1. Image Processing
고려대학교 컴퓨터 그래픽스 연구실
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2. Overview Image Representation Halftoning and Dithering
What is an image?
Halftoning and Dithering
Trade spatial resolution for intensity resolution
Reduce visual artifacts due to quantization
Sampling and Reconstruction
Key steps in image processing
Avoid visual artifacts due to aliasing
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3. What is an Image? An image is a 2D rectilinear array of pixels
Continuous image
Digital image
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4. What is an Image? An image is a 2D rectilinear array of pixels
Continuous image
Digital image
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5. A pixel is a sample, not a little square!!
What is an Image?
An image is a 2D rectilinear array of pixels
Continuous image
Digital image
A pixel is a sample, not a little square!!
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6. Image Acquisition Pixels are samples from continuous function
Photoreceptors in eye
CCD cells in digital camera
Rays in virtual camera
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7. Image Display Re-create continuous function from samples
Example: cathode ray tube
Image is reconstructed by displaying pixels with finite area (Gaussian)
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8. Image Resolution Intensity resolution Spatial resolution
Each pixel has only “Depth” bits for colors/intensities
Spatial resolution
Image has only “Width” x “Height” pixels
Temporal resolution
Monitor refreshes images at only “Rate” Hz
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9. Sources of Error Intensity quantization Spatial aliasing
Not enough intensity resolution
Spatial aliasing
Not enough spatial resolution
Temporal aliasing
Not enough temporal resolution
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10. Overview Image Representation Halftoning and Dithering
What is an image?
Halftoning and Dithering
Trade spatial resolution for intensity resolution
Reduce visual artifacts due to quantization
Sampling and Reconstruction
Key steps in image processing
Avoid visual artifacts due to aliasing
cgvr.korea.ac.kr

11. Quantization Artifact due to limited intensity resolution
Frame buffers have limited number of bits per pixel
Physical devices have limited dynamic range
255
150 75
255
150 75
255
150 75
Blue channel
Green channel
Red channel
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12. Uniform Quantization
I(x, y)
P(x, y)
2 bits per pixel
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13. Uniform Quantization Image with decreasing bits per pixel: 8 bits
Notice contouring
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14. Reducing Effects of Quantization
Halftoning
Classical halftoning
Dithering
Random dither
Ordered dither
Error diffusion dither
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15. Classical Halftoning
Use dots of varying size to representation intensities
Area of dots proportional to intensity in image
I(x, y)
P(x, y)
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16. Classical Halftoning Newspaper image From New York Times 9/21/99
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17. Halftone Patterns Use cluster of pixels to represent intensity
Trade spatial resolution for intensity resolution
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18. Halftone Patterns How many intensities in a n x n cluster?
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19. Dithering Distribute errors among pixels
Exploit spatial integration in our eye
Display greater range of perceptible intensities
Original
(8 bits)
Uniform
Quantization
(1 bit)
Floyd-Steinberg
Dither
(1 bit)
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20. Random Dither Randomize quantization errors Errors appear as noise
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21. Random Dither Original (8 bits) Uniform Quantization (1 bit) Random
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22. Ordered Dither Pseudo-random quantization errors
Matrix stores pattern of thresholds
j = x mod n
i = y mod n
e = I(x, y) – trunc(I(x, y))
if( e > D(i, j) )
P(x, y) = ceil(I(x, y))
else
P(x, y) = floor(I(x, y))
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23. Ordered Dither Original (8 bits) Uniform Quantization (1 bit) Ordered
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24. Error Diffusion Dither
Spread quantization error over neighbor pixels
Error dispersed to pixels right and below α β δ γ
α + β + γ + δ = 1.0
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25. Error Diffusion Dither
Original
(8 bits)
Random
Dither
(1 bit)
Ordered
Dither
(1 bit)
Floyd-Steinberg
Dither
(1 bit)
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26. Overview Image Representation Halftoning and Dithering
What is an image?
Halftoning and Dithering
Trade spatial resolution for intensity resolution
Reduce visual artifacts due to quantization
Sampling and Reconstruction
Key steps in image processing
Avoid visual artifacts due to aliasing
cgvr.korea.ac.kr

27. Sampling and Reconstruction
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28. Sampling and Reconstruction
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29. Aliasing In general: Specifically, in graphics:
Artifacts due to under-sampling or poor reconstruction
Specifically, in graphics:
Spatial aliasing
Temporal aliasing
Under-sampling
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30. Spatial Aliasing Artifacts due to limited spatial resolution
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31. Spatial Aliasing Artifacts due to limited spatial resolution “Jaggies”
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32. Temporal Aliasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
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33. Temporal Aliasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
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34. Temporal Aliasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
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35. Temporal Aliasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
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36. Must consider sampling theory!
Antialiasing
Sample at higher rate
Not always possible
Doesn’t always solve problem
Pre-filter to form bandlimited signal
Form bandlimited function (low-pass filter)
Trades aliasing for blurring
Must consider sampling theory!
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37. Sampling Theory
How many samples are required to represent a given signal without loss of information?
What signals can be reconstructed without loss for a given sampling rate?
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38. Sampling Theorem
A signal can be reconstructed from its samples, if the original signal has no frequencies above ½ the sampling frequency – Shannon
The minimum sampling rate for bandlimited function is called “Nyquist rate”
A signal is bandlimited if its highest frequency is bounded.
The frequency is called the bandwidth.
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39. Image Processing Quantization Filtering Warping Pixel operations
Uniform quantization
Random dither
Ordered dither
Floyd-Steinberg dither
Pixel operations
Add random noise
Add luminance
Add contrast
Add saturation
Filtering
Blur
Detect edge
Warping
Scale
Rotate
Warps
Combining
Morphs
Composite
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