Generative modeling of biological shapes and images using a probabilistic α-shape sampler.

Understanding morphological variation is an important task in many areas of computational biology. Recent studies have focused on developing computational tools for the task of sub-image selection which aims at identifying structural features that best describe the variation between classes of shapes. A major part in assessing the utility of these approaches is to demonstrate their performance on both simulated and real datasets. However, when creating a model for shape statistics, real data can be difficult to access and the sample sizes for these data are often small due to them being expensive to collect. Meanwhile, the current landscape of generative models for shapes has been mostly limited to approaches that use black-box inference-making it difficult to systematically assess the power and calibration of sub-image models. In this paper, we introduce the α-shape sampler: a probabilistic framework for generating realistic 2D and 3D shapes based on probability distributions which can be learned from real data. We demonstrate our framework using proof-of-concept examples and in two real applications in biology where we generate (i) 2D images of healthy and septic neutrophils and (ii) 3D computed tomography (CT) scans of primate mandibular molars. The α-shape sampler R package is open-source and can be downloaded at https://github.com/lcrawlab/ashapesampler.