Related papers: Using fractional differentiation in astronomy
In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We present a two-dimensional (2-D) fitting algorithm (GALFIT, Version 3) with new capabilities to study the structural components of galaxies and other astronomical objects in digital images. Our technique improves on previous 2-D fitting…
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
High-dimensional astronomical data cubes provide a wealth of spectral and structural information that can be used to study astrophysical and chemical processes. The complexity and sheer size of these datasets pose significant challenges in…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
While tunable filters are a recent development in night time astronomy, they have long been used in other physical sciences, e.g. solar physics, remote sensing and underwater communications. With their ability to tune precisely to a given…
Many image segmentation techniques have been developed over the past two decades for segmenting the images, which help for object recognition, occlusion boundary estimation within motion or stereo systems, image compression, image editing.…
We present a new technique - photon folding - for imaging in non-focusing telescopes. Motivated by the epoch-folding method in timing analysis, the photon folding technique directly provides the statistical significance of signals in…
The output of image the segmentation process is usually not very clear due to low quality features of Satellite images. The purpose of this study is to find a suitable Conditional Random Field (CRF) to achieve better clarity in a segmented…
A new method for improving the resolution of astronomical images is presented. It is based on the principle that sampled data cannot be fully deconvolved without violating the sampling theorem. Thus, the sampled image should not be…
Wavelets have been used extensively for several years now in astronomy for many purposes, ranging from data filtering and deconvolution, to star and galaxy detection or cosmic ray removal. More recent sparse representations such ridgelets…
Astronomy is by nature a visual science. The high quality imagery produced by the world's observatories can be a key to effectively engaging with the public and helping to inspire the next generation of scientists. Creating compelling…
Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…
This work presents a differentiable rendering approach that allows latent fractal flame parameters to be learned from image supervision using gradient descent optimization. The approach extends the state-of-the-art in differentiable…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
Researchers try to model the aesthetic quality of photographs into low and high- level features, drawing inspiration from art theory, psychology and marketing. We attempt to describe every feature extraction measure employed in the above…
The numerical kernel approach to difference imaging has been implemented and applied to gravitational microlensing events observed by the PLANET collaboration. The effect of an error in the source-star coordinates is explored and a new…
Difference imaging or image subtraction is a method that measures differential photometry by matching the pointing and point-spread function (PSF) between image frames. It is used for the detection of time-variable phenomena. Here we…