A statistical analysis of mathematical measures for linear simplification

The implementation of automated cartography has resulted in the digitization of linear data and the development of simplification algorithms for generalizing these data. Some algorithms, such as the nth point and random point methods are simple in both practice and operation. Others, such as polynomial reconstruction, appear to be conceptually overly complex and computationally time consuming.This study presents a method for the evaluation of simplification algorithms. Thirty mathematical measures are developed for this purpose, including both single attribute measurements, which may be applied to a single line, and measures of displacement for evaluating differences between a line and its simplification. These measures are used to compare thirty-one unsimplified naturally-occurring lines with two simplifications of each. Using principal components analysis, correlation matrices, and cartographic judgment, the thirty measures are reduced to six by eliminating statistical redundancy. The resulting six measures should be useful in analyzing the efficiency of the multitude of simplification algorithms currently in use.