Related papers: The Radon transform and the Hough transform: a uni…
We study multilinear generalized Radon transforms using a graph-theoretic paradigm that includes the widely studied linear case. These provide a general mechanism to study Falconer-type problems involving $(k+1)$-point configurations in…
Data acquisition in array signal processing (ASP) is costly because achieving high angular and range resolutions necessitates large antenna apertures and wide frequency bandwidths, respectively. The data requirements for ASP problems grow…
In 1917 Johann Radon introduced the Radon transform which is used in 1963 by A. M. Cormack for application in the context of tomographic image reconstruction. He proposed to reconstruct the spatial variation of the material density of the…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
The development of compact indirect microwave holographic set-up by the implementation of low cost, specifically designed directive antennae as transmitter and receiver is proposed. Microwave holograms are recorded by 2D scanning over a…
An approach to textures pattern recognition based on inverse resonance filtration (IRF) is considered. A set of principal resonance harmonics of textured image signal fluctuations eigen harmonic decomposition (EHD) is used for the IRF…
Rough sheets are two-parameter analogs of rough paths. In this work the theory of integration over functions of two parameters is extended to cover the case of irregular functions by developing an appropriate notion of rough sheet. The main…
We propose an integral geometric approach for computing dual distributions for the parameter distributions of multilinear models. The dual distributions can be computed from, for example, the parameter distributions of conics, multiple view…
Collimation in X-ray imaging restricts exposure to the region-of-interest (ROI) and minimizes the radiation dose applied to the patient. The detection of collimator shadows is an essential image-based preprocessing step in digital…
Image registration is fundamental in medical imaging applications, such as disease progression analysis or radiation therapy planning. The primary objective of image registration is to precisely capture the deformation between two or more…
Here we present new $L^2$ injectivity results for 2-D and 3-D Compton scattering tomography (CST) problems in translational geometries. The results are proven through the explicit inversion of a new toric section and apple Radon transform,…
This paper proposes a new technique for automatic face recognition using integrated peaks of the Hough transformed significant blocks of the binary gradient image. In this approach firstly the gradient of an image is calculated and a…
We demonstrate that simultaneous reconstruction of scattering and absorption of a mesoscopic system using angularly-resolved measurements of scattered light intensity is possible. Image reconstruction is realized based on the algebraic…
We consider a one-dimensional Radon transform on the group SO(3) which is motivated by texture goniometry. In particular we will derive several inversion formulae and compare them with the inversion of the one-dimensional spherical Radon…
In this paper, we consider the imaging problem of terahertz (THz) tomography, in particular as it appears in non-destructive testing. We derive a nonlinear mathematical model describing a full THz tomography experiment, and consider linear…
The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
This paper presents a predictive model for estimating regularization parameters of diffeomorphic image registration. We introduce a novel framework that automatically determines the parameters controlling the smoothness of diffeomorphic…
A new fangled method for ship wake detection in synthetic aperture radar (SAR) images is explored here. Most of the detection procedure applies the Radon transform as its properties outfit more than any other transformation for the…
Image moments are weighted sums over pixel values in a given image and are used in object detection and localization. Raw image moments are derived directly from the image and are fundamental in deriving moment invariants quantities. The…