The paper introduces the Geometric Observability Index (GOI), a per-feature sensitivity metric for SE(3) pose estimation that quantifies the pose perturbation induced by a single measurement via the Gauss‑Newton curvature restricted to the observable subspace. GOI is shown to equal the norm of the M‑estimator influence function, to coincide with the Fisher information operator, and its smallest observable eigenvalue determines both worst‑case measurement amplification and a finite‑sample stability radius. Experiments on synthetic data and real RGB‑D/KITTI sequences validate that GOI accurately predicts leave‑one‑out pose shifts and explains the robustness of residual gating while highlighting the pitfalls of raw‑influence gating in weakly observable geometries.
arXiv:2609.37114v1 Announce Type: new Abstract: DANCo (Dimensionality from Angle and Norm Concentration) jointly calibrates nearest-neighbor distance and angular statistics and consistently reaches s...
DANCo (Dimensionality from Angle and Norm Concentration) jointly calibrates nearest-neighbor distance and angular statistics and consistently reaches state-of-the-art accuracy on clean intrinsic-dimen...
arXiv:2608.21066v1 Announce Type: new Abstract: Deploying autonomous systems in safety-critical domains demands guaranteed robustness against physically plausible geometric perturbations rather than...
Accurate six-degree-of-freedom (6-DOF) motion estimation is essential for robotic manipulation, autonomous systems, and structural displacement monitoring. Conventional 3D-2D methods estimate absolute camera poses independently at each time and recover platform motion through camera-to-platform extrinsics, making them sensitive to extrinsic calibration errors, especially for micromotion.
arXiv:2608.21402v1 Announce Type: cross Abstract: World action models (WAMs) jointly denoise future video frames and robot actions, and the video prior is expected to generalize their control. Camera...
arXiv:2606. 28432v1 Announce Type: cross Abstract: We study the spectral perturbation of the empirical Fisher Information Matrix (FIM) of a parametric statistical model under two structured perturbations: departure of the input from a reference (in-distribution) ensemble, and finite-precision (quantized) perturbation of the model's parameters.
DefVINS is a visual‑inertial odometry pipeline tailored for deformable scenes, breaking the rigidity assumption of traditional VIO. It decomposes the odometry state into a rigid, IMU‑anchored component and a non‑rigid scene warp using an embedded deformation graph. The authors also introduce VIMandala, the first real‑world benchmark with ground‑truth camera poses for deformable VIO, and extend the synthetic Drunkard’s benchmark with inertial data, demonstrating that DefVINS outperforms both rigid and non‑rigid baselines.
arXiv:2606. 18306v1 Announce Type: new Abstract: Gaussian width is a central geometric complexity measure in high-dimensional probability, compressed sensing, convex optimization, and learning theory.
GINIO is a geometric SO(3)-equivariant interface designed for neural inertial odometry that ensures learned measurements transform consistently under any IMU mounting convention. It predicts motion measurements and uncertainties that obey vector and tensor transformation laws, and introduces Last-Frame Alignment to enable efficient sensor-frame learning equivalent to world-frame training. The interface is instantiated in several architectures—filter-connected NIO, AirIO-style recurrent aerial prediction, EqNIO-style full-SO(3) canonicalization, and ResNet-style temporal backbones—achieving significant accuracy and efficiency gains across multiple benchmarks.
arXiv:2609.00713v1 Announce Type: new Abstract: Estimation of the absolute pose of an object is an essential task for various robotic applications. Recently, incorporating gravity direction as prior...
arXiv:2608. 01547v1 Announce Type: cross Abstract: Drifting objectives compare a target and model distribution through a vector field observed noisily at finitely many locations.
arXiv:2608. 10566v1 Announce Type: cross Abstract: How many directions does a neural representation use to encode a concept?