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Researcher profile

Alan Williams

Alan Williams contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.COComputer VisionRobotics

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Published work

3 published item(s)

preprint2026arXiv

Sonar-GPS Fusion for Seabed Mapping in Turbid Shallow Waters with an Autonomous Surface Vehicle

Accurate seabed mapping is essential for habitat monitoring and infrastructure inspection. In turbid, shallow coastal waters, such as shellfish aquaculture farms, the effectiveness of traditional optical methods is limited. Autonomous surface vehicles (ASVs) equipped with forward-looking sonar (FLS) offer a promising alternative. However, existing sonar-based systems face challenges in achieving fine resolution mapping over long trajectories due to low-resolution positioning measurements and accumulated drift over long trajectories. In this paper, we present a drift-resilient seabed mapping framework that integrates local FLS frame alignment using the Fourier-Mellin transform (FMT) with global trajectory optimization based on an extended Kalman filter (EKF) that fuses global positioning system (GPS), inertial measurement unit (IMU), and compass data. A variance-based image blending strategy is used to further reduce visual artifacts in overlapping regions. Field trials on a structured oyster farm site show that our framework helps reduce drift in RMSE by 9.5% relative to the FMT-only baseline. This framework also enables sub-meter reconstruction accuracy and preservation of high-resolution textures needed for oyster inventory estimation within the mapped areas.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

$N$-detachable pairs in 3-connected matroids III: the theorem

Let $M$ be a 3-connected matroid, and let $N$ be a 3-connected minor of $M$. A pair $\{x_1,x_2\} \subseteq E(M)$ is $N$-detachable if one of the matroids $M/x_1/x_2$ or $M \backslash x_1 \backslash x_2$ is both 3-connected and has an $N$-minor. This is the third and final paper in a series where we prove that if $|E(M)|-|E(N)| \ge 10$, then either $M$ has an $N$-detachable pair after possibly performing a single $Δ$-$Y$ or $Y$-$Δ$ exchange, or $M$ is essentially $N$ with a spike attached. Moreover, we describe the additional structures that arise if we require only that $|E(M)|-|E(N)| \ge 5$.

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preprint2020arXiv

$N$-detachable pairs in 3-connected matroids I: unveiling $X$

Let $M$ be a 3-connected matroid, and let $N$ be a 3-connected minor of $M$. We say that a pair $\{x_1,x_2\} \subseteq E(M)$ is $N$-detachable if one of the matroids $M/x_1/x_2$ or $M \backslash x_1 \backslash x_2$ is both 3-connected and has an $N$-minor. This is the first in a series of three papers where we describe the structures that arise when it is not possible to find an $N$-detachable pair in $M$. In this paper, we prove that if $M$ has no $N$-detachable pairs, then either $M$ has a 3-separating set, which we call $X$, with certain strong structural properties, or $M$ has one of three particular 3-separators that can appear in a matroid with no $N$-detachable pairs.

0 citations0 reviewsNo code linkedOpen access