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![Page 1: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/1.jpg)
Medical Image AnalysisMedical Image AnalysisImage Formation
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
![Page 2: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/2.jpg)
Color representation◦RGB: red, green, blue◦ISH: intensity, saturation, hue
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
![Page 3: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/3.jpg)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
From www.wikipedia.org
![Page 4: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/4.jpg)
Image Coordinate SystemImage Coordinate SystemObject: Image:TranslationRotation
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
),,( f),,( zyxg
![Page 5: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/5.jpg)
Image Coordinate SystemImage Coordinate System
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
z
Image-Formation System h
Object Domain
Image Domain
x
y
Radiating Object f() Image g(x,y,z)
Figure 2.1. The object and image domain coordinates systems.
![Page 6: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/6.jpg)
Linear Systems and Impulse Linear Systems and Impulse ResponseResponse
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
}{}{}{ 2121 IbhIahbIaIh
![Page 7: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/7.jpg)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Reconstructed Cross-Sectional Image
Radiation Source
z
Image-Formation Systemh
Object Domain
Image Domain
Selected Cross-Section
x
yRadiating Object
Image
Figure 2.2. A schematic block diagram of a general 3-D image formation system requiring an external radiation source (such as light) for photographic imaging or x-ray for transmission imaging.
![Page 8: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/8.jpg)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
z
Reconstructed Cross-Sectional Image
Image-Formation Systemh
Object Domain
Image Domain
Selected Cross-Section
x
y
Radiating Object
Image
Figure 2.3. A schematic block diagram of an emission based image formation system commonly used for fluorescence or nuclear medicine imaging modalities.
![Page 9: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/9.jpg)
Pin-hole ImagingPin-hole Imaging
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Pin-hole
Object Plane Focal Plane Image Plane
f(x1,y1)
g(x2,y2)z1z2
x
z
y
Figure 2.4. A schematic diagram of a pin-hole imaging camera.
![Page 10: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/10.jpg)
Fourier TransformFourier TransformLinearityScalingTranslationConvolutionCross-correlationAuto-correlationParseval’s theoremSeparability
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
![Page 11: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/11.jpg)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Figure 2.5. (a) A vertical stripe image generated from a sinusoidal waveform of a period of 8 pixels and (b) the logarithmic magnitude image of its Fourier transform
![Page 12: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/12.jpg)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Figure 2.6. (a) A rotated stripe image and (b) the logarithmic magnitude image of its Fourier transform.
![Page 13: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/13.jpg)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Figure 2.7. (a) An image with a square region at the center and (b) the logarithmic magnitude image of its Fourier transform.
![Page 14: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/14.jpg)
Radon TransformRadon Transform
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
x
y
q
p
p
f(x,y)
P(p,)
Figure 2.8. Line integral projection P(p,q) of the two-dimensional Radon transform.
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Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Projection p1
Projection p2
Projection p3
Reconstruction Space
A
B
Figure 2.9. A schematic diagram for reconstructing images from projections. Three projections are back-projected to reconstruct objects A and B.
![Page 16: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/16.jpg)
SamplingSamplingNyquist rate
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Figure 2.10. (a) A 2-D distribution of Gaussian impulses in the spatial domain and (b) its representation in the Fourier domain.
![Page 17: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/17.jpg)
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
x
y
ymax
xmaxxmax
ymax
Fa(x,y)
(a)
Figure 2.11. (a) The Fouier spectrum of a bandlimited two-dimensional signal; (b) Sampling of the bandlimited signal with a sampling frequency higher than the Nyquist rate; (c). Undersampling of the bandlimited signal with a sampling frequency lower than the Nyquist rate.
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Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
(b)
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Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
(c)
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Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
Figure 2.12. (a) A vertical stripe image generated from a sinusoidal waveform of a period of 1.8 pixels, (b) the logarithmic magnitude image of its Fourier transform, (c) the central cross section of the logarithmic magnitude of the Fourier transform, along the horizontal direction, of the signal shown in Figure 2.5 (a), which is sampled satisfying the Nyquist criterion, and (d) the central cross section along the horizontal direction of the logarithmic magnitude of the Fourier transform of the aliasing pattern shown in Figure 2.12 (a).
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Over-sampled
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
x
Log |F(x, 0)|
![Page 22: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/22.jpg)
Aliasing
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
x
Log |F(x, 0)|
![Page 23: Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.](https://reader030.fdocuments.us/reader030/viewer/2022033100/56649cda5503460f949a4000/html5/thumbnails/23.jpg)
Discrete Fourier Discrete Fourier TransformTransform
Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.
1
0
1
0
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