A novel mathematical model to measure individuals' perception of the symmetry level of building facades

Symmetry is one of the key parameters in aesthetic judgement, and development of computational aesthetic approaches. Various experimental, statistical, and machine learning-based methods have been developed to parametrically measuring the symmetry, yet mathematical symmetry measurement models were barely studied. The development of mathematical symmetry measurement models can contribute to the development of symmetry-related models, computational aesthetic approach, and architectural design review. Accordingly, this research aims 1) to develop a mathematical model (symmetry index), and 2) to investigate the relationship between symmetry and aesthetic judgment. For this purpose, two surveys were conducted amongst 337 participants, the symmetry and aesthetic of 13 building images were evaluated, and the survey results were compared to the developed symmetry index. According to the findings, a positive correlation between symmetry and aesthetic appreciation was found and the influence of demographic differences on the symmetry, and aesthetic perception was discussed. The developed model successfully predicts the symmetry of studied buildings' images.