arXiv Computer Vision
Invariant Shape Analysis of Surfaces with Spherical Topology
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Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling
arXiv:2605. 26702v2 Announce Type: replace-cross Abstract: Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations.
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Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality
arXiv:2608. 27774v1 Announce Type: cross Abstract: Efficiently and robustly analyzing shape data is critical across many scientific disciplines.
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A library for differentiable signal processing and machine learning on the sphere
arXiv:2609.39737v1 Announce Type: new Abstract: The two-dimensional sphere embedded in three-dimensional Euclidean space S2, plays a central role in a variety of scientific and engineering domains, i...
arXiv Machine Learning
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Group-Invariant Statistics Determine Embedding Geometry: Harmonic Analysis of Representations from Bach to the Night Sky
The paper shows that the geometric patterns seen in language model embeddings—such as circles for months and saddle-shaped manifolds—arise from group-invariant statistics in word co‑occurrence data. By extending previous work on translation symmetry to arbitrary finite, compact, and homogeneous groups, the authors prove that embeddings correspond to matrix elements of the irreducible representations of the symmetry group. They validate this theory experimentally with the cyclic group <Z_{12}> for months, a dihedral group for musical chords, and a spherical‑harmonic embedding for celestial objects.
arXiv Computer Vision
Sep 15
Multi-View Structure-from-Motion Enables Oriented Projective Shape Analysis in Three Dimensions
arXiv:2609.13263v1 Announce Type: new Abstract: Projective shape analysis provides a geometric framework for studying landmark configurations in digital images acquired by pinhole cameras. In the cla...
arXiv Machine Learning
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Partial Symmetry Detection for 3D Geometry using Contrastive Learning with Geodesic Point Cloud Patches
arXiv:2312. 08230v2 Announce Type: replace-cross Abstract: Detecting partial extrinsic symmetry in 3D geometry is a fundamental yet persistent challenge in computer vision and graphics, critical for tasks ranging from shape completion to procedural generation.