Surface reconstruction and shape matching are critical challenges in 3D geometry, underpinning the creation of detailed digital models and enabling the robust alignment of complex shapes - capabilities that drive advancements in computer vision, robotics, and medical imaging.
In this talk, we introduce a method that leverages a novel view synthesis algorithm (3DGS) to reconstruct 3D surfaces from real-world data, outperforming existing techniques. We then tackle the challenge of analyzing such reconstructions, where a common issue is that only part of an object is visible - which complicates shape analysis and in particular shape correspondence.
Traditional methods often fail to produce reliable matches under these conditions. Through both theoretical and quantitative examinations of prior approaches, we identified critical flaws in their workflows, which motivated the development of a new pipeline specifically for partial shape correspondence.
Furthermore, to mitigate errors throughout the learning process, we propose a new loss function based on the Gromov-Wasserstein distance that by utilizing both geodesic and Euclidean distances effectively excludes geometric distortions introduced by missing parts of the shape.