Still Image Coding

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Still Image Coding

• Scalar quantization (SQ).
• Vector quantization (VQ).
• DCT Compression
• JPEG.
• Wavelet Compression
• SPIHT.
• GTW.
• EBCOT.
• JPEG2000.

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Why Lossy?

• Images are meant to be viewed by the human eye
  (usually).
• The eye is very good at interpolation, that is,
  the eye can tolerate some distortion. So lossy
  compression is not necessarily bad. The eye has
  more acuity for luminance (gray scale) than
  chrominance (color).
• Gray scale (rods) is more important than color
  (cones).
• Compression is usually done in the YUV color
  coordinates, Y for luminance and U,V for color.
• U and V should be compressed more than Y.
• This is why we will concentrate on compressing
  gray scale (8 bits per pixel) images.

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Example Color TV

• Done in YIQ space
• Y is luminance
• I and Q are chrominance
• Y 0.3R 0.59G 0.11B for white light
• R Y 0.7R 0.59G 0.11B
• G Y -0.3R 0.41G 0.11B (redundant)
• B Y -0.3R 0.59G 0.89B

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Color TV
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Distortion

• Lossy compression
• Measure of distortion is commonly mean squared
  error (MSE). Assume x has n real components
  (pixels).

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Scalar Quantization
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Uniform Quantization Example
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Uniform Quantization Example
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Non-Uniform Quantization
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JPEG Standards

• JPEG - Joint Photographic Experts Group.
• Current image compression standard.
• Uses discrete cosine transform, scalar
  quantization, and Huffman coding.
• JPEG 2000
• uses wavelet compression.

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Color Space in JPEG

• Operates on YCbCr color space, so must convert
  from RBG

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Principle of Transform Coding
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The DCT

• The DCT of a sequence, f(n), for 0 lt n lt N, is
• Its inverse for 0 lt n lt N, is

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The DCT

• For an image, need 2-D DCT
• Accomplish by doing it along rows, then columns
• In practice, do along rows, do corner turn, then
  do along rows again.

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Methodology

• In practice, DCT applied to blocks of image
  pixels.
• Typically 8x8 or 16x16.
• Block coefficients then quantized and coded
  separately.
• Allows for variable quantization to exploit
  variation in frequency content across image.
• Image contains regions with different frequency
  properties.
• We dont know the regions, hence use simple
  blocks.
• Better than using complete image.

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DCT Block Diagram
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DCT Example

• 8x8 image block

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DCT Example

• 8x8 DCT coefficients

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Step 2 Thresholding Quantization

• DCT coefficients in each block are thresholded.
• Only those above threshold retained.
• Remaining coefficients are quantised.
• Quantization varied with frequency.
• High frequencies not so important - coarser
  quantization.

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Quantization Matrix

• Thresholding and quantization achieved by using
  quantization matrix.
• Each coefficient divided by QM element and then
  rounded
• Elements T(k l) are integers.
• Represent quantization step size.

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Quantization Example
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Encoding

• zig-zag scan coefficients, starting at (0 0).
• run length encode, forming symbols (run level)
• entropy code symbols, eg Huffman
• Motivation - small magnitudes at higher freqs -
  greater chance of zero runs with zig-zag
  scanning.

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The JPEG Standard

• Joint Photographic Experts Group.
• Describes family of compression techniques for
  continuous tone (mono or color) still images.
• Allows lossy and lossless coding.
• Employs block based DCT coding strategy.
• Four different modes of operation
• sequential (baseline) mode
• progressive DCT mode
• lossless mode
• hierarchical mode

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Sequential (Baseline) JPEG

• Standard DCT block based coding scheme with
  blocks considered in raster scan fashion
  (sequential).
• Block based DCT 8x8 blocks, with pre - grey
  level shift
• (remove average reduce redundancy).
• Quantization
• thresholding and quantization using block
  dependent QMs.
• Entropy coding (codeword assignment)
• AC coefficients zig-zag scan RLE Huffman
  symbol encoding