Finding a closest point in a lattice of Voronoi's first kind

We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network

The Farey Series in Synchronisation and Intercept-Time Analysis for Electronic Support

Abstract In Electronic Support, periodic search strategies for swept-frequency superheterodyne receivers (SHRs) can cause synchronisation with the radar it seeks to detect. Synchronisation occurs when the periods governing the search strategies of the SHR and radar are commensurate. As a result, the radar may never be detected. In this paper, we find that, under certain conditions, the number of ratios of periods that can cause synchronisation is finite. We develop theory that can enumerate all of the ratios and determine the intercept time. Index Terms Electronic support, superheterodyne receiver, emitter intercept, synchronisation, Farey series, radar warning receiver, scan-on-scan. I. Introduction The superheterodyne receiver (SHR) has long been a primary tool for Electronic Support (ES). The swept-frequency SHR has the advantage of being able to cover a wide bandwidth and, by virtue of its narrow instantaneous bandwidth, it is selective and sensitive. However, a key element to the effectiveness of the swept-frequency SHR in operational environments is its search strategy. The simplest strategy, and traditionally the most widely used, wholly or partly, is a simple periodic strategy, whereby the SHR repeatedly sweeps through the entire band of interest at a constant rate When a swept-frequency SHR is searching for a radar which is also employing a periodic search strategy, such as a circularly scanned or raster scanned radar, it is well known that synchronisation can be a problem [1]

Estimation of Epipolar Geometry via the Radon Transform

One of the key problems in computer vision is the recovery of epipolar geometry constraints between different camera views. The majority of existing techniques rely on point correspondences, which are typically perturbed by mismatches and noise, hence limiting the accuracy of these techniques. To overcome these limitations, we propose a novel approach that estimates epipolar geometry constraints based on a statistical model in the Radon domain. The method requires no correspondences, explicit constraints on the data or assumptions regarding the scene structure. Results are presented on both synthetic and real data that show the method's robustness to noise and outliers

Linear-time nearest point algorithms for Coxeter lattices

The Coxeter lattices, which we denote $A_{n/m}$, are a family of lattices containing many of the important lattices in low dimensions. This includes $A_n$, $E_7$, $E_8$ and their duals $A_n^*$, $E_7^*$ and $E_8^*$. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexity $O(n\log{n})$ and the other with worst case complexity O(n) where $n$ is the dimension of the lattice. We show that for the particular lattices $A_n$ and $A_n^*$ the algorithms reduce to simple nearest point algorithms that already exist in the literature.Comment: submitted to IEEE Transactions on Information Theor

Robust Fundamental Matrix Determination without Correspondences

Estimation of the fundamental matrix is key to many problems in computer vision as it allows recovery of the epipolar geometry between camera images of the same scene. The estimation from feature correspondences has been widely addressed in the literature, particularly in the presence of outliers. In this paper, we propose a new robust method to estimate the fundamental matrix from two sets of features without any correspondence information. The method operates in the frequency domain and the underlying estimation process considers all features simultaneously, thus yielding a high robustness with respect to noise and outliers. In addition, we show that the method is well-suited to widely separate viewpoints

Comments on “On the performance of the weighted linear predictor frequency estimator”

Handel, in a recent correspondence, provides an alternate analysis to that of Clarkson, Kootsookos and Quinn of Kay's linear predictor frequency estimator, claiming that his proof is more concrete. We show, in fact, that his proof is in error, and emphasise the care needed when carrying out such analyses