S4A: Scalable Spectral Statistical Shape Analysis

Statistical shape analysis is a crucial technique for studying deformations within collections of shapes, particularly in the field of Medical Imaging. However, the high density of meshes typically used to represent medical data poses a challenge for standard geometry processing tools due to their limited efficiency. While spectral approaches offer a promising solution by effectively handling high-frequency variations inherent in such data, their scalability is questioned by their need to solve eigendecompositions of large sparse matrices. In this paper, we introduce S4A, a novel and efficient method based on spectral geometry processing, that addresses these issues with a low computational cost. It operates in four stages: (i) establishing correspondences between each pair of shapes in the collection, (ii) defining a common latent space to encode deformations across the entire collection, (iii) computing statistical quantities to identify, highlight, and measure the most representative variations within the collection, and iv) performing information transfer from labeled data to large collections of shapes. Unlike previous methods, S4A provides a highly efficient solution across all stages of the process.We demonstrate the advantages of our approach by comparing its accuracy and computational efficiency to existing pipelines, and by showcasing the comprehensive statistical insights that can be derived from applying our method to a collection of medical data.