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