Rethinking Image Data through Functional Representations of Shapes and Surfaces
Date:
This is an upcoming invited talk at Université Laval.
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 much more parsimonious. We show how to represent contours using coordinate functions, which can be expanded in a Fourier basis. This provides an elegant solution to the alignment problem and enables the use of a wide range of functional data analysis tools developed in the literature, such as functional principal component analysis and functional regression, for shape analysis. We then discuss how to extend our approach to more complex images containing multiple objects. We illustrate the performance of the proposed framework through a variety of statistical applications, including sampling, classification, and clustering on multiple real image datasets. Finally, we discuss representing entire images as smooth surfaces via basis expansions. This representation again offers a parsimonious and flexible description of images, well suited for statistical analysis.