ComputedTomography
Biomedical ImageAnalysis
Prof. Dr. Philippe Cattin
MIAC, University of Basel
April 11th/12h, 2016
April 11th/12h, 2016Biomedical Image Analysis
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Prof. Dr. Philippe Cattin: Computed Tomography
Contents
Abstract
1 Computed Tomography Basics
Introduction
Computed Tomography
Hounsfield's CT Prototype
EMI-Scanner
Detectors
Important Terminology
2 Single Slice CT
First Generation CT Scanner Design
Second Generation CT Scanner Design
Third Generation CT Scanner Design
Fourth Generation CT Scanner Design
Spiral Scanning CT
Spiral Scanning CT (2)
Spiral Scanning CT (3)
Drawback of these Designs
3 Multi-Detector Row CT
Multi-Detector Row CT
Detector Design
Detector Design (2)
Detector Design (3)
Detector Design (4)
Detector Design (5)
Detector Design (6)
Dual Source CT
Open Dual Source CT
Advantage of the DSCT
4 Image Reconstruction
4.1 Introduction April 11th/12h, 2016Biomedical Image Analysis
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Image Reconstruction
Image Reconstruction (2)
4.2 Radon Transform
Radon Transform
Parallel Projection
The Radon Transform
The Discrete Radon Transform
Radon Transform Examples
Radon Transform Examples (2)
4.3 Fourier Slice Theorem
Fourier Slice Theorem
Fourier Slice Theorem (2)
Reconstruction with the Fourier Slice Theorem
Reconstruction with the Fourier Slice Theorem(2)
4.4 Filtered Backprojection
Principle of Filtered Back-Projection
Numerical Back-Projection Example
Example Reconstructions
Example Reconstructions (2)
4.5 Helical Reconstruction
Helical Reconstruction
360° Linear Interpolation
180° Linear Interpolation
4.6 Hounsfield Unit
Hounsfield Unit
5 Artefacts
Artefacts
Partial Volume Effect
High Density Artefacts
Gating in Cardio CT
CT and Medical Image Analysis
April 11th/12h, 2016Biomedical Image Analysis
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Prof. Dr. Philippe Cattin: Computed Tomography
Abstract
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ComputedTomography Basics
April 11th/12h, 2016Biomedical Image Analysis
(4)Introduction
One of the major disadvantages associated with conventionalplanar radiography is its inability to produce sectional information.
The images produced on film represent the total attenuation of theX-ray beam as it passes through the patient. Depth information iscompletely lost!
Two general classes of tomography exist that solve this problem:
Linear tomography, which produces longitudinal sections
Computed axial tomography, which produces sectional or axial
slices
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Computed Tomography Basics
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Prof. Dr. Philippe Cattin: Computed Tomography
Computed Tomography
→ Computed Tomography (CT)[http://en.wikipedia.org
/wiki/Computed_axial_tomography] originallyknown as Computed Axial Tomography(CAT) or Body Section Röntgenographyis a medical imaging modality used togenerate 3D images of the internals ofan object from a large series of 2DX-ray images taken around a single axisof rotation.
→ Godfrey Newbold Hounsfield[http://en.wikipedia.org
/wiki/Godfrey_Newbold_Hounsfield] conceivedthe CT scanner idea in 1967 andpublicly announced it in 1972. → AllanMcLeod Cormack [http://en.wikipedia.org
/wiki/Allan_McLeod_Cormack] independentlyinvented a similar process and theyshared the Nobel price in 1979.
Fig 9.1: CT Apparatus
It is claimed that the CT scanner was the greatest legacy ofthe Beatles; the massive profits from their record salesenabled EMI to fund scientific research
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Computed Tomography Basics
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Prof. Dr. Philippe Cattin: Computed Tomography
Hounsfield's CT Prototype
The original 1971 prototype took parallel readings through angles, each apart, with each scan taking a little over fiveminutes. The images from these scans took hours to beprocessed by algebraic reconstruction techniques on a largecomputer.
Fig 9.2: Hounsfield's original CT prototype Fig 9.3: Principle of theprototype
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Prof. Dr. Philippe Cattin: Computed Tomography
EMI-Scanner
The EMI-Scanner was the firstproduction X-ray CT machine. It waslimited to scan two adjacent slices ofthe brain, but acquired the image datain about . The computation timewas about per picture.
The scanner required the use of awater-filled Perspex tank with apre-shaped rubber head-cap at thefront. The water-tank was used toreduce the dynamic range of theradiation reaching the detectors(scanning outside the head vs. throughthe skull).
The images were relatively lowresolution, being composed of a matrixof only .
The CT scanner was a huge success: by1977 1130 machines were installedacross the world.
Fig 9.4: EMI brain scanner witha Data General Nova
minicomputer. The first scannerwas installed at Atkinson
Morley's Hospital, Wimbledon,England in 1971
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Prof. Dr. Philippe Cattin: Computed Tomography
Detectors
→ Scintillator [http://en.wikipedia.org/wiki/Scintillator] Detectors
Low maximum count rate leads to longer scan times or more imagenoise
Xenon Gas Detectors
Pressurised Xe gas capable of higher count rates, but low detectionefficiency
Modern Ceramic → Scintillators [http://en.wikipedia.org/wiki/Scintillator]
Coupled with photodiodes these detectors offer the bestperformance
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Computed Tomography Basics
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Prof. Dr. Philippe Cattin: Computed Tomography
Important Terminology
In-plane resolution:
acquisition resolution in the
-plane
Out-of-plane, through-plane
resolution: slice distance in
axis
Anisotropic scan: the
resolution in the axis is
generally less than in the
axis
Isotropic scan: the voxel
dimensions are equal in the
, and axis
Fig 9.5: Coordinate system generallyused
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Single Slice CT
April 11th/12h, 2016Biomedical Image Analysis
(11)First Generation CT ScannerDesign
The generation of CT scanner usedthe translate-rotate geometry.
The EMI scanner, for instance, used apencil X-ray beam and a singledetector. During translation of thegantry, the X-ray beam was sampled160 times. After a rotation of a newprofile was acquired. This procedurewas repeated for 180 different anglesand took roughly .
To minimise patient movement the headwas usually clamped.
Fig 9.6: First generation CTprinciple
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Single Slice CT
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Second Generation CTScanner Design
The generation scanner tried toreduce the excessive scan times byusing a small fan beam with multipledetectors (up to 30 in some designs).
Scan times of between werepossible with this design.
The introduction of multiple detectorswas an important development.
Fig 9.7: Second generation CTprinciple
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Single Slice CT
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Third Generation CT ScannerDesign
The generation brought down scantimes even further by using the rotate-rotate geometry.
As the large fan beam encompasses thepatient completely the translatorymotion of the previous designs can beavoided. The X-ray tube and thedetector array rotate as one about thepatient.
The number of detector elements istypically in the hundreds.
To avoid excessive variations in signalstrength various manufacturers use abow-tie shaped filter to suit the body orhead shape.
Fig 9.8: Third generation CTprinciple
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Single Slice CT
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Prof. Dr. Philippe Cattin: Computed Tomography
Fourth Generation CTScanner Design
The generation CT uses arotate-fixed ring geometry where thering of detectors completely surroundsthe patient.
As the X-ray tube must be closer to thepatient than the detectors it has a poorradiographic geometry, i.e. largegeometric magnification.
Scan times as low as withinterscan delays of can beachieved with this type of geometry.
Using many thousand detectorelements a in-plane resolution of
can be obtained.
Fig 9.9: Fourth generation CTprinciple
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Single Slice CT
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Spiral Scanning CT
Advances in slip-ring technologyhave enabled the X-ray tube torotate continuously in the samedirection which overcomesproblems of interscan delays.
If the continuous motion of thegantry is combined with acontinuous advance of thepatient table along thelongitudinal axis we have aspiral/helical scanner.
The spiral scanning technologybrought about a significantreduction in scan times.
The gained speed came at aprice of increased complexity forreconstructing the helical data.
Fig 9.10: Illustration of helical scanning
Fig 9.11: Nice 3D rendering of helicalCT
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Single Slice CT
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Prof. Dr. Philippe Cattin: Computed Tomography
Spiral Scanning CT (2)
The X-ray source iscollimated to a fan beamrotating around thepatient.
The X-ray tube and thedetectors are fixedtogether as a singlerotating unit.
Post patient collimationdefines the slicesensitivity profile.
Fig. 9.12: Basic design of a single slice CT usedin a spiral CT
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Single Slice CT
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Spiral Scanning CT (3)
In the context of helical scanning aparameter called Pitch is defined as the
Ratio of the distance that thepatient couch moves in onerotation to the collimationthickness (number of slices slice thickness)
(9.1)
In other words, for a couch advance of and a nominal collimation width
of , the pitch is 1. Pitch valuesare typically in the range of 1 to 2depending on the required spatialresolution in the direction of the couchmotion. Its a coverage indicator, inother words.
Fig 9.13: Pitch
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Single Slice CT
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Drawback of these Designs
Ideally, volume data are of high isotropic spatial resolution, haveminimal motion artefacts, and optimally utilise the contrast agentbolus.
To reduce motion artefacts CT examinations need to be completedwithin a certain time frame, e.g. on breath hold, forthe heart.
If, however, a large scan range such as the entire thorax has to becovered
a thick collimation (large inter slice distance)
must be used, leading to anisotropic voxel sizes (whilst the in-planeresolution only depends on the system geometry).
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Multi-Detector RowCT
April 11th/12h, 2016Biomedical Image Analysis
(20)Multi-Detector Row CT
Strategies to achieve a betterlongitudinal resolution andfaster scans include thesimultaneous acquisition ofmultiple slices at a time, thustermed Multi-Detector Row CTor Multi-Slice CT (MSCT).
Interestingly, the very firstcommercial CT systems(EMI-Scanner and SiemensSiretom) were already two-slicesystems. Only the introduction ofthe helical scanning principleallowed to fully leverage theadvantages of multi-detector rowCT.
Fig 9.14: Multi-slice CT
Fig 9.15: SOMATOM Sensation 16Gantry (Siemens)
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Multi-Detector Row CT
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Detector Design
The figure shows, how different slice widths can be achieved byprepatient collimation for a single slice detector .
Fig 9.16: Prepatient collimation of the X-ray beam to obtain different slicethicknesses with a single detector row CT.
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Multi-Detector Row CT
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Detector Design (2)
The principle can be easily extended to slices if the sensor isseparated midway along the axis.
Fig 9.17: Collimation of the X-ray beam to obtain different slice thicknesses with atwo detector row CT.
For detectors a more elaborate detector design is required.
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Multi-Detector Row CT
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Detector Design (3)
The various manufacturers introduceddifferent detector designs in order toallow utmost flexibility in selecting slicewidths.
All designs combine several detectorrows electronically to a smaller numberof slices according to the selected slicewidth.
The total coverage of this detectordesign is (measured in theisocenter).
With prepatient collimation thefollowing slice widths can be realised:
, , , and .
Fig 9.18: Fixed array detector,16 rows, 4 slices
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Multi-Detector Row CT
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Detector Design (4)
A more efficient approach (needs lessdetector channels) uses the adaptivearray design.
This design allows the followingcollimated slice widths: two slices at
, four at , four at ,two at , and two at .
Fig 9.19: Adaptive arraydetector, 8 rows, 4 slices
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Multi-Detector Row CT
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Detector Design (5)
Sixteen-slice CT systems usually haveadaptive array detectors similar to theone depicted in Fig 9.20. It uses 24detector rows with a total coverage of
at the isocenter.
By properly combining the detectorrows, either 12 or 16 slices with
or can be acquiredsimultaneously.
Fig 9.20: Adaptive arraydetector, 24 rows, 16 slices
(Siemens)
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Detector Design (6)
32, 40, and 64 slice systems are now available.
Fig 9.21: Toshiba detector mock-ups
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Dual Source CT
A different approach to acquire moreslices in parallel was followed bySiemens with their → Dual SourceCT [http://www.siemens.com/dualsource]
(SOMATOM Definition).
Fig 9.22: Dual Source CT (SiemensSOMATOM Definition)
Fig 9.23: Comparison of LAD & Cxin diastole and systole
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Multi-Detector Row CT
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Open Dual Source CT
Fig 9.24: Movie of the an open rotating dual source CT
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Multi-Detector Row CT
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Prof. Dr. Philippe Cattin: Computed Tomography
Advantage of the DSCT
The scan is in cardiac-mode virtually independent of the heart
rate → no -blocker needed
If the two X-Ray tubes are operated with two different tube
voltages (other spectra) tissue types can be better
differentiated
Fig 9.25: HU values for different tissue types (theoretical simulation)
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ImageReconstruction
Introduction
April 11th/12h, 2016Biomedical Image Analysis
(32)Image Reconstruction
From the scanning process we have a set of image projections.Given these projections we want to determine the X-rayattenuation coefficients of the original image as accurate aspossible.
Fig 9.26: Image projections
Fig 9.27: A small section of the finalmatrix showing individual attenuation
values combined as a ray-sum
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Introduction
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Image Reconstruction (2)
Already in 1917 → Johann Radon [http://en.wikipedia.org/wiki/Johann_Radon]
published a paper with the mathematical theory, the → Radontransform [http://en.wikipedia.org/wiki/Radon_transform], useful toreconstruct a 2D image from multiple projections such as in CTsystems.
Hounsfield used, for the first CT scanner, an iterative technique toexactly solve the Radon transform. Its disadvantages are that it isslow and that all data must be collected before reconstruction canbegin.
Todays CT systems mainly use variants of the filteredback-projection approach that is computationally more efficient.
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Radon Transform
April 11th/12h, 2016Biomedical Image Analysis
(35)Radon Transform
A straight line in Cartesiancoordinates can be either describedby its slope-intercept form
(9.2)
or by its normal representation
(9.3)
see Fig 9.28.
Fig. 9.28: Different linerepresentations
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Radon Transform
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Parallel Projection
An arbitrary point in the projection is given by the raysum alongthe line
(9.4)
in the continuous space the raysum is then given by
(9.5)
where is the impulse
function.
(9.6)
with .
The integrand is zerounless the argument inthe delta function is
zero. This is valid for allpoints on the line
.
Fig. 9.29: Projection geometry
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Radon Transform
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The Radon Transform
We can generalise this equation to arbitrary lines
(9.7)
This projection is called Radon transform. Often used notations forthe Radon transform of are
(9.8)
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Radon Transform
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The Discrete RadonTransform
In the discrete case the integrals in the Radon transform arereplaced by sums
(9.9)
The Radon transform forms the corner stone ofreconstruction from projections used e.g. in ComputedTomography, PET, SPECT.
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Radon Transform
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Radon Transform Examples
The figure below shows an example image with its Radontransform. The interpretation of the sinogram is still quite easy.
Fig. 9.30: Double box image
Fig. 9.31: Sinogram of the double boximage with projections over
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Radon Transform
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Radon Transform Examples(2)
The figure below shows an example phantom with its Radontransform. The interpretation of the sinogram is not possibleanymore, although the phantom's structure is quite simple.
Fig. 9.32: Shepp-Logan phantom
Fig. 9.33: Sinogram of the phantomwith projections over
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Fourier SliceTheorem
April 11th/12h, 2016Biomedical Image Analysis
(42)Fourier Slice Theorem
In the following slide we will relate the Fourier transform of 1-Dprojection with the 2-D Fourier transform of the scanned object.Without loss of generality, we take the projection line to be the -axis in the derivation below. Given is the image and its
projection onto the -axis where
(9.10)
The Fourier transform of is
(9.11)
the slice at is then
(9.12)
which is the Fourier transform of .
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Fourier Slice Theorem
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Prof. Dr. Philippe Cattin: Computed Tomography
Fourier Slice Theorem (2)
Fig. 9.34: Graphical representation of the Fourier slice theorem
The Fourier slice theorem states that, the 1-dimensionalFourier transform of a projection corresponds to the slice(line) - at the same angle - in the 2-dimensional Fouriertransform of the object
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Fourier Slice Theorem
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Reconstruction with theFourier Slice Theorem
In principle we could reconstruct the image by filling up the
Fourier space with the Fourier transforms of the individual
projections and then calculate the inverse Fourier transform. Thisapproach is, however, computationally very expensive.
Fig. 9.35: Image reconstructing using the Fourier slice theorem
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Fourier Slice Theorem
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Prof. Dr. Philippe Cattin: Computed Tomography
Reconstruction with theFourier Slice Theorem (2)
If we just sum the spectra ofthe individual projectionbeams, the spectral densityfor low frequencies would betoo high as the beams arecloser to each other for smallradii → lower frequencies toostrong.
We therefore must correctthe spectrum with a suitableweighting factor. As thedensity of the projectionbeam goes with
(Frequency) the spectra mustbe multiplied with → ramp
filter.
Each projection directionthus has to be multiplied witha suitable weighting function
. As will be seen in the
next section, this can also beperformed as a convolutionwith the inverse Fouriertransform of in the
spatial domain → filteredback-projection.
Fig. 9.36: Spectral density must becorrected to get suitable results
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FilteredBackprojection
April 11th/12h, 2016Biomedical Image Analysis
(47)Principle of FilteredBack-Projection
(1) The measured projections are smeared back, i.e. combined as aray-sum, across the output matrix. (2) As the back-projected imageis heavily blurred and shows star artefacts it has to be filtered witha highpass yielding the final reconstructed image.
Fig 9.37: Filtered back-projection principle
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Filtered Backprojection
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Prof. Dr. Philippe Cattin: Computed Tomography
Numerical Back-ProjectionExample
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Filtered Backprojection
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Prof. Dr. Philippe Cattin: Computed Tomography
Example Reconstructions
Back-projectionwithout filteringusing 2, 4, 8,16, and 32projections.
Strong artefactscan be seen andthe images areheavily blurred.
Fig 9.38: Back-projection without filter
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Filtered Backprojection
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Example Reconstructions (2)
Back-projectionwith highpassfiltering usingthe same 2, 4, 8,16, and 32projections.
Strong artefactscan be seen andthe images areheavily blurred.
Fig 9.39: Back-projection with filter
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HelicalReconstruction
April 11th/12h, 2016Biomedical Image Analysis
(52)Helical Reconstruction
We would like to use the same filtered back-projection method asbefore:
Choose the
interpolation
position along
the z-axis
Only one
projection is
from the
reconstruction
position, others
are from
different
z-positions
Fig 9.40: Problem of the helical reconstruction
→ Introduces artefacts when the structures change along thez-axis.
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Helical Reconstruction
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Prof. Dr. Philippe Cattin: Computed Tomography
360° Linear Interpolation
Idea: Use attenuation data from points apart on the helix forinterpolation
Fig 9.41: Interpolation
→ Interpolation makes the effective image width broader.
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Helical Reconstruction
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Prof. Dr. Philippe Cattin: Computed Tomography
180° Linear Interpolation
Idea: Use attenuation data from complementary projections inaddition to points apart on the helix
Fig 9.42:Complementary
projections
Fig 9.43: Interpolation
→ Slice profile is narrower, as the z-axis distances are shorter thanin interpolation.
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Hounsfield Unit
April 11th/12h, 2016Biomedical Image Analysis
(56)Hounsfield Unit
The tissue absorption coefficient depends on the tube voltage.
To make them comparable, theabsorption coefficients have tobe related to that of water a thesame tube voltage. This way anumber [Hounsfield unit = Hu]insensitive to tube voltage canbe obtained:
(9.13)
In practice CT values areproduced from for air,
for water, and between for bone.
Fig 9.44: Common CT numbers
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Artefacts
April 11th/12h, 2016Biomedical Image Analysis
(58)Artefacts
Several inherent CT artefacts have an important influence on theapplied Medical Image Analysis Methods and generally need to beaccounted for:
Partial Volume Effect
High density artefacts
Gating in Cardio CT
The Good News: CT data is geometrically very accurate. IfMR/US data is to be registered with CT, then CT should beused as the reference!
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Artefacts
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Prof. Dr. Philippe Cattin: Computed Tomography
Partial Volume Effect
The partial volume effect,common to most medicalimaging modalities, poses animportant problem for manymedical image analysis methods.
The sampling of the imagingvolume renders itdifficult/impossible to exactlylocate the boundary of an object.
If not taken special care of, asimple shift of the object candrastically change the result,e.g. area measurement in Fig9.45(c)+(d). The measured areaof (d) is higher than thearea of (c).
Fig 9.45: (a) Original object, (b) objectsampled on a discrete grid, (c)
thresholded object, (d) thresholdedshifted object
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Artefacts
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High Density Artefacts
High density streak artefacts or Windmill artefacts result from thefinite width of the detector rows, which require interpolation. Theartefacts appear close to high contrast gradients.
Fig 9.46: High density artefact example
Fig 9.47: Windmill effect
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Artefacts
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Prof. Dr. Philippe Cattin: Computed Tomography
Gating in Cardio CT
For many acquisitions of the heart and arterial system ECG gatingis used. To reduce exposure, the AEC reduces the tube current to
during systole (when no images are captured). Proper gating,however, depends on a regular sine rhythm not present in alldiseased patients.
Fig 9.48: Image of good quality withdecent SNR
Fig 9.49: Gating failed, image wasacquired with of the dose → very
noisy image
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Artefacts
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Prof. Dr. Philippe Cattin: Computed Tomography
CT and Medical ImageAnalysis
Medical image analysis is an indispensable tool in CT. Without theaid of advanced image analysis methods, radiologists would needsubstantially more time to find interesting location in the CTdatasets.
Fig 9.50: Plaque detection aid
Fig 9.51: Automatic dissectionsegmentation
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