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Medical Image Analysis Image Formation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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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.

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From www.wikipedia.org

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Image Coordinate System Object: Image: Translation Rotation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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Image 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.

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Linear Systems and Impulse Response Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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Reconstructed Cross-Sectional Image Radiation Source z Image-Formation System h Object Domain Image Domain Selected Cross-Section x y Radiating 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.

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Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. z Reconstructed Cross-Sectional Image Image-Formation System h 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.

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Pin-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(x 1,y 1 ) g(x 2,y 2 ) z1z1 z2z2 x z y Figure 2.4. A schematic diagram of a pin-hole imaging camera.

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Fourier Transform Linearity Scaling Translation Convolution Cross-correlation Auto-correlation Parseval’s theorem Separability Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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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

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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.

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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.

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Radon 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 p 1 Projection p 2 Projection p 3 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.

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Sampling Nyquist 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.

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Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. xx yy ymax xmax xmax ymax F a ( 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. xx Log |F( x, 0)|

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Aliasing Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. xx Log |F( x, 0)|

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Discrete Fourier Transform Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

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