相关论文: Generalized spiral transformation for high-resolut…
Mode sorting is an essential function for optical systems exploiting the orthogonality of photonic orbital angular momentum mode space. The familiar log-polar optical transformation provides an efficient yet simple approach, however with…
Reconstructing a 3D scene from unordered images is pivotal in computer vision and robotics, with applications spanning crowd-sourced mapping and beyond. While global Structure-from-Motion (SfM) techniques are scalable and fast, they often…
Conventional linear crop layouts, optimised for tractors, hinder robotic navigation with tight turns, long travel distances, and perceptual aliasing. We propose a robot-centric square spiral layout with a central tramline, enabling simpler…
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational…
The implementation of log-pol transformation has recently introduced a new boost in electron optics with charged matter vortices, allowing to map conformally between linear and orbital angular momentum (OAM) states and to measure them. That…
Sorting spatial optical modes is a key challenge that underpins many applications from super-resolved imaging to high-dimensional quantum key distribution. However, to date implementations of optical mode sorters only operate on specific…
In this paper we discuss the variety of planar spiral segments and their applications in objects in both the real and artificial world. The discussed curves with monotonic curvature function are well-known in geometric modelling and…
The Hamiltonian limit of the corner transfer matrix (CTM) of a generalised free Fermion vertex system of finite size leads to a quantum spin Hamiltonian of the particular form: \[ {\cal H}_N=-\sum_{n=1}^{N-1}\left\{ n\left(…
We propose a scheme for manipulations of a variety of topological states in fractional optical systems through spiral modulation of the local refraction index. An analytical approximation, based on a truncated finite-mode system, and direct…
We present algebraic projective geometry definitions of 3D rotations so as to bridge a small gap between the applications and the definitions of 3D rotations in homogeneous matrix form. A general homogeneous matrix formulation to 3D…
This paper is concerned with so-called index $d$ generalized cyclotomic mappings of a finite field $\mathbb{F}_q$, which are functions $\mathbb{F}_q\rightarrow\mathbb{F}_q$ that agree with a suitable monomial function $x\mapsto ax^r$ on…
Spatial mode sorting has come to prominence as an optical processing modality capable of saturating fundamental limits to numerous sensing tasks including wavefront sensing, coronagraphy, and superresolution imaging. But despite their…
The Hermite-Gaussian (HG) modes, sometimes also referred to as transverse electromagnetic modes in free space, form a complete and orthonormal basis that have been extensively used to describe optical fields. In addition, these modes have…
A general Archimedean spiral lattice is a Delone set in the relative distance if and only if its rotation angle is badly approximable.
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the…
This study presents a spiral-based complete coverage strategy for ball-end milling on freeform surfaces, utilizing conformal slit mapping to generate milling trajectories that are more compact, smoother, and evenly distributed when…
We address rotation averaging (RA) and its application to real-world 3D reconstruction. Local optimisation based approaches are the de facto choice, though they only guarantee a local optimum. Global optimisers ensure global optimality in…