Tomographic Reconstruction from Fan Beam Geometry Using Radon's Integration Method

Beattie, John W.

doi:10.1109/tns.1975.4327662

Cited by 20 publications

(4 citation statements)

References 3 publications

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“…It is not trivial that k i (p,) can describe the geometric properties of the detection system in the third dimension; that this is possible is related to the conservation of the étendue through optical detection systems. 10 Some ideas of the coverage of projection space by a function similar to k i (p,) have been described in the past by Beattie 15 and Lindgren and Rattey, 1 and a relationship similar to Eq. ͑4͒ below ͑and an equivalent statement to the conservation of the étendue͒ has been given for transmission tomography by Verly, 16 but we are not aware of a similar consistent application to projection space as in Ref.…”

Section: Characterization Of Geometric Propertiesmentioning

confidence: 99%

Characterization of geometrical detection-system properties for two-dimensional tomography

Ingesson

Maggi

Reichle

2000

Review of Scientific Instruments

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Quantities that characterize the three-dimensional geometrical properties of detection systems for two-dimensional tomography are reviewed and compared. It is discussed how the quantities can be calculated and how they can be measured, including a measuring technique that uses a parallel laser beam. In many detection systems the finite detector size and the finite sizes of bounding apertures are not negligible, and these result in instrument functions with finite widths. Line-integral measurements are referred to as ideal measurements, whereas measurements by systems with instrument functions with finite width are nonideal. The quantities discussed make it possible to take into account these finite sizes in several tomography algorithms. If the spacing between adjacent lines of sight is much smaller than the widths of the instrument functions, the ideal measurements can be approximately reconstructed from the nonideal measurements. Such a reconstruction has been applied to bolometer measurements in a high plasma-density discharge in the Joint European Torus tokamak by sweeping the plasma in front of the bolometer detectors. The sweeping creates many extra virtual lines of sight and thus increases the resolution of the measurements close to the X point, where in high-density plasmas a peak in the radiation is found.

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Section: Characterization Of Geometric Propertiesmentioning

confidence: 99%

Characterization of geometrical detection-system properties for two-dimensional tomography

Ingesson

Maggi

Reichle

2000

Review of Scientific Instruments

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“…Thus the function o is a distribution, or generalized function which assigns to the function f(x,y) the number pc(~,e) which is equal to the line integral of f(x,y) along the ray defined by g [13]. (11) and for a flat detector as Bf:pf + bf such that bf is given by the equation…”

Section: Fan-beam Prqjeci'ion Operatorsmentioning

confidence: 99%

“…Radon's integration method [10,11]. The projection data are first differentiated, then followed by a Hilbert transform or an approximation using the trapezoidal method of intergration.…”

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confidence: 99%

The reconstruction of fan-beam data by filtering the back-projection

Gullberg

1979

Computer Graphics and Image Processing

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Expressions for the fan-beam projection and back-projection operators are given along with an evaluation of the impulse response for the composite of the projection and back-projection operations. The fan-beam geometries for both curved and flat detectors have back-projection operators such that the impulse response for the composite of the projection and backprojection operations is equal to 1/ l.r -r I if the data are taken over 360° 0 and thus two-dimensional Fourier filter techniques can be used to reconstruct transverse sections from fan-beam projection data. It will be shown that the impulse response for the composite of the projection and back-projection operators for fan-beam geometry is not spatially invariant if the data are taken over 180° as is true for parallel-beam projection data. The convolution algorithm is approximately four times faster and requires 40% less memory than the filter of the back-projection algorithm. However, the filter of the backprojection algorithm has the advantage of easily implementing different frequency space filters which lends itself to easily changing the noise propagation vs. resolution properties of the convolution kernel. iii 0 0 : ~ t,.JI 6 0

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“…It can be seen from the accumulator data of Fan beam that after 180 degrees the signals encore itself in the head over heels direction. This is because projections taken from 0 to 180 degrees are exactly equal to the projections taken from 181 to 360 degrees [18]. The average value of the procured projection data is computed in order to build the feature vector.…”

Section: The Saudi Arabia Vehicle Feature Extractionmentioning

confidence: 99%

The Kingdom of Saudi Arabia Vehicle License Plate Recognition using Learning Vector Quantization Artificial Neural Network

Perwej¹,

Akhtar²,

Parwej³

2014

IJCA

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In the today scenario technological intelligence is a higher demand after commodity even in traffic-based systems. These intelligent systems do not only help in traffic monitoring but also in commuter safety, law enforcement and commercial applications. The proposed Saudi Arabia Vehicle License plate recognition system splits into three major parts, firstly extraction of a license plate region secondly segmentation of the plate characters and lastly recognition of each character. This act is quite challenging due to the multiformity of plate formats and the nonuniform outdoor illumination conditions during image collection. In this paper recognition of the license plates is achieved by the implementation of the Learning Vector Quantization artificial neural network. Their results are based upon their completeness in the Saudi Arabia Vehicle License plate character recognition and theirs have obtained encouraging results from proposed technique.

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Tomographic Reconstruction from Fan Beam Geometry Using Radon's Integration Method

Cited by 20 publications

References 3 publications

Characterization of geometrical detection-system properties for two-dimensional tomography

Characterization of geometrical detection-system properties for two-dimensional tomography

The reconstruction of fan-beam data by filtering the back-projection

The Kingdom of Saudi Arabia Vehicle License Plate Recognition using Learning Vector Quantization Artificial Neural Network

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