On shape reconstruction & analysis via synthetic stereo, handling missing parts cuts and holes.

Geometry reconstruction, the recovering of geometric structures in 3D from 2D images, is a central challenge in computer vision. Stereo vision techniques, especially when applied to random-dot stereograms, underscore how crucial prior information is in resolving ambiguous depth cues and achieving reliable shape inference. At the other end, Gaussian Splatting offers a highly efficient representation for novel-view synthesis by modeling scenes as collections of 3D Gaussians. Yet, it remains difficult to extract coherent geometry directly from these representations. A pragmatic solution is to render stereo-image pairs from these Gaussian models, apply pre-trained stereo-matching networks to infer depth maps, and fuse these maps into realistic meshes yielding impressive reconstructions.

Turning to partial shape matching, I will first revisit the Wormhole Loss framework, which offers a principled strategy by aligning manifold fragments using intrinsic and extrinsic cues, specifically geodesic distances and proximity to boundaries. Next, we’ll explore a spectral matching approach, first introduced by Rampini et al.. The method encodes partiality masks within Hamiltonian operators, then, aligns correspondences by matching operator spectra, yielding a robust solution for partial matching.

These advances offer a leap in both full-surface reconstruction via efficient Gaussian-based pipelines and partial-shape matching using spectral geometry.