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Axial X-Ray Microscopy in Nanotomography. [PDF]
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Hough Transform from the Radon Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1981An appropriate special case of a transform developed by J. Radon in 1917 is shown to have the major properties of the Hough transform which is useful for finding line segments in digital pictures. Such an observation may be useful in further efforts to generalize the Hough transform.
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The Exponential Radon Transform
SIAM Journal on Applied Mathematics, 1980The exponential Radon transform, a generalization of the Radon transform, is defined and is studied as a mapping of function spaces. An inversion formula is derived. The exponential Radon transform is represented in terms of Fourier transforms of its domain and range, and this leads to a characterization of the range of the transform.The exponential ...
Tretiak, Oleh, Metz, Charles
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IEEE Transactions on Image Processing, 1997
This article formally defines partial Radon transforms for functions of more than two dimensions. It shows that a generalized projection-slice theorem exists which connects planar and hyperplanar projections of a function to its Fourier transform. In addition, a general theoretical framework is provided for carrying out n-dimensional backprojection ...
Zhi-Pei Liang, David C. Munson Jr.
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This article formally defines partial Radon transforms for functions of more than two dimensions. It shows that a generalized projection-slice theorem exists which connects planar and hyperplanar projections of a function to its Fourier transform. In addition, a general theoretical framework is provided for carrying out n-dimensional backprojection ...
Zhi-Pei Liang, David C. Munson Jr.
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Mediterranean Journal of Mathematics, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abouelaz, Ahmed, Rouvière, François
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abouelaz, Ahmed, Rouvière, François
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1988
A new algorithm is presented whereby the Radon transform may be computed in a time commensurate with real-time computer vision applications. The computation and storage requirments are optimized using the four-fold symmetry of the image plane and the properties of the transform.
Violet F. Leavers, Mark B. Sandler
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A new algorithm is presented whereby the Radon transform may be computed in a time commensurate with real-time computer vision applications. The computation and storage requirments are optimized using the four-fold symmetry of the image plane and the properties of the transform.
Violet F. Leavers, Mark B. Sandler
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The polynomial discrete Radon transform
Signal, Image and Video Processing, 2014This paper presents a new approach called polynomial discrete Radon transform (PDRT), regarded as a generalization of the classical finite discrete Radon transform. Specifically, the PDRT transforms an image into Radon space by summing the pixels according to polynomial curves. The PDRT can be applied on square
Ines Elouedi +3 more
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SIAM Journal on Applied Mathematics, 1992
The interior Radon transform arises from a limited data problem in computerized tomography when only rays traveling through a specified region of interest are measured. This problem occurs due to technical restrictions of the sampling apparatus or in an endeavor to reduce the \(X\)-ray dose.
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The interior Radon transform arises from a limited data problem in computerized tomography when only rays traveling through a specified region of interest are measured. This problem occurs due to technical restrictions of the sampling apparatus or in an endeavor to reduce the \(X\)-ray dose.
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1980
It was proved by J. Radon in 1917 that a differentiable function on R3 can be determined explicitly by means of its integrals over the planes in R3. Let J(ω, p) denote the integral of f over the hyperplane 〈x, ω〉 = p, ω denoting a unit vector and 〈,〉 the inner product.
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It was proved by J. Radon in 1917 that a differentiable function on R3 can be determined explicitly by means of its integrals over the planes in R3. Let J(ω, p) denote the integral of f over the hyperplane 〈x, ω〉 = p, ω denoting a unit vector and 〈,〉 the inner product.
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On the Invertibility of the Discrete Radon Transform
SIAM Journal on Discrete Mathematics, 1989Summary: The Radon transform is a useful device for analyzing multidimensional data. It is closely connected to what has become known as ``projection pursuit''. For the case of discrete data, theorems that address its invertibility are proven. Connections to the projective group over GF(2) and block designs naturally arise.
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