CT utilizes x-rays to produce cross-sectional slices of the body. Multiple x-ray projections are taken at different angles and are reconstructed using algorithms like filtered backprojection to generate detailed images of internal structures. CT is advantageous over regular x-rays as it can distinguish between overlapping tissues. However, it also exposes patients to ionizing radiation. The number of projections taken is a tradeoff between image quality and radiation dose.
Gyroscope sensors measure angular velocity by detecting the Coriolis effect on a vibrating mass. They have specifications including measurement range, number of sensing axes, nonlinearity, temperature range, and noise parameters. MEMS gyroscopes typically use a vibrating proof mass driven electrostatically while rotation is detected via sense electrodes measuring the Coriolis-induced deflection perpendicular to the drive mode. The Coriolis effect causes an apparent deflection in a rotating reference frame due to inertial forces.
This document provides information about image reconstruction in multi-detector computed tomography (MDCT). It begins with an overview of the basic principles of CT imaging, including image formation steps and reconstruction methods. It then describes the principles of helical CT scanning and how this enables volumetric data acquisition. Finally, it discusses image reconstruction techniques for MDCT, including interpolation methods needed to reconstruct images from the helical scan data. In particular, it notes that multi-detector arrays allow acquisition of multiple slices with each rotation, significantly increasing scan speed and coverage compared to earlier single-detector row CT.
This document provides an introduction to real-time rendering concepts. It discusses 3D mathematics including coordinate systems, primitives, and affine transformations. It then explains the graphics pipeline including programmable shaders and GPU architecture. Finally, it covers simulating light through reflection models and shading models. Key topics include primitive types and topologies, constructing polygon meshes, transforming objects, the view and projection transforms, and how shaders are used in the graphics pipeline to simulate lighting effects.
MDCT provides high resolution images through rapid acquisition of multiple slices during a single rotation. It uses multiple detector arrays rather than a single row, allowing acquisition of more data in less time. Image reconstruction involves back projection, iterative, or analytical methods to assign CT numbers based on x-ray attenuation. Applications include angiography, cardiac imaging, and virtual endoscopy due to improved temporal and spatial resolution compared to earlier CT technologies.
The document discusses texture measurement using X-ray diffraction. It describes the Schulz reflection method for measuring pole figures using a 5-axis goniometer. The key steps are to first identify diffraction peaks via a Bragg scan, then fix the Bragg angle and measure intensity while rotating the sample through angles φ and ψ to map the intensity distribution on a pole figure for the chosen diffraction plane. Intensity variations reveal the texture components present in the material.
This report summarizes research on the motion of particles on curves. It was found that:
1) The center of mass of 3 points on an ellipse that divide its perimeter evenly traces out a smaller ellipse of the same shape.
2) The maximum product of distances between 4 particles on a rectangle occurs when particles are at the corners for small rectangles, but 2 particles move off the corners for larger rectangles.
3) The center of mass of n points on a square that divide its perimeter evenly traces out a smaller square n times for odd n, and remains fixed at the center for even n.
The document discusses computed tomography (CT) scanning. It begins by introducing CT and comparing it to conventional radiography. CT provides more accurate diagnostic information by reconstructing 3D structures from multiple 2D projections, unlike conventional radiography which produces 2D shadow images. The document then covers key aspects of CT scanning including the components involved in data acquisition, the reconstruction process, and parameters such as slice thickness and radiation dose. It also describes advances in CT technology over generations from narrow single detector scans to modern multi-detector scanners.
Gyroscope sensors measure angular velocity by detecting the Coriolis effect on a vibrating mass. They have specifications including measurement range, number of sensing axes, nonlinearity, temperature range, and noise parameters. MEMS gyroscopes typically use a vibrating proof mass driven electrostatically while rotation is detected via sense electrodes measuring the Coriolis-induced deflection perpendicular to the drive mode. The Coriolis effect causes an apparent deflection in a rotating reference frame due to inertial forces.
This document provides information about image reconstruction in multi-detector computed tomography (MDCT). It begins with an overview of the basic principles of CT imaging, including image formation steps and reconstruction methods. It then describes the principles of helical CT scanning and how this enables volumetric data acquisition. Finally, it discusses image reconstruction techniques for MDCT, including interpolation methods needed to reconstruct images from the helical scan data. In particular, it notes that multi-detector arrays allow acquisition of multiple slices with each rotation, significantly increasing scan speed and coverage compared to earlier single-detector row CT.
This document provides an introduction to real-time rendering concepts. It discusses 3D mathematics including coordinate systems, primitives, and affine transformations. It then explains the graphics pipeline including programmable shaders and GPU architecture. Finally, it covers simulating light through reflection models and shading models. Key topics include primitive types and topologies, constructing polygon meshes, transforming objects, the view and projection transforms, and how shaders are used in the graphics pipeline to simulate lighting effects.
MDCT provides high resolution images through rapid acquisition of multiple slices during a single rotation. It uses multiple detector arrays rather than a single row, allowing acquisition of more data in less time. Image reconstruction involves back projection, iterative, or analytical methods to assign CT numbers based on x-ray attenuation. Applications include angiography, cardiac imaging, and virtual endoscopy due to improved temporal and spatial resolution compared to earlier CT technologies.
The document discusses texture measurement using X-ray diffraction. It describes the Schulz reflection method for measuring pole figures using a 5-axis goniometer. The key steps are to first identify diffraction peaks via a Bragg scan, then fix the Bragg angle and measure intensity while rotating the sample through angles φ and ψ to map the intensity distribution on a pole figure for the chosen diffraction plane. Intensity variations reveal the texture components present in the material.
This report summarizes research on the motion of particles on curves. It was found that:
1) The center of mass of 3 points on an ellipse that divide its perimeter evenly traces out a smaller ellipse of the same shape.
2) The maximum product of distances between 4 particles on a rectangle occurs when particles are at the corners for small rectangles, but 2 particles move off the corners for larger rectangles.
3) The center of mass of n points on a square that divide its perimeter evenly traces out a smaller square n times for odd n, and remains fixed at the center for even n.
The document discusses computed tomography (CT) scanning. It begins by introducing CT and comparing it to conventional radiography. CT provides more accurate diagnostic information by reconstructing 3D structures from multiple 2D projections, unlike conventional radiography which produces 2D shadow images. The document then covers key aspects of CT scanning including the components involved in data acquisition, the reconstruction process, and parameters such as slice thickness and radiation dose. It also describes advances in CT technology over generations from narrow single detector scans to modern multi-detector scanners.
The document discusses computed tomography (CT) scanning. It begins by introducing CT and comparing it to conventional radiography. CT provides more accurate diagnostic information by reconstructing 3D structures from multiple 2D projections, unlike conventional radiography which produces 2D shadow images. The document then covers key aspects of CT scanning including the components involved in data acquisition, the reconstruction process, and parameters such as slice thickness and radiation dose. It also describes advances in CT technology over generations from narrow single detector scans to current multi-detector scanners.
The document describes an experiment using a diffraction grating spectrometer to measure emission spectra of elements and identify unknown elements. Sodium light is used to calibrate the spectrometer by measuring the angles of the first and second order spectra and calculating the grating spacing. Then an unknown light is analyzed by measuring spectral line angles and wavelengths, which are compared to reference tables to identify the element.
Computed tomography (CT) has evolved through several generations of technology over time:
- First generation CT used a single narrow beam and single detector for head imaging only, taking 5 minutes per scan.
- Second generation CT used a fan-shaped beam and multiple detectors, allowing full-body scans in 10-90 seconds.
- Third generation CT introduced a curvilinear detector array and rotate-rotate motion, lowering scan time to 1 second or less but introducing ring artifacts.
- Current multi-detector CT uses multiple rows of detectors, covering a large body section faster with thin slices or 3D imaging.
1. The document discusses techniques for analyzing motion in video sequences, including optical flow estimation. Optical flow describes image motion vectors at each point.
2. Two main approaches to estimating optical flow are discussed: gradient-based methods using pixel intensity conservation, and feature point detection and matching between frames.
3. The Lucas-Kanade method is described, which assumes optical flow is locally constant and estimates it using a least squares approach on neighboring pixels.
Solid state chemistry- laws of crystallography- Miller indices- X ray diffraction- Bragg equation- Spectrophotometer- Determination of interplanar distance- Types of crystal
The document summarizes the history and development of computed tomography (CT) scanning technology. It describes the key events and innovations such as the development of the first CT scanner by Godfrey Hounsfield in 1972 (1), the introduction of whole body scanning in 1975 (2), and Hounsfield and Cormack being awarded the Nobel Prize in 1979 (3). Subsequent generations of CT scanners incorporated improvements like faster scanning speeds, multiple detectors, and eliminating moving parts to enable ultra-fast scanning.
This document describes the basic principles and historical development of computed tomography (CT) imaging. It discusses how CT uses mathematical principles and X-ray projections to create 3D images of internal anatomy. The document then summarizes the key innovations and technologies of each generation of CT scanners, from early pencil beam systems to current multi-detector array systems, which provide faster and higher resolution volumetric imaging.
Lecture 3 & 4 anam sanam chick ldkfdlsfldfjdlsjfdlks .pptxfaiz3334
Computed tomography (CT) scans create cross-sectional images of the body by using X-rays and computer processing. An X-ray tube rotates around the body and produces multiple images from different angles, which are used to reconstruct cross-sectional slices using back projection. These slices can be combined to create 3D images. CT scans provide more detailed images than basic X-rays due to their ability to distinguish between different tissue densities and visualize structures throughout the body.
The document provides an overview of the basic principles of CT scanning. It discusses key differences between radiography and CT imaging, including that CT produces cross-sectional images without overlaying structures. It describes the CT scanning process where an X-ray beam passes through the patient and is measured to construct voxel values and pixels. CT numbers represent attenuation coefficients measured in Hounsfield units. The document also covers topics like polychromatic beams, volume averaging effects, raw vs image data, and different scan modes like step-and-shoot and helical scanning.
Computed Tomography and Spiral Computed Tomography JAMES JACKY
1. Computed Tomography / Spiral Computed Tomography
2. Clinical and Principle Operation of Computed Tomography
3. Law and Regulation in Malaysia
4. Radiation Dose
This document provides an overview of 2D NMR spectroscopy and COSY NMR experiments. It discusses how 2D NMR addresses limitations of 1D NMR for analyzing complex protein spectra by introducing additional spectral dimensions. COSY NMR specifically correlates hydrogen atoms that are directly bonded to each other, showing their interactions on a grid plot with chemical shifts on both axes. Interpreting COSY spectra involves identifying off-diagonal peaks that indicate correlations between different hydrogen atoms.
This legal document provides several notices and disclaimers regarding the information presented. Specifically:
- The presentation is for informational purposes only and Intel makes no warranties regarding the information or summaries of the information.
- Any performance claims depend on system configuration and hardware/software/service activation. Performance varies depending on system configuration.
- The sample source code is released under the Intel Sample Source Code License Agreement.
- Intel and the Intel logo are trademarks of Intel Corporation in the U.S. and other countries. Other names may belong to other owners.
- Copyright of the content is held by Intel Corporation and all rights are reserved.
The document discusses the basic components and functioning of an ultrasound machine. It describes the transmitter/pulser, transducer, receiver and processor, display, and recording components. The transducer is made of piezoelectric crystals and converts electrical energy to ultrasound energy and vice versa. Different controls like gain, zoom, and Doppler are used by the radiographer to optimize the ultrasound image.
Computerized tomography (CT) was pioneered by Godfrey Hounsfield and Allan Cormack in the 1970s. CT uses X-rays and computer processing to create cross-sectional images of the body. The first CT scanners used a translate-rotate design, while later generations used multiple detectors and spiral scanning for faster, more detailed imaging. Image reconstruction uses back projection to convert attenuation measurements into pixel values and display slices. CT provides excellent anatomical detail and is widely used for diagnosing conditions of the brain, blood vessels, lungs and other organs.
The document contains announcements and instructions for an assignment in a computer graphics course. It discusses file formats for outputting images, implementing ray casting and ray tracing, and transforming objects through translation, rotation and scaling. It also covers generating shadow rays, reflection and refraction. Transforming rays through inverse transforms allows intersecting rays with canonical objects to determine scene intersections.
This document provides an introduction to the topic of kinematics in physics. It begins with introducing physics as an experimental science based on experiments and mathematics. It then discusses concepts related to motion such as frames of reference, types of motion including linear, circular, rotational, and vibratory motion. It also discusses motion in one, two and three dimensions. Key concepts in vector algebra like scalars, vectors, addition and subtraction of vectors are introduced. The document provides examples to explain these concepts in physics.
Surveying techniques are used to establish the position of objects in 2D or 3D. Primary surveys are done when no previous data exists, while secondary surveys add to existing data or measure changes. Plan position is determined through techniques like triangulation, trilateration, or offset measurements from baselines. Elevation is found by direct or inclined leveling between points of known height. Theodolites allow simultaneous measurement of horizontal angles, slopes, and slant distances.
The document discusses computed tomography (CT) scanning. It begins by introducing CT and comparing it to conventional radiography. CT provides more accurate diagnostic information by reconstructing 3D structures from multiple 2D projections, unlike conventional radiography which produces 2D shadow images. The document then covers key aspects of CT scanning including the components involved in data acquisition, the reconstruction process, and parameters such as slice thickness and radiation dose. It also describes advances in CT technology over generations from narrow single detector scans to current multi-detector scanners.
The document describes an experiment using a diffraction grating spectrometer to measure emission spectra of elements and identify unknown elements. Sodium light is used to calibrate the spectrometer by measuring the angles of the first and second order spectra and calculating the grating spacing. Then an unknown light is analyzed by measuring spectral line angles and wavelengths, which are compared to reference tables to identify the element.
Computed tomography (CT) has evolved through several generations of technology over time:
- First generation CT used a single narrow beam and single detector for head imaging only, taking 5 minutes per scan.
- Second generation CT used a fan-shaped beam and multiple detectors, allowing full-body scans in 10-90 seconds.
- Third generation CT introduced a curvilinear detector array and rotate-rotate motion, lowering scan time to 1 second or less but introducing ring artifacts.
- Current multi-detector CT uses multiple rows of detectors, covering a large body section faster with thin slices or 3D imaging.
1. The document discusses techniques for analyzing motion in video sequences, including optical flow estimation. Optical flow describes image motion vectors at each point.
2. Two main approaches to estimating optical flow are discussed: gradient-based methods using pixel intensity conservation, and feature point detection and matching between frames.
3. The Lucas-Kanade method is described, which assumes optical flow is locally constant and estimates it using a least squares approach on neighboring pixels.
Solid state chemistry- laws of crystallography- Miller indices- X ray diffraction- Bragg equation- Spectrophotometer- Determination of interplanar distance- Types of crystal
The document summarizes the history and development of computed tomography (CT) scanning technology. It describes the key events and innovations such as the development of the first CT scanner by Godfrey Hounsfield in 1972 (1), the introduction of whole body scanning in 1975 (2), and Hounsfield and Cormack being awarded the Nobel Prize in 1979 (3). Subsequent generations of CT scanners incorporated improvements like faster scanning speeds, multiple detectors, and eliminating moving parts to enable ultra-fast scanning.
This document describes the basic principles and historical development of computed tomography (CT) imaging. It discusses how CT uses mathematical principles and X-ray projections to create 3D images of internal anatomy. The document then summarizes the key innovations and technologies of each generation of CT scanners, from early pencil beam systems to current multi-detector array systems, which provide faster and higher resolution volumetric imaging.
Lecture 3 & 4 anam sanam chick ldkfdlsfldfjdlsjfdlks .pptxfaiz3334
Computed tomography (CT) scans create cross-sectional images of the body by using X-rays and computer processing. An X-ray tube rotates around the body and produces multiple images from different angles, which are used to reconstruct cross-sectional slices using back projection. These slices can be combined to create 3D images. CT scans provide more detailed images than basic X-rays due to their ability to distinguish between different tissue densities and visualize structures throughout the body.
The document provides an overview of the basic principles of CT scanning. It discusses key differences between radiography and CT imaging, including that CT produces cross-sectional images without overlaying structures. It describes the CT scanning process where an X-ray beam passes through the patient and is measured to construct voxel values and pixels. CT numbers represent attenuation coefficients measured in Hounsfield units. The document also covers topics like polychromatic beams, volume averaging effects, raw vs image data, and different scan modes like step-and-shoot and helical scanning.
Computed Tomography and Spiral Computed Tomography JAMES JACKY
1. Computed Tomography / Spiral Computed Tomography
2. Clinical and Principle Operation of Computed Tomography
3. Law and Regulation in Malaysia
4. Radiation Dose
This document provides an overview of 2D NMR spectroscopy and COSY NMR experiments. It discusses how 2D NMR addresses limitations of 1D NMR for analyzing complex protein spectra by introducing additional spectral dimensions. COSY NMR specifically correlates hydrogen atoms that are directly bonded to each other, showing their interactions on a grid plot with chemical shifts on both axes. Interpreting COSY spectra involves identifying off-diagonal peaks that indicate correlations between different hydrogen atoms.
This legal document provides several notices and disclaimers regarding the information presented. Specifically:
- The presentation is for informational purposes only and Intel makes no warranties regarding the information or summaries of the information.
- Any performance claims depend on system configuration and hardware/software/service activation. Performance varies depending on system configuration.
- The sample source code is released under the Intel Sample Source Code License Agreement.
- Intel and the Intel logo are trademarks of Intel Corporation in the U.S. and other countries. Other names may belong to other owners.
- Copyright of the content is held by Intel Corporation and all rights are reserved.
The document discusses the basic components and functioning of an ultrasound machine. It describes the transmitter/pulser, transducer, receiver and processor, display, and recording components. The transducer is made of piezoelectric crystals and converts electrical energy to ultrasound energy and vice versa. Different controls like gain, zoom, and Doppler are used by the radiographer to optimize the ultrasound image.
Computerized tomography (CT) was pioneered by Godfrey Hounsfield and Allan Cormack in the 1970s. CT uses X-rays and computer processing to create cross-sectional images of the body. The first CT scanners used a translate-rotate design, while later generations used multiple detectors and spiral scanning for faster, more detailed imaging. Image reconstruction uses back projection to convert attenuation measurements into pixel values and display slices. CT provides excellent anatomical detail and is widely used for diagnosing conditions of the brain, blood vessels, lungs and other organs.
The document contains announcements and instructions for an assignment in a computer graphics course. It discusses file formats for outputting images, implementing ray casting and ray tracing, and transforming objects through translation, rotation and scaling. It also covers generating shadow rays, reflection and refraction. Transforming rays through inverse transforms allows intersecting rays with canonical objects to determine scene intersections.
This document provides an introduction to the topic of kinematics in physics. It begins with introducing physics as an experimental science based on experiments and mathematics. It then discusses concepts related to motion such as frames of reference, types of motion including linear, circular, rotational, and vibratory motion. It also discusses motion in one, two and three dimensions. Key concepts in vector algebra like scalars, vectors, addition and subtraction of vectors are introduced. The document provides examples to explain these concepts in physics.
Surveying techniques are used to establish the position of objects in 2D or 3D. Primary surveys are done when no previous data exists, while secondary surveys add to existing data or measure changes. Plan position is determined through techniques like triangulation, trilateration, or offset measurements from baselines. Elevation is found by direct or inclined leveling between points of known height. Theodolites allow simultaneous measurement of horizontal angles, slopes, and slant distances.
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2. Overview
• Different names, same device:
❑ Computed tomography (CT)
❑ CT scan
❑ Computed Axial Tomography (CAT) scan
• CT utilizes computer-processed x-rays to produce ‘slices’ of specific areas
of the body.
4. Pixels vs Voxels
• CT slice thickness is
typically 1 - 10 mm.
• CT images are comprised
of pixels.
• A voxel is the 3D volume
element represented by
one pixel in a CT image.
5. Projection vs Tomography
• CT is advantageous over projection X-ray imaging because it shows overlaying
structures.
6. CT Equipment
• A bore ➔ contains a gantry
that x-ray tubes as well as x-ray
detectors and spin around this
bore.
• A table ➔ the patient lays on.
A table slides into and out of
the bore in order to make CT
image od any slice within the
body.
• A computer ➔ used to process
the images.
7. Imaging Method
• X-ray source and detector rotates around
the patient.
• Acquired data is processed with
tomographic reconstruction methods.
• A series of cross-sectional image slices are
produced.
8. Multiple Projections (1)
• When gantry is rotating around the patient, we pass x-
rays through this representation of the body, and we get
a view of the amount of absorption.
• The view tells us that there was very little absorption and
high absorption where the circle is located, meaning
that the x-rays were absorbed and blocked from the
detector.
9. Multiple Projections (2)
• We rotate our view and do the same for
x-rays passing through this projection
angle.
• We get a similar profile of the
absorption.
• There is a little shifted to the left
compared to the view 1, and then lower
absorption.
10. Multiple Projections (3)
• Then, we can again rotate and get a
third view that similarly represents
the amount of absorption.
• Therefore, CT measures the linear
attenuation between a source and a
detector.
• Attenuation is basically measure of
how rapidly x-rays are absorbed and
views one to three represents a
radon transform.
Views 1-3 represent a
Radon Transform
11. What is radon transform?
• We can represent this as an
image by stacking up
multiple different views
• The lower values in the
profile can be represented
as black, similar to an X-ray
image, meaning that most
of the X-rays were passed
through in this view.
• The brightest regions can
be represented as white ➔
x-rays were absorbed.
• Everything in between ➔
shades of grey.
• We do this for not just 3
views, but views of degrees
varying from 0 – 1800.
12. Sinogram (1)
• Sinogram ➔ graphical representation of the 2D Radon transform.
• We get a line profile through
one of the earlier degrees.
• Line 1: We get a peak in line
profile toward the bottom of
the detector.
• Line 2: another slice after
rotating a little bit more ➔ a
peak shifts more toward the
center of the detector.
• Line 3: rotate 900 from the
original profile ➔ a peak
shifts upward even more.
• Image views from 0 – 1800 ➔
sinogram.
13. Sinogram (2)
• Sinogram ➔ graphical representation of the 2D Radon transform.
• This is the same principle as
projections from 0 – 3600.
• Depending on where the
detector is rotated around
the source, sometimes the
projection peak is closer to
an earlier element of the
source or farther away.
14. Predict The Sinogram (1)
• We’re rotating the gantry around the object and getting projections with each rotation.
• For this example, notice that no matter where we project, the peak should always be at
the center.
• In this object (circle at the center), the sinogram would expect it to be a straight line ➔
so no matter what angle we’re looking at this object from, we see the same projection
on as a function of a detector number.
15. Predict The Sinogram (2)
• What if instead we have a square and not a circle?
• When we’re looking through the two corners of the square, we get the maximum intensity.
• When we’re off on the side, the values should be lower than the values at the center of the detector that passes
through the most, widest part of the square, or it passes through the part of the square that has a maximum value of
whiteness.
• We get two sinusoidal looking patterns that correspond to the square tips, the x-rays passing through the tips of this
white square.
• So, every time x-ray passes through the tips, that’s where we get a maximum projection on the detector.
16. Predict The Sinogram (3)
• When x-rays pass the direction horizontally, the detector would see the maximum
projection value at the center ➔ absorbed all of the x-rays.
• However, when we’re looking at any other angle (ex: vertically), the detector would
pink up values that pass through the black and white regions ➔ it’s going to be less
white ➔ it’s going to have a shade of gray.
• The regions correspond to “x” sign
side of the detector in passing X-rays.
➔ absorb x-rays.
• Gray ➔ indicating that x-rays have
passed through both black and white
regions.
x x
17. Predict The Sinogram (4)
• X-rays pass through the corners of the square (diagonally) ➔ it will give a
slightly higher profile value ➔ in sinogram, we will see sinusoidal pattern
because this object is off to the lower right quadrant.
• In sinogram, we see sign sort of oscillations due to the corners of the square.
18. Sinogram of
Head
Phantom
• Shepp-Logan head phantom: white ribbon ➔ the outside of the skull, black ➔
ventricles within the brain, gray ➔ slightly absorbs the tissue.
• Different shapes contribute differently to the overall sinogram.
• This model should look like in the sense that is the various levels of gray, black, and
white in a sort of a sinusoidal pattern that can be traced to one specific geometry
within the body.
19. Radon Transform
• All of the sinogram are graphical
representations of the radon transform.
• Rotation of (x,y) coordinate system to
(R,θ) where x cosθ + y sinθ = R for any
point on a line projection.
• That would give us where the point is
located in this (R,θ) coordinate system and
notice that it holds true for any point along
this x-ray.
20. Change of Coordinate Systems
• Now, we have multiple x-rays, in this case three, notice that all of
these points have same theta, but different are x and y values.
• All of these points can be described as the coordinate system g,
with subscript are representing each one of these x-rays and theta.
• Then, we change coordinate system from f(x,y) to coordinate
system g(R, θ).
• Coordinate system 1:
f(x,y) = fx,y
• Coordinate system 2:
g(R, θ) = gR,θ
• In CT imaging, we vary θ, take measurements for the same values of
R, and reconstruct back to (x,y) coordinate system.
• So, there’s a lot of math involved in CT imaging and it’s highly
computational work! ➔ that’s why called COMPUTED tomography.
21. Acquiring CT Data (1)
• Imagine that we are in the f coordinate system
f(x,y).
• If x-rays are passing through this way, CT images
measure the linear attenuation between the
source and detector ➔ it’s basically measure of
how rapidly x-rays are absorbed.
• We can sum the attenuation coefficients in this
manner to get a measure of the line profile that
pass through these three different pixels in the CT
image.
• There are different voxels that will eventually turn
into a pixel.
22. Acquiring CT Data (2)
• The line that passes through here can be
converted from the f coordinates system
to the g coordinate system.
• System of equations:
f11 + f12 = g11
f21 + f22 = g21
source detector
23. Acquiring CT Data (3)
• Now, if we’re rotating the coordinate
system, and we want to measure the
attenuation coefficient.
• The attenuation is sum of the attenuation
in each region of the body and each
voxel.
• System of equations:
f11 + f12 = g11
f21 + f22 = g21
f12 + f22 = g12
f11 + f21 = g22
source
detector
24. Acquiring CT Data (4)
• System of equations:
f11 + f12 = g11
f21 + f22 = g21
f12 + f22 = g12
f11 + f21 = g22
f11 + f12 + f22 = g13
f11 + f21 + f22 = g23
• 6 equations, 4 unknowns.
source
detector
Solve this system of equations
25. You’ve Acquired CT Data…
• The following values were measured
for each line projection:
• Given this data and solve your
solution to the system of equations,
what are the values of f11, f12, f21, f22
(i.e. the pixels in your CT image)?
26. Solution
• These are the values of the pixels
in your CT image :
• Do the values agree with the
projection line integrals?
g11 = 10, g12 = 13, g13 = 19,
g21 = 12, g22 = 9, g23 = 18
Remember, we don’t only have these 3 detection angle projections, but we have multiple projection angles!
27. Matrix Size
• A typical CT image uses more than 3 projections and 2 detectors.
• Matrix Reconstruction, also known as the Algebraic Reconstruction Techniques
(ART), is not commonly used in practice, because it is time consuming and
computationally intensive.
• So, that method is not used in the clinics today.
• Instead, a method known as backprojection could be used.
28. Backprojection
• Implemented by taking the line
profile and smearing it back
across a region.
• Then, we do that for each
projection at each different angle.
• This is what the sum of the
different smears look like when
they’re superimposed on one
another.
• We do this not just 3 views, but
many views!
• The results of image like the
original image, but we see some
blurring around the point in the
lower right quadrant.
29. Filtered Backprojection
• The measured data is first
filtered before it’s smeared
back across the region.
• Then, the linear
superposition of these three
different smears looks like
similar to the original point
image.
30. Image Formation Recapitulation
We take multiple projection at different angles ➔ form a sinogram ➔ the sinogram
can be reconstructed into an image using filtered backprojection ➔ we get CT image.
31. How Many Projections?
• An infinite number of
projection make our
original image ➔ But, we
can’t use an infinite
number of projections
because limited to the
space.
• How many detectors we
can actually fit?
32. Ideal Number of Projections
• Based on the application ➔ if we want to image a different region of the body, we
don’t necessarily need a lot of projections ➔ it depends on the type of resolution we
need.
• Trade-off between dose and image quality ➔ if we want to an infinite number of
projections, it means an infinite number of doses ➔ it’s harmful to the patient. If we want
to lower the doses to reduce the risk to the patient, it will make lowers the image quality.
• Measurements of image quality include:
❑ Noise
❑ Contrast: the brightness ratio between one region and another (e.g. bone and soft
tissue)
❑ Signal-to-noise ratio (SNR)
❑ Contrast-to-noise ratio (CNR)
❑ Resolution
34. Liver Cancer
• This is a picture of a liver.
• The patient has liver cancer
• The cancer look very smooth in the
picture.
35. Liver Metastases
• When a patient has metastatic liver
cancer, we see not just one lession on
the image ➔ multiple lesions or spots
within the liver.
• This is what happens when one liver
cancer spreads throughout the liver and
metastases.
36. Head CT – Basal Ganglia
• This is the head of an 86
years old man who has a
complication in the region
(arrow pointed).
• The complication looks
different before death
(antemortem) and after
death (post-mortem).
• There’s more attenuation in
the region of the head
(postmortem)
37. Aneurysm Coils
• Aneurysm ➔ little bubble in a blood vessel ➔
bubbles can rupture ➔ dangerous!
• Stop the aneurysm from rupturing without cutting
off blood circulation ➔ Aneurysm Coils ➔
Catheter inserted in leg to access the arteries in the
brain ➔ Coils are inserted in the aneurysm.
• A blood clot forms around the coils to prevent
rupturing ➔ Coils permanently remain in
aneurysm throughout the rest of patient’s life.
38. Streak Artifact Due to Aneurysm Coils
• The coils are made from metal ➔ metal
causes streak artifacts in CT images ➔
image is very distorted.
• Radiating white streaks due to metallic coil
used to prevent an aneurysm from
rupturing.
• In CT images, streak artifacts are common
around metal, bone, and other materials
that block x-rays.
39. Motion Artifact
• Patient moves when taking
CT image ➔ Shift between
one rotation and another
➔ the image will not be
reconstructed very
faithfully ➔ sometimes will
form line in CT image ➔
motion artifact.
40. Motion Artifact Correction
• Sometimes we would have
made another CT image if
patient moves ➔ increase
the radiation doses.
• So, patient must remain as
still as possible when
taking CT image!
• We can correct motion
artifact using Image
Registration (image
processing).
41. CT: Pros and Cons
Advantages
• Multi-planar images.
• High contrast resolution
(especially between bone and
soft tissue).
• Detailed anatomy, because it
shows image depth.
• Capable of whole-body
imaging.
Disadvantages
• Adverse effects of ionizing
radiation. The images are
created by making multiple
projections through the body
➔ each production requires
radiation doses.
• Noise artifacts, some of which
can not be corrected.
55. Other Modalities
1. Fluoroscopy
2. Diffusion Weighted Imaging (DWI)
3. Functional Magnetic Resonance Imaging (fMRI)
4. Single Photon Emission Computed Tomography (SPECT)
5. Coronary Computed Tomographic Angiography (CCTA)
6. Scintigraphy or Gamma scan
7. Elastography
8. Photoacoustic imaging
9. Functional near-infrared spectroscopy (fNIRS)
10. Magnetic particle imaging (MPI)
11. Infrared Thermography
Assignment 1:
- Bentuk kelompok 3 orang.
- Cari referensi dan pelajari terkait modalitas yang ditunjuk
- Buat laporan dan presentasikan minggu depan
- Konten : Konsep modalitas, cara kerja, proses rekonstruksi citra, contoh aplikasi, pros dan kons, video youtube.