The Radon Transform

By R. Easton. 2010

796 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/48e4990bb95f38de35ae880a2baba0806693ae59

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In Computer Vision and Pattern Recognition

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

A geometric study of Wasserstein spaces: Euclidean spaces (2008, background): “ty. Proof. — This is a consequence of Radon’s theorem, which asserts that a function (compactly supported and smooth, say) in Rn is characterized by its integrals along all hyperplanes [14] (also see [8]). Given µ ∈ W2(R2), one can determine by purely metric means its orthogonal projectiononanyﬁxedl”
Support Theorems for the Radon Transform and Cramér-Wold Theorems (2008, background): “Proof This theorem was first proved by Helgason, see [10].”
A stereoscopic look into the bulk (2016, background): “1 A Brief Introduction to X-ray Transforms Integral geometry supplies us with canonical maps from local functions defined on a manifold M to functions on the space of totally geodesic submanifolds of dimension k [32, 33].”
The geodesic X-ray transform with fold caustics (2010, methodology): “We refer to [11, 20] for more details about Euclidean X-ray and Radon transforms.”
The Calderón problem with partial data on manifolds and applications (2012, background): “If the integral of f ∈ C(Ω0), extended by zero to Rn−1, vanishes over all line segments in O, then the integral over all hyperplanes that do not meet ∂Ω0 \E also vanishes, and it follows from the Helgason support theorem [He99] that the local ray transform is injective on O.”
Learning monocular reactive UAV control in cluttered natural environments (2012, methodology): “To address this issue, we provided partial feedback to the pilot by showing a vertical line in the camera image seen by the pilot that would slide left or right based on the current joystick command performed.”
ANALYZING THE RANDOM COEFFICIENT MODEL NONPARAMETRICALLY (2009, methodology): “See also Natterer (2001) or Helgason (1999) for an overview of the mathematics of Radon transforms.”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, background): “See for instance [193] for more details and applications.”