A1767
Title: Multivariate planar curves: Definition, alignment and statistical analysis
Authors: Cedric Beaulac - Universite Du Quebec a Montreal (Canada) [presenting]
Abstract: A functional framework for the analysis of multivariate planar curves extracted from images is proposed. 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, methods are developed to jointly align multiple contours while preserving their spatial relationships. This allows capturing both individual shape variability and interactions between objects, such as relative size, position, and orientation. Statistical models are introduced 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. 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.
