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

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