A Metric for Polygon Comparison and Building Extraction Evaluation

The standardization of evaluation techniques for building extraction is an unresolved issue in the fields of remote sensing, photogrammetry, and computer vision. In this letter, we propose a metric with a working title "PoLiS metric" to compare two polygons. The PoLiS metric is a positive-definite and symmetric function that satisfies a triangle inequality. It accounts for shape and accuracy differences between the polygons, is straightforward to apply, and requires no thresholds. We show through an example that the PoLiS metric between two polygons changes approximately linearly with respect to small translation, rotation, and scale changes. Furthermore, we compare building polygons extracted from a digital surface model to the reference building polygons by computing PoLiS, Hausdorff, and Chamfer distances. The results show that quantification by the PoLiS distance of the dissimilarity between polygons is consistent with visual perception. Furthermore, Hausdorff and Chamfer distances overrate the dissimilarity when one polygon has more vertices than the other. We propose an approach toward standardizing building extraction evaluation, which may also have broader applications in the field of shape similarity.