A Comparative Study of Descriptors for Quadrant-Convexity

Many different descriptors have been proposed to measure the convexity of digital shapes. Most of these are based on the definition of continuous convexity and exhibit both advantages and drawbacks when applied in the digital domain. In contrast, within the field of Discrete Tomography, a special type of convexity—called Quadrant-convexity—has been introduced. This form of convexity naturally arises from the pixel-based representation of digital shapes and demonstrates favorable properties for reconstruction from projections. In this paper, we present an overview of using Quadrant-convexity as the basis for designing shape descriptors. We explore two different approaches: the first is based on the geometric features of Quadrant-convex objects, while the second relies on the identification of Quadrant-concave pixels. For both approaches, we conduct extensive experiments to evaluate the strengths and limitations of the proposed descriptors. In particular, we show that all our descriptors achieve an average accuracy of approximately $95\%$ to $97.5\%$ on noisy retina images for a binary classification task. Furthermore, in a multiclass classification setting using a dataset of desmids, all our descriptors outperform traditional low-level shape descriptors, achieving an accuracy of 76.74%.