Analysis of the effectiveness of constraining metrics of geometric simplification algorithms based on expert evaluation of line detail

Abstract

The paper reveals dependencies between the character of the line shape and combination of constraining metrics that allows comparable reduction in detail by different geometric simplification algorithms. The study was conducted in a form of the expert survey. geometrically simplified versions of three coastline fragments were prepared using three different geometric simplification algorithms—Douglas-peucker, Visvalingam-Whyatt and Li-Openshaw. Simplification was constrained by similar value of modified hausdorff distance (linear offset) and similar reduction of number of line bends (compression of the number of detail elements). Respondents were asked to give a numerical estimate of the detail of each image, based on personal perception, using a scale from one to ten. The results of the survey showed that lines perceived by respondents as having similar detail can be obtained by different algorithms. however, the choice of the metric used as a constraint depends on the nature of the line. Simplification of lines that have a shallow hierarchy of small bends is most effectively constrained by linear offset. As the line complexity increases, the compression metric for the number of detail elements (bends) increases its influence in the perception of detail. For one of the three lines, the best result was consistently obtained with a weighted combination of the analyzed metrics as a constraint. None of the survey results showed that only reducing the number of bends can be used as an effective characteristic of similar reduction in detail. It was therefore found that the linear offset metric is more indicative when describing changes in line detail.