Exploring 2D shape complexity

Abstract

In this paper, we explore different notions of shape complexity, drawing from established work in mathematics, computer science, and computer vision. Our measures divide naturally into three main categories: skeleton-based, symmetry-based, and those based on boundary sampling. We apply these to an established library of shapes, using k-medoids clustering to understand what aspects of shape complexity are captured by each notion. Our contributions include a new measure of complexity based on the Blum medial axis and the notion of persistent complexity as captured by histograms at multiple scales rather than a single numerical value.