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.

翻译：形状值数据在应用科学领域，尤其是在医学影像学中具有重要研究价值。本文受特定医学影像案例启发，提出了一种基于光滑欧拉特征变换的假设检验方法，用于检测形状集合间的显著差异。该方法具有坚实的数学基础且计算高效。通过仿真实验，我们展示了所提方法的性能。我们将该方法应用于国家肺癌筛查试验数据库中的肺癌肿瘤影像，并将其性能与当前最先进的机器学习模型进行了比较。