Image Processing and Sampling

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Image Processing and Sampling

• Aaron Bloomfield
• CS 445 Introduction to Graphics
• Fall 2006

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Overview

• Image representation
• What is an image?
• Halftoning and dithering
• Trade spatial resolution for intensity resolution
• Reduce visual artifacts due to quantization

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What is an Image?

• An image is a 2D rectilinear array of pixels

Continuous image
Digital image
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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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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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Image Acquisition

• Pixels are samples from continuous function
• Photoreceptors in eye
• CCD cells in digital camera
• Rays in virtual camera

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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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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

Width x Height Depth Rate NTSC 640 x 480
8 30 Workstation 1280 x 1024 24 75 Film 3000 x
2000 12 24 Laser Printer 6600 x 5100 1 -
Typical Resolutions
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Sources of Error

• Intensity quantization
• Not enough intensity resolution
• Spatial aliasing
• Not enough spatial resolution
• Temporal aliasing
• Not enough temporal resolution

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Overview

• Image representation
• What is an image?
• Halftoning and dithering
• Reduce visual artifacts due to quantization

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Quantization

• Artifacts due to limited intensity resolution
• Frame buffers have limited number of bits per
  pixel
• Physical devices have limited dynamic range

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Uniform Quantization
P(x, y) trunc(I(x, y) 0.5)
I(x,y)
P(x,y) (2 bits per pixel)
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Uniform Quantization

• Images with decreasing bits per pixel
• 256 bpp 32 bpp 8 bpp 2 bpp

8 bits
4 bits
2 bits
1 bit
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Reducing Effects of Quantization

• Halftoning
• Classical halftoning
• Dithering
• Error diffusion dither
• Random dither
• Ordered dither

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Classical Halftoning

• Use dots of varying size to represent intensities
• Area of dots proportional to intensity in image

P(x,y)
I(x,y)
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Classical Halftoning
Newspaper image from North American Bridge
Championships Bulletin, Summer 2003
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Halftone patterns

• Use cluster of pixels to represent intensity
• Trade spatial resolution for intensity resolution

Figure 14.37 from HB
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Dithering

• Distribute errors among pixels
• Exploit spatial integration in our eye
• Display greater range of perceptible intensities
• Uniform quantization discards all errors
• i.e. all rounding errors
• Dithering is also used in audio, by the way

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Floyd-Steinberg dithering

• Any rounding errors are distributed to other
  pixels
• Specifically to the pixels below and to the right
• 7/16 of the error to the pixel to the right
• 3/16 of the error to the pixel to the lower left
• 5/16 of the error to the pixel below
• 1/16 of the error to the pixel to the lower right
• Assume the 1 in the middle gets rounded to 0

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Error Diffusion Dither

• Spread quantization error over neighbor pixels
• Error dispersed to pixels right and below

?
?
?
?
? ? ? ? 1.0
Figure 14.42 from HB
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Floyd-Steinberg dithering

• Floyd-Steinberg dithering is a specific error
  dithering algorithm

Uniform Quantization (1 bit)
Floyd-Steinberg Dither (1 bit)
Floyd-Steinberg Dither (1 bit) (pure BW)
Original (8 bits)
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Random Dither

• Randomize quantization errors
• Errors appear as noise

P(x, y) trunc(I(x, y) noise(x,y) 0.5)
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Random Dither
Uniform Quantization (1 bit)
Random Dither (1 bit)
Original (8 bits)
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Ordered Dither

• Pseudo-random quantization errors
• Matrix stores pattern of thresholds

i x mod n j y mod n e I(x,y) -
trunc(I(x,y)) if (e gt D(i,j)) P(x,y)
ceil(I(x, y)) else P(x,y) floor(I(x,y))
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Ordered Dither

• Bayers ordered dither matrices
• Reflections and rotations of these are used as
  well

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Ordered Dither
Uniform Quantization (1 bit)
4x4 Ordered Dither (1 bit)
Original (8 bits)
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Dither Comparison
Random Dither (1 bit)
Original (8 bits)
Ordered Dither (1 bit)
Floyd-Steinberg Dither (1 bit)
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Color dithering comparison

• Original image Web-safe palette, no
  dithering Web-safe palette, FS dithering

Optimized 256 color palette
Optimized 16 color palette Optimized
16 color palette FS dithering No
dithering FS dithering
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Summary

• Image representation
• A pixel is a sample, not a little square
• Images have limited resolution
• Halftoning and dithering
• Reduce visual artifacts due to quantization
• Distribute errors among pixels
• Exploit spatial integration in our eye
• Sampling and reconstruction
• Reduce visual artifacts due to aliasing
• Filter to avoid undersampling
• Blurring is better than aliasing