Image Representation via Bivariate Spline Surface Smoothing
Date:
This is a invited talk given at the SSC 2026 Annual Meeting.
Abstract:
In contemporary data science, images are widely used as predictors and responses in complex modeling tasks, such as magnetic resonance imaging (MRI) for disease classification. Traditionally, images are represented as pixel grids, and most analysis techniques, including deep learning, operate directly on this representation. While effective, such approaches often raise challenges related to interpretability, scalability, and resolution dependence. In this talk, I introduce an alternative representation of images as smooth surfaces using penalized tensor-product spline smoothing. This framework provides a low-dimensional, resolution-independent description of image structure grounded in nonparametric regression methodology. I illustrate its application to stable multi-scale gradient evaluation and polynomial-resolution changes, which are key components for contour detection and image segmentation. I conclude with a discussion of surface-based image representations.
You can download the slides here later.