From Pixels to Shapes: A Functional Framework for Image Analysis
Date:
This is an invited talk given at the 2025 International Conference on Statistics and Data Science.
In this presentation, we introduce a novel perspective on image analysis that emphasizes objects and their shapes rather than individual pixels. By moving away from pixel-based approaches and analyzing images as collections of objects characterized by both color and contour, we establish a new framework that is more interpretable, less sensitive to resolution changes, and better aligned with the real-world geometry of the objects in images. To achieve this, we propose representing contours using coordinate functions—bivariate functional observations. Representing these functions through Fourier expansion provides an elegant solution to the alignment problem and allows us to apply a wide range of functional approaches to shape analysis, such as multivariate functional principal component analysis. We also discuss how to extend our approach to more complex images containing multiple objects. Finally, we illustrate the proposed method through a range of statistical applications, including sampling (generation), classification, and clustering on real image datasets.