Multivariate planar curves: definition, alignment and statistical analysis

This is a invited talk given at EcoSta 2026.

Abstract:

We consider the statistical analysis of images containing multiple objects of interest, where shapes can be represented through a collection of planar curves. While most existing approaches focus on single-object shape analysis, many applications, such as medical imaging, require modeling several contours jointly, along with their relative geometry. In this work, we propose a functional framework for the analysis of multivariate planar curves extracted from images. Each object is represented as a parametric curve, and the collection of curves is treated as a structured functional variable. Building on recent advances in functional shape analysis, we develop methods to jointly align multiple contours while preserving their spatial relationships. This allows us to capture both individual shape variability and interactions between objects, such as relative size, position, and orientation. We then introduce statistical models to describe this joint variability and demonstrate how these representations can be used for tasks such as classification and anomaly detection. The proposed framework is illustrated on medical imaging data, where the joint analysis of anatomical structures provides clinically relevant information. Our results highlight the importance of modeling shapes as interacting objects rather than independent entities, and show that functional representations offer a flexible and interpretable approach to multivariate shape analysis.

You can download the slides here later.