Related papers: Computation of 2D Fourier transforms and diffracti…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
Fast, reliable shape reconstruction is an essential ingredient in many computer vision applications. Neural Radiance Fields demonstrated that photorealistic novel view synthesis is within reach, but was gated by performance requirements for…
In recent years there has been a growing interest in the fractional Fourier transform driven by its large number of applications. The literature in this field follows two main routes. On the one hand, the areas where the ordinary Fourier…
In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…
Our aim is to find a complex continued fraction algorithm finding all the best Diophantine approximations to a complex number. Using the sequence of minimal vectors in a two dimensional lattice over Gaussian integers, we obtain an algorithm…
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
Gravitational waves (GWs) exhibit wave-optics effects when their wavelength is comparable to the scale of the gravitational lens. This may occur in lensing from galactic subhalos in GWs emitted by binary black-hole mergers, and is gaining…
Depth estimation is a fundamental task in 3D geometry. While stereo depth estimation can be achieved through triangulation methods, it is not as straightforward for monocular methods, which require the integration of global and local…
We propose and experimentally validate a joint estimation method for chromatic dispersion and time-frequency offset based on the fractional Fourier transform, which reduces computational complexity by more than 50% while keeping estimation…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fifth paper, the usual structural analysis of plates on an elastic foundation…
The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…
We propose a Gaussian mixture model for background subtraction in infrared imagery. Following a Bayesian approach, our method automatically estimates the number of Gaussian components as well as their parameters, while simultaneously it…
In this paper, we provide a solution to the open problem of computing the Fourier transform of a binary function defined over $n$-bit vectors taking $m$-bit vector values. In particular, we introduce the two-modular Fourier transform (TMFT)…
The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…
The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…
The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain material. It demonstrates the properties of this material and thus it is critical. However, dispersion relation…