling the regions of a map (e.g., US states) such that their areas are proportional to some data associated with them (e.g., population). Thus the cartogram computation problem can be considered as a map deformation problem where the input is a planar polygonal map M and an assignment of some positive weight for each region. The goal is to create a deformed map M′, where the area of each region realizes the weight assigned to it (no cartographic error) while the overall map remains readable and recognizable (e.g., the topology, relative positions and shapes of the regions remain as close to those before the deformation as possible). Although several such measures of cartogram quality are well-known, different cartogram generation methods optimize different features and there is no standard set of quantitative metrics. In this paper we define such a set of seven quantitative measures, designed to evaluate how faithfully a cartogram represents the desired weights and to estimate the readability of the final representation. We then study several cartogram-generation algorithms and compare them in terms of these quantitative measures.

Original language | English (US) |
---|---|

Pages (from-to) | 351-360 |

Number of pages | 10 |

Journal | Computer Graphics Forum |

Volume | 34 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2015 |

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### ASJC Scopus subject areas

- Computer Networks and Communications

### Cite this

*Computer Graphics Forum*,

*34*(3), 351-360. https://doi.org/10.1111/cgf.12647

**Quantitative Measures for Cartogram Generation Techniques.** / Alam, Md Jawaherul; Kobourov, Stephen G; Veeramoni, Sankar.

Research output: Contribution to journal › Article

*Computer Graphics Forum*, vol. 34, no. 3, pp. 351-360. https://doi.org/10.1111/cgf.12647

}

TY - JOUR

T1 - Quantitative Measures for Cartogram Generation Techniques

AU - Alam, Md Jawaherul

AU - Kobourov, Stephen G

AU - Veeramoni, Sankar

PY - 2015/6/1

Y1 - 2015/6/1

N2 - Cartograms are used to visualize geographically distributed data by scaling the regions of a map (e.g., US states) such that their areas are proportional to some data associated with them (e.g., population). Thus the cartogram computation problem can be considered as a map deformation problem where the input is a planar polygonal map M and an assignment of some positive weight for each region. The goal is to create a deformed map M′, where the area of each region realizes the weight assigned to it (no cartographic error) while the overall map remains readable and recognizable (e.g., the topology, relative positions and shapes of the regions remain as close to those before the deformation as possible). Although several such measures of cartogram quality are well-known, different cartogram generation methods optimize different features and there is no standard set of quantitative metrics. In this paper we define such a set of seven quantitative measures, designed to evaluate how faithfully a cartogram represents the desired weights and to estimate the readability of the final representation. We then study several cartogram-generation algorithms and compare them in terms of these quantitative measures.

AB - Cartograms are used to visualize geographically distributed data by scaling the regions of a map (e.g., US states) such that their areas are proportional to some data associated with them (e.g., population). Thus the cartogram computation problem can be considered as a map deformation problem where the input is a planar polygonal map M and an assignment of some positive weight for each region. The goal is to create a deformed map M′, where the area of each region realizes the weight assigned to it (no cartographic error) while the overall map remains readable and recognizable (e.g., the topology, relative positions and shapes of the regions remain as close to those before the deformation as possible). Although several such measures of cartogram quality are well-known, different cartogram generation methods optimize different features and there is no standard set of quantitative metrics. In this paper we define such a set of seven quantitative measures, designed to evaluate how faithfully a cartogram represents the desired weights and to estimate the readability of the final representation. We then study several cartogram-generation algorithms and compare them in terms of these quantitative measures.

UR - http://www.scopus.com/inward/record.url?scp=84937951346&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937951346&partnerID=8YFLogxK

U2 - 10.1111/cgf.12647

DO - 10.1111/cgf.12647

M3 - Article

VL - 34

SP - 351

EP - 360

JO - Computer Graphics Forum

JF - Computer Graphics Forum

SN - 0167-7055

IS - 3

ER -