Perceptually grounded quantification of 2D shape complexity

The importance of measuring the complexity of shapes can be seen by the wide range of its application such as computer vision, robotics, cognitive studies, eye tracking, and psychology. However, it is very challenging to define an accurate and precise metric to measure the complexity of the shapes. In this paper, we explore different notions of shape complexity, drawing from established work in mathematics, computer science, and computer vision. We integrate results from user studies with quantitative analyses to identify three measures that capture important axes of shape complexity, out of a list of almost 300 measures previously considered in the literature. We then explore the connection between specific measures and the types of complexity that each one can elucidate. Finally, we contribute a dataset of both abstract and meaningful shapes with designated complexity levels both to support our findings and to share with other researchers.