Approximate local reflection symmetry of projected land cadastre data

Abstract Symmetry is an essential feature of many geometric objects. However, the world also contains many asymmetrical or approximately symmetrical objects. Detecting approximate symmetries is a rather weakly defined problem, as computer-detected approximate symmetry may not correspond to human opinion. The situation is even worse if the symmetry is not global but local. This paper investigates whether approximate local reflection symmetries found by a computer in real data are acceptable for human observers. To answer this question, a new simple approximate local reflection symmetry detection is proposed and run on land cadastre data in the form of planar point sets. The resulting symmetries are subject to user tests to study human acceptance of approximate local symmetry. The results show a relatively good correlation between symmetry detected by computers and perceived by humans. This finding provides a solid foundation for integrating both approaches in specific applications. To achieve this, further research is needed on how to utilize specific aspects of human symmetry perception in computer solutions, so that computer symmetry detection can better approximate human perception.