arXiv subjects

Alan T. Asbeck

Publications and source records attributed to Alan T. Asbeck.

3 recordsLinked to original sources

arXiv2025

Fast, Robust, Permutation-and-Sign Invariant SO(3) Pattern Alignment

We address the correspondence-free alignment of two rotation sets on $SO(3)$, a core task in calibration and registration that is often impeded by missing time alignment, outliers, and unknown axis conventions. Our key idea is to decompose each rotation into its \emph{Transformed Basis Vectors} (TBVs)-three unit vectors on $S^2$-and align the resulting spherical point sets per axis using fast, robust matchers (SPMC, FRS, and a hybrid). To handle axis relabels and sign flips, we introduce a \emph{Permutation-and-Sign Invariant} (PASI) wrapper that enumerates the 24 proper signed permutations, scores them via summed correlations, and fuses the per-axis estimates into a single rotation by projection/Karcher mean. The overall complexity remains linear in the number of rotations ($\mathcal{O}(n)$), contrasting with $\mathcal{O}(N_r^3\log N_r)$ for spherical/$SO(3)$ correlation. Experiments on EuRoC Machine Hall simulations (axis-consistent) and the ETH Hand-Eye benchmark (\texttt{robot\_arm\_real}) (axis-ambiguous) show that our methods are accurate, 6-60x faster than traditional methods, and robust under extreme outlier ratios (up to 90\%), all without correspondence search.

cs.RO↗

arXiv2025

Correspondence-Free Fast and Robust Spherical Point Pattern Registration

Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities greater than cubic $O(n^3)$ with respect to rotation space discretization and lack extensive evaluation under significant outlier contamination. To this end, we propose a rotation estimation algorithm between two spherical patterns with linear time complexity $O(n)$. Unlike existing spherical-function-based methods, we explicitly represent spherical patterns as discrete 3D point sets on the unit sphere, reformulating rotation estimation as a spherical point-set alignment (i.e., Wahba problem for 3D unit vectors). Given the geometric nature of our formulation, our spherical pattern alignment algorithm naturally aligns with the Wahba problem framework for 3D unit vectors. Specifically, we introduce three novel algorithms: (1) SPMC (Spherical Pattern Matching by Correlation), (2) FRS (Fast Rotation Search), and (3) a hybrid approach (SPMC+FRS) that combines the advantages of the previous two methods. Our experiments demonstrate that in the $\mathbb{S}^2$ domain and in correspondence-free settings, our algorithms are over 10x faster and over 10x more accurate than current state-of-the-art methods for the Wahba problem with outliers. We validate our approach through extensive simulations on a new dataset of spherical patterns, the ``Robust Vector Alignment Dataset. "Furthermore, we adapt our methods to two real-world tasks: (i) Point Cloud Registration (PCR) and (ii) rotation estimation for spherical images.

cs.CV↗

arXiv2023

RIS-Aided Kinematic Analysis for Remote Rehabilitation

This paper is the first to introduce the idea of using reconfigurable intelligent surfaces (RISs) as passive devices that measure the position and orientation of certain human body parts over time. In this paper, we investigate the possibility of utilizing the available geometric information provided by on-body RISs that reflect signals from an off-body transmitter to an off-body receiver for stroke rehabilitation. More specifically, we investigate the possibility of using on-body RISs to estimate the location information over time of upper limbs that may have been impaired due to stroke. This location information can help medical professionals to estimate the possibly time varying pose and obtain progress on the rehabilitation of the upper limbs. Our analysis is focused on two scenarios: i) after assessment exercises for stroke rehabilitation when the upper limbs are resting at predefined points in the rehabilitation center, and ii) during the assessment exercises. In the first scenario, we explore the possibility of upper limb orientation estimation by deriving the Fisher information matrix (FIM) under near-field and far-field propagation conditions. It is noteworthy that the FIM quantifies how accurately we can estimate location information from a signal, and any subsequent algorithm is bounded by a function of the FIM. Coming to our propagation assumptions, the difference between the near-field and far-field regimes lies in the curvature of the wavefront. In the near-field, a receiver experiences a spherical wavefront, whereas in the far-field, the wavefront is approximately linear. The threshold to be within the near-field can be on the order of $10 \text{ m}.$

eess.SP↗