Analysis of large scale 3D shape collection with learning based approaches

Overview & Synopsis

Robotics, medical imaging, and digital design increasingly depend on 3D shape analysis for tasks like correspondence, reconstruction, and generative modeling. While geometry-based optimization once dominated, deep learning shifted attention to data-driven feature extraction. Yet current approaches remain limited by reliance on supervised data, noise sensitivity, and poor cross-category generalization.This thesis proposes learning-based solutions that merge geometric insights with efficient neural representations. We present frameworks for analyzing 3D shapes, focusing on three challenges: non-rigid shape correspondence, surface reconstruction, and shape optimization. Our approach to correspondence learns to deform one shape into another through robustly regularized deformation fields, yielding data-efficient alignment. For reconstruction, we introduce a self-supervised method that converts implicit representations into explicit meshes without ground truth, preserving intricate geometry. Finally, we offer a generative framework that integrates geometric learning with physical constraints, enabling the design of optimized and structurally sound 3D shapes. Together, these contributions form a robust, efficient, and generalizable strategy for 3D shape processing.