Medial-axis-based cartograms

@article{Keim2005MedialaxisbasedC,
  title={Medial-axis-based cartograms},
  author={Daniel A. Keim and Christian Panse and Stephen C. North},
  journal={IEEE Computer Graphics and Applications},
  year={2005},
  volume={25},
  pages={60-68}
}
Cartographers and geographers were making cartograms for centuries before digital computers and displays became available. In data visualization, an area cartogram distorts a map by resizing its regions according to some external geography-related parameter, such as population or epidemiological data. Cartograms are difficult to draw by hand because it's difficult to simultaneously optimize shape and area error while preserving the original map's topology. Automated methods for drawing… 

Figures from this paper

Studies on New Cartogram Construction Algorithms and Their Applications

This paper proposes construction algorithms for three types of cartograms and illustrates their applicability to the visualization of statistical data.

The State of the Art in Cartograms

This work surveys cartogram research in visualization, cartography and geometry, covering a broad spectrum of different cartogram types: from the traditional rectangular and table cartograms, to Dorling and diffusion cartograms.

A Multi-scale Dynamic Map Using Cartograms to Reflect User Focus

A dynamic map that recursively uses a cartogram algorithm in a nested structure to distort shape, enlarging any areas of user interest or focus, has been implemented and tested and is proposed to be more usable than traditional methods of multi-scale representation or moving between scales.

Task Taxonomy for Cartograms

This paper considers a set of cartogram visualization tasks, based on standard taxonomies from cartography and information visualization, and proposes a cartogram task taxonomy that can be used to organize not only the tasks considered here but also other tasks that might be added later.

Cartograms via mathematical morphology

It is inferred from the comparative error analysis that the proposed morphology-based approach could be further extended by exploring the applicability of additional characteristics of B, which controls the dilation propagation speed and direction of dilation while performing weighted skeletonization by zone of influence, to minimize the local shape errors and area errors.

Quantitative Measures for Cartogram Generation Techniques

A set of seven quantitative measures is defined, designed to evaluate how faithfully a cartogram represents the desired weights and to estimate the readability of the final representation.

Value-by-alpha Maps: An Alternative Technique to the Cartogram

A new kind of representation, termed a value-by-alpha map, which visually equalizes the basemap by adjusting the alpha channel, rather than the size, of each enumeration unit, is described.

An Experimental Study of Algorithms for Cartogram Generation

Some quantitative measures that can be used to evaluate how faithfully a cartogram represents the weights, as well as several measures for evaluating the readability of the final representation are defined.

Design and Implementation of Travel-time Cartograms

This paper proposes three design principles to keep the scale of the transformed map the same with its original map; a number of constraints to adjust topological errors generated by the process of transformation based on Moving Least Squares; and 3-D visualization methods to represent travel-time cartograms and their deformation.

Manual construction of continuous cartograms through mesh transformation

A computer-assisted framework employs a joint triangulation, similar to that used in rubber-sheeting, to define a piecewise affine transformation between map space and cartogram space that guarantees preservation of all topological relations within and among transformed datasets with insertion of a finite number of points.

References

SHOWING 1-10 OF 15 REFERENCES

Continuous cartogram construction

A new algorithm for the construction of continuous area cartograms is presented that was developed by viewing their construction as a constrained optimization problem and uses a relaxation method that exploits hierarchical resolution, constrained dynamics, and a scheme that alternates goals of achieving correct region areas and adjusting region shapes.

Efficient cartogram generation: a comparison

This work compares two algorithms to solve the problem of making continuous cartograms that strictly retain the topology of the input mesh, which uses pixel-based distortion based on a quadtree-like data structure.

AN ALGORITHM TO CONSTRUCT CONTINUOUS AREA CARTOGRAMS

A computer algorithm is presented which can handle more realistic descriptions of polygon boundaries than previous algorithms and manual methods, thus enhancing visual recognition.

CartoDraw: a fast algorithm for generating contiguous cartograms

An efficient iterative scanline algorithm to reposition edges while preserving local and global shapes and a shape similarity function, which is based on a Fourier transformation of the polygons' curvatures are proposed.

Cartographic transformations and the piezopleth maps method

AbstractNumerous types of anamorphoses, or cartographic transformations, have been perfected, leading to a distorted picture as compared to the usual map representations. Piezopleth maps are a

A combinatorial approach to cartograms

An algorithm is described that constructs homeomorphisms with prescribed area distortion that can be used to generate cartograms, which are geographic maps purposely distorted so its area distribution reflects a variable different from area.

Population Maps

THE possibilities of the quantitative representation of geographical data as regards population distribution are discussed in some detail by the originator of a new method, Mr. S. de Geer, in the

Using ArcView to Create Contiguous and Noncontiguous Area Cartograms

An enhanced Avenue “programming” code for constructing thematic canograms in the ArcVeiw GIS environment is described and methods of interpreting the canograms are described.

A New Technique for Constructing Continuous Cartograms

This paper deals with the problem of constructing graphic images of territories that make the density of a variable (e.g., thedensity of population) uniform and describes a new algorithm and the results of its applications.