Hypothesis testing for medical imaging analysis via the smooth Euler characteristic transform

Shape-valued data are of interest in applied sciences, particularly in medical imaging. In this paper, inspired by a specific medical imaging example, we introduce a hypothesis testing method via the smooth Euler characteristic transform to detect significant differences among collections of shapes. Our proposed method has a solid mathematical foundation and is computationally efficient. Through simulation studies, we illustrate the performance of our proposed method. We apply our method to images of lung cancer tumors from the National Lung Screening Trial database, comparing its performance to a state-of-the-art machine learning model.