NHO introduces a neural Hamiltonian operator that uses sparse anchors and the intrinsic geometry of a partial shape to learn a localized eigenspace encoding both region support and intrinsic coordinates for dense correspondence. The method parameterizes the Hamiltonian potential as an intrinsic neural field and optimizes it with anchor evidence, spectral, and geometric constraints, employing reciprocal refinement between operator estimation and correspondence recovery. After iterative refinement, aggregated eigenfunction energy yields final localization and initializes dense correspondence refinement, achieving competitive accuracy and robustness to scaling and rotation.
arXiv:2609.37048v2 Announce Type: replace Abstract: Non-rigid partial-to-full shape correspondence from sparse anchors requires identifying the corresponding region on the full surface and recovering...
Creating photorealistic 3D assets requires bridging the appearance gap between real-world observations and synthetic models. A promising approach is to transfer visual attributes from real images onto synthetic 3D surfaces.
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
RecGen3D is a framework that merges feed‑forward reconstruction and diffusion‑based generation to address the trade‑off between reconstruction fidelity and generative plausibility in sparse‑view 3D modeling. By aligning both models in a shared canonical space and using decoupled cooperative learning, the system stabilizes training and allows the reconstruction module to supply canonical geometric anchors while the diffusion generator refines and completes the structure. Experiments show that RecGen3D outperforms existing methods in producing complete and consistent 3D models from sparse observations.
arXiv:2606. 30131v1 Announce Type: cross Abstract: Functional maps are the cornerstone of recent non-rigid 3D shape matching methods due to their efficiency and performance.
arXiv:2602.02611v2 Announce Type: replace Abstract: A prevailing paradigm in modern representation learning is the map-first approach, in which a representation map is learned from reconstruction, em...
Non-rigid 3D shape matching is a fundamental task in computer vision and graphics. In this paper, we propose a hybrid self-supervised method based on a coarse-to-fine strategy, which ensures consistency between the coarse mapping and the refined correspondence produced by our refinement module.
arXiv:2602. 03082v2 Announce Type: replace Abstract: A growing number of neural architectures have been proposed to enforce geometric constraints, including projection-based networks, exponential-map updates, constrained output layers, and manifold neural ODEs.
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:2607. 04661v1 Announce Type: cross Abstract: Reconstructing 3D scene structures from sparse, low-overlap observations remains a fundamental challenge in autonomous driving.
Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored.
This paper proposes ``FlatVPR,'' a novel geometric rectification paradigm that effectively bridges the trade-off between map lightweightness and localization accuracy in visual place recognition (VPR) by enforcing a feature manifold structure where any descriptor between two adjacent anchors $\mathbf{z}_A$ and $\mathbf{z}_B$ can be accurately reconstructed via linear interpolation $\hat{\mathbf{z}}_{pseudo} = (1-t)\mathbf{z}_A + t\mathbf{z}_B$, where $t \in [0,1]$ denotes the relative position. While state-of-the-art foundation models such as DINOv2-ViT-S/14 provide robust semantic features, their latent manifolds exhibit prominent curvature, projecting uniform linear motion in physical space onto highly non-linear trajectories in the feature space, which hinders reliable reconstruction under sparse anchor conditions.