Cartograms via mathematical morphology

Visualization of geographic variables as spatial objects of size proportional to variable strength is possible via generating cartograms. We developed a methodology based on mathematical morphology to generate contiguous cartograms. This methodology relies on weighted skeletonization by zone of influence. This weighted skeletonization by zone of influence determines the points of contact of multiple frontlines propagating from centroids of various planar sets (states) at the traveling rates depending upon the variable's strength. The contiguous cartogram generated via this morphology-based algorithm preserves the global shape and local shapes and yields minimal area errors. We generated a cartogram for a population variable to demonstrate the proposed approach. Furthermore, the population cartograms for the United States generated via four other approaches are compared with the morphology-based cartogram in terms of errors with respect to area, local shape, and global shape. This approach for generating cartograms preserves the global shape at the expense of compromising with area errors. 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.