graphics graphics lab @ korea university cgvr.korea.ac.kr image processing 고려대학교 컴퓨터...
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![Page 1: Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr Image Processing 고려대학교 컴퓨터 그래픽스 연구실](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649de55503460f94addae8/html5/thumbnails/1.jpg)
Graphics
Graphics Lab @ Korea University
Image Processing
고려대학교 컴퓨터 그래픽스 연구실
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CGVR
Graphics Lab @ Korea University
Overview
Image Representation 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
![Page 3: Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr Image Processing 고려대학교 컴퓨터 그래픽스 연구실](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649de55503460f94addae8/html5/thumbnails/3.jpg)
CGVR
Graphics Lab @ Korea University
What is an Image?
An image is a 2D rectilinear array of pixels
Continuous image Digital image
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CGVR
Graphics Lab @ Korea University
What is an Image?
An image is a 2D rectilinear array of pixels
Continuous image Digital image
![Page 5: Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr Image Processing 고려대학교 컴퓨터 그래픽스 연구실](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649de55503460f94addae8/html5/thumbnails/5.jpg)
CGVR
Graphics Lab @ Korea University
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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CGVR
Graphics Lab @ Korea University
Image Acquisition
Pixels are samples from continuous function Photoreceptors in eye CCD cells in digital camera Rays in virtual camera
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CGVR
Graphics Lab @ Korea University
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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CGVR
Graphics Lab @ Korea University
Image Resolution
Intensity 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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CGVR
Graphics Lab @ Korea University
Sources of Error
Intensity quantization Not enough intensity resolution
Spatial aliasing Not enough spatial resolution
Temporal aliasing Not enough temporal resolution
yx
yxPyxIE,
22 ,,
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CGVR
Graphics Lab @ Korea University
Overview
Image Representation 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
![Page 11: Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr Image Processing 고려대학교 컴퓨터 그래픽스 연구실](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649de55503460f94addae8/html5/thumbnails/11.jpg)
CGVR
Graphics Lab @ Korea University
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 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
255 150 75 0
Blue channel
Green channel
Red channel
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CGVR
Graphics Lab @ Korea University
Uniform Quantization
5.0,trunc, yxIyxP
I(x, y)
P(x, y)2 bits per pixel
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CGVR
Graphics Lab @ Korea University
Uniform Quantization
Image with decreasing bits per pixel:
8 bits 4 bits 2 bits 1 bit
Notice contouring
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CGVR
Graphics Lab @ Korea University
Reducing Effects of Quantization
Halftoning Classical halftoning
Dithering Random dither Ordered dither Error diffusion dither
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CGVR
Graphics Lab @ Korea University
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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CGVR
Graphics Lab @ Korea University
Classical Halftoning
Newspaper image
From New York Times 9/21/99
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CGVR
Graphics Lab @ Korea University
Halftone Patterns
Use cluster of pixels to represent intensity Trade spatial resolution for intensity resolution
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CGVR
Graphics Lab @ Korea University
Halftone Patterns
How many intensities in a n x n cluster?
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CGVR
Graphics Lab @ Korea University
Dithering
Distribute errors among pixels Exploit spatial integration in our eye Display greater range of perceptible intensities
Original(8 bits)
UniformQuantization
(1 bit)
Floyd-SteinbergDither(1 bit)
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CGVR
Graphics Lab @ Korea University
Random Dither
Randomize quantization errors Errors appear as noise
5.0,noise,trunc, yxyxIyxP
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CGVR
Graphics Lab @ Korea University
Random Dither
Original(8 bits)
UniformQuantization
(1 bit)
RandomDither(1 bit)
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CGVR
Graphics Lab @ Korea University
Ordered Dither
Pseudo-random quantization errors Matrix stores pattern of thresholds
20
132D
j = x mod ni = y mod ne = 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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CGVR
Graphics Lab @ Korea University
Ordered Dither
Original(8 bits)
UniformQuantization
(1 bit)
OrderedDither(1 bit)
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CGVR
Graphics Lab @ Korea University
Error Diffusion Dither
Spread quantization error over neighbor pixels Error dispersed to pixels right and below
α
α + β + γ + δ = 1.0
δγ
β
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CGVR
Graphics Lab @ Korea University
Error Diffusion Dither
Original(8 bits)
OrderedDither(1 bit)
RandomDither(1 bit)
Floyd-SteinbergDither(1 bit)
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CGVR
Graphics Lab @ Korea University
Overview
Image Representation 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
![Page 27: Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr Image Processing 고려대학교 컴퓨터 그래픽스 연구실](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649de55503460f94addae8/html5/thumbnails/27.jpg)
CGVR
Graphics Lab @ Korea University
Sampling and Reconstruction
Sampling
Reconstruction
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CGVR
Graphics Lab @ Korea University
Sampling and Reconstruction
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CGVR
Graphics Lab @ Korea University
Aliasing
In general: Artifacts due to under-sampling or poor
reconstruction
Specifically, in graphics: Spatial aliasing Temporal aliasing
Under-sampling
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CGVR
Graphics Lab @ Korea University
Spatial Aliasing
Artifacts due to limited spatial resolution
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CGVR
Graphics Lab @ Korea University
Spatial Aliasing
Artifacts due to limited spatial resolution
“Jaggies”
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CGVR
Graphics Lab @ Korea University
Temporal Aliasing
Artifacts due to Limited Temporal Resolution Strobing Flickering
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CGVR
Graphics Lab @ Korea University
Temporal Aliasing
Artifacts due to Limited Temporal Resolution Strobing Flickering
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CGVR
Graphics Lab @ Korea University
Temporal Aliasing
Artifacts due to Limited Temporal Resolution Strobing Flickering
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CGVR
Graphics Lab @ Korea University
Temporal Aliasing
Artifacts due to Limited Temporal Resolution Strobing Flickering
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CGVR
Graphics Lab @ Korea University
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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CGVR
Graphics Lab @ Korea University
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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CGVR
Graphics Lab @ Korea University
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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CGVR
Graphics Lab @ Korea University
Image Processing
Quantization 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