Search results for "Radon transform."
showing 10 items of 23 documents
Automated detection of microaneurysms using robust blob descriptors
2013
International audience; Microaneurysms (MAs) are among the first signs of diabetic retinopathy (DR) that can be seen as round dark-red structures in digital color fundus photographs of retina. In recent years, automated computer-aided detection and diagnosis (CAD) of MAs has attracted many researchers due to its low-cost and versatile nature. In this paper, the MA detection problem is modeled as finding interest points from a given image and several interest point descriptors are introduced and integrated with machine learning techniques to detect MAs. The proposed approach starts by applying a novel fundus image contrast enhancement technique using Singular Value Decomposition (SVD) of fun…
Subpixel determination of imperfect circles characteristics
2008
This article deals with the problem of the determination of characteristics of imperfect circular objects in discrete images, namely the radius and center coordinates. To limit distortion, a multi-level method based on active contours was developed. Its originality is to furnish a set of geometric envelopes in one pass, with a correspondence between grayscale and a regularity scale. The adequacy of this approach was tested with several methods, among them is the Radon-based method. More particularly, this study indicates the relevance of the use of active contours combined with a Radon transform-based method which was improved using a fitting considering the discrete implementation of the R…
On the Problem of Well-Posedness for the Radon Transform
1981
In this note, we first discuss some continuity and discontinuity properties of the inverse Radon transform (R.t.). Any such property gives a positive (or negative) answer to the question, whether under certain contitions the problem of inverting the R.t. is well-posed.
Computer-aided detection of cerebral microbleeds in susceptibility-weighted imaging.
2014
Susceptibility-weighted imaging (SWI) is recognized as the preferred MRI technique for visualizing cerebral vasculature and related pathologies such as cerebral microbleeds (CMBs). Manual identification of CMBs is time-consuming, has limited reliability and reproducibility, and is prone to misinterpretation. In this paper, a novel computer-aided microbleed detection technique based on machine learning is presented: First, spherical-like objects (potential CMB candidates) with their corresponding bounding boxes were detected using a novel multi-scale Laplacian of Gaussian technique. A set of robust 3-dimensional Radon- and Hessian-based shape descriptors within each bounding box were then ex…
Radon transform as a set of probability distributions
2009
It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.
Continuity of the radon transform and its inverse on Euclidean space
1983
Loomis-Whitney inequalities in Heisenberg groups
2021
This note concerns Loomis-Whitney inequalities in Heisenberg groups $\mathbb{H}^n$: $$|K| \lesssim \prod_{j=1}^{2n}|\pi_j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb{H}^n.$$ Here $\pi_{j}$, $j=1,\ldots,2n$, are the vertical Heisenberg projections to the hyperplanes $\{x_j=0\}$, respectively, and $|\cdot|$ refers to a natural Haar measure on either $\mathbb{H}^n$, or one of the hyperplanes. The Loomis-Whitney inequality in the first Heisenberg group $\mathbb{H}^1$ is a direct consequence of known $L^p$ improving properties of the standard Radon transform in $\mathbb{R}^2$. In this note, we show how the Loomis-Whitney inequalities in higher dimensional Heisenberg groups can be deduced…
On Radon Transforms on Tori
2014
We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere. We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients. These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.
On Radon transforms on compact Lie groups
2016
We show that the Radon transform related to closed geodesics is injective on a Lie group if and only if the connected components are not homeomorphic to $S^1$ nor to $S^3$. This is true for both smooth functions and distributions. The key ingredients of the proof are finding totally geodesic tori and realizing the Radon transform as a family of symmetric operators indexed by nontrivial homomorphisms from $S^1$.