Learning Geometry Through Intrinsic Representations and Data-Driven Processing

Abstract

This thesis explores data-driven and intrinsic methods for efficient 3D shape representation and processing. While many learning-based approaches rely on large labeled datasets or shallow geometric cues, we instead leverage intrinsic structures—such as curvature, geodesic distance, and the logarithmic map—to enhance generalization, robustness, and geometric fidelity. We first investigate learning-based methods for efficient mesh representation. To better capture local geometric structure, we propose an improved pooling operator for 3D morphable models that incorporates intrinsic geometric information through vertex normals. Building on this representation, we introduce Neural QSLIM, a geometry-aware framework that learns QSLIM-guided topological updates to improve mesh reconstruction quality in autoencoders. Beyond mesh representation, we study intrinsic geometry for non-rigid shape analysis by proposing a fully unsupervised method for discovering compact, stable, and ordered intrinsic landmarks via Karcher means, which can be directly incorporated into existing shape correspondence methods. Finally, we extend these ideas to mesh repair with a data-free learning framework that reconstructs missing regions directly on the input mesh while preserving the original topology and geometric fidelity, eliminating the need for external training datasets. Together, these contributions demonstrate how intrinsic geometry and self-supervision can reduce reliance on large-scale annotations in neural geometric pipelines.