arXiv:2605. 26702v2 Announce Type: replace-cross Abstract: Reliable watermarking of panoramic imagery is fundamentally challenged by arbitrary 3D rotations.
arXiv:2608. 27774v1 Announce Type: cross Abstract: Efficiently and robustly analyzing shape data is critical across many scientific disciplines.
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...
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: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: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.
arXiv:2601. 03326v2 Announce Type: replace-cross Abstract: PCA can be used for rotation invariant features, describing a shape with its $p_{ab}=E[(x_i-E[x_a])(x_b-E[x_b])]$ covariance matrix approximating shape by ellipsoid, allowing for rotation invariants like its traces of powers.
The paper introduces GSF-χ, a graph transformer that incorporates global stereochemical fields to handle chiral molecules. Unlike traditional models that focus on a single atom, GSF-χ modulates all pairwise interactions using stereogenic units, producing a reflection‑even phase field and a handedness pseudoscalar that guide relative rotations in latent query–key blocks. The authors prove the operator’s even–odd decomposition and demonstrate that GSF-χ improves central‑ECD, axial Rotation, and Symbol metrics over strong baselines, while maintaining enantiomer‑pair consistency through a C₂ projection.
arXiv:2608.31045v1 Announce Type: new Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...
TokenMatch is a transformer-based model that estimates 3D shape correspondences by adaptively tokenising meshes into curvature-guided patches. Trained only on the BeCoS partial-to-partial dataset, it generalises to full-shape matching without retraining, using self‑ and cross‑attention to learn patch‑ and point‑level relations. Evaluated on CP2P, PSMAL, BeCoS, FAUST, SCAPE, and SHREC'19, TokenMatch consistently outperforms existing methods in mean geodesic error and intersection‑over‑union while achieving sub‑second inference speeds.
arXiv:2606. 04108v1 Announce Type: cross Abstract: Single-view 3D generative models have achieved impressive visual quality, yet they are not designed to satisfy structural or functional requirements, and in practice, often fall short.
arXiv:2607. 15536v1 Announce Type: cross Abstract: 3D Gaussian Splatting (3DGS) captures scenes by coupling explicit geometry (position, covariance) with view-dependent photometry (Spherical Harmonics).