Related papers: A Discrete Radon Transform Based on the Area of Cu…
The discrete cosine transform (DCT) is a relevant tool in signal processing applications, mainly known for its good decorrelation properties. Current image and video coding standards -- such as JPEG and HEVC -- adopt the DCT as a…
Proton radiography is a technique extensively used to resolve magnetic field structures in high energy density plasmas, revealing a whole variety of interesting phenomena such as magnetic reconnection and collisionless shocks found in…
The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special…
This paper presents a mutual information (MI) based algorithm for the estimation of full 6-degree-of-freedom (DOF) rigid body transformation between two overlapping point clouds. We first divide the scene into a 3D voxel grid and define…
In the study of computer codes, filling space as uniformly as possible is important to describe the complexity of the investigated phenomenon. However, this property is not conserved by reducing the dimension. Some numeric experiment…
An alternative method to invert the Radon transforms without the use of Courant-Hilbert's identities has been proposed and developed independently from the space dimension. For the universal representation of inverse Radon transform, we…
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,…
Using content-based binary codes to tag digital images has emerged as a promising retrieval technology. Recently, Radon barcodes (RBCs) have been introduced as a new binary descriptor for image search. RBCs are generated by binarization of…
We define a thin category $\mathrm{Dim}^+$ of dimension shifts and a category $\mathrm{RadMeas}$ of positive Radon measures with Radon--Nikodym density morphisms. We classify scaling-covariant functors $\mathrm{Dim}^+\to\mathrm{RadMeas}$…
We discuss how to apply regularization by dimensional reduction for computing hadronic cross sections at next-to-leading order. We analyze the infrared singularity structure, demonstrate that there are no problems with factorization, and…
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…
Proton radiography is a widely-fielded diagnostic used to measure magnetic structures in plasma. The deflection of protons with multi-MeV kinetic energy by the magnetic fields is used to infer their path-integrated field strength. Here, the…
Dominant areas of computer science and computation systems are intensively linked to the hypercube-related studies and interpretations. This article presents some transformations and analytics for some example algorithms and Boolean domain…
The row-column addressed array is an emerging probe for ultrafast 3-D ultrasound imaging. It achieves this with far fewer independent electronic channels and a wider field of view than traditional 2-D matrix arrays, of the same channel…
We present a 3D zigzag rafter (first in literature) which allows us to obtain the exact sequence of spectral components after application of Discrete Cosine Transform 3D (DCT-2D) over a cube. Such cube represents part of a video or…
Most robot mapping techniques for lidar sensors tessellate the environment into pixels or voxels and assume uniformity of the environment within them. Although intuitive, this representation entails disadvantages: The resulting grid maps…
A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing…
Radar is a critical perception modality in autonomous driving systems due to its all-weather characteristics and ability to measure range and Doppler velocity. However, the sheer volume of high-dimensional raw radar data saturates the…
We present an efficient voxelization method to encode the geometry and attributes of 3D point clouds obtained from autonomous vehicles. Due to the circular scanning trajectory of sensors, the geometry of LiDAR point clouds is inherently…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…