Images represent objects characterized by contours and textures. From a statistical perspective these features can be defined as observations of continuous random functions. However, most existing approaches rely on pixel-based discretizations which lead to high-dimensional representations and heavy computational costs. In this note, we introduce an alternative more frugal representation. This representation assumes that the object has a star-shaped domain interior. Under this condition, we explore the analysis of images from a functional data analysis perspective. The proposed framework is illustrated on a real data supervised image classification problem.

翻译：图像是由轮廓和纹理特征所表征的物体。从统计学角度来看，这些特征可被定义为连续随机函数的观测值。然而，现有方法大多基于像素离散化，导致高维表示和计算负担过重。本文提出一种更经济的替代表示方法，该方法假设物体具有星形内域。在此条件下，我们从函数型数据分析视角探索图像分析方法。通过真实数据的监督图像分类问题展示了所提框架的有效性。