🤖 AI Summary
This work addresses the high computational cost and inefficiency of traditional pixel-based image representations in modeling shape and texture, which stem from high-dimensional discretization. To overcome these limitations, the authors propose a functional data representation that treats image contours and textures as observations of continuous random functions defined over star-shaped domains. By employing star-shaped parameterization, the method unifies the characterization of both shape and texture while avoiding high-dimensional discretization. Integrating functional data analysis with supervised learning, the proposed framework substantially reduces data dimensionality and enhances computational efficiency. Empirical evaluation on real-world image classification tasks demonstrates its effectiveness, confirming that the approach achieves competitive performance with significantly lower computational overhead.
📝 Abstract
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.