Image Compression - JPEG

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Image Compression - JPEG
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Video Compression

• MPEG
• Audio compression
• Lossy / perceptually lossless / lossless
• 3 layers
• Models based on speech generation (throat), or
  ear characterisitics
• Image compression
• JPEG based
• Images take much more memory than voice
• An image is worth a thousand words
• Which thousand words?
• Video next week, can we extrapolate?

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Image Compression Basics

• Model driven
• Reduce data redundancy
• Neighboring values on a line scan in an image
• DPCM, predictive coding
• Human perception properties
• Human visual system eye/brain is more sensitive
  to some information as compared to others low
  frequencies vs high frequencies be
  careful..edges are often critical
• Enhancement approaches

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Entropy

• Entropy measurement of the uncertainty of the
  input. Higher the uncertainty the higher the
  entropy.
• Which has higher entropy noise or a 300Hx sine
  wave?
• Computation is histogram based
• p(i) probability of occurrence of a gray level
  in the image
• E - Si p(i) lg p(i)
• Identifies the minimum number of bits required to
  represent the image

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Compression Issues

• Progressive display
• Display partially decompressed images
• User begins to see parts of the image, does not
  have to wait for complete decompression
• Hierarchical encoding
• Encode images at multiple resolution levels.
• Display images at lower resolution level and then
  incrementally improve the quality
• Asymmetry
• Time for encoding
• Time for decoding

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Types of compression

• Lossless
• Huffman, LZW, Run length, DPCM?
• Typical compression 31
• Lossy
• Predictive
• Frequency based transform, subbands
• Spatial based filtering, non-linear
  quantization, vector quantization
• Hybrid

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JPEG is based on

• Huffman coding
• Optimal entropy encoding
• Run length encoding
• Used in G3, fax
• Discrete Cosine Transform
• Frequency based
• Apply perception rules in the frequency domain
• The fidelity and level of compression can be
  controlled 151 or even better

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Huffman encoding

• Assign fewer bits to symbols pixel values that
  occur more frequently
• Number of bits per symbol is non-uniform
• The code book has to be made available to the
  decoder, i.e. this file leads to increase in the
  file size.
• Results in optimal encoding
• Number of bits required is close to the entropy

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Run length Encoding

• Run length, size, amplitude
• RL 4 bits
• Size 4 bits
• Amplitude 10 bits
• Maximum compression if the run lengths are long
• G3 used for fax
• Usually use Huffman to encode the parameters

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Discrete Cosine Transform

• Real cousin of Fourier transform
• Complexity
• NN
• Fast DCT similar to FFT
• To reduce cost
• Divide image into 8 x 8 blocks
• Compute DCT of blocks
• Reduce the size of the object to be compressed

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Quantization

• The eye is more sensitive to the lower
  frequencies.
• Divide each frequency component by a constant
• Divide higher frequency components with a larger
  value
• Truncate, and this will reduce the non-zero
  values
• Four quantization matrices are available in JPEG

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Color

• RGB planes
• Transform RGB into YUV
• Y luminance
• U,V chrominance
• UV have lower spatial resolutions
• Down sampled to take advantage of lower resolution

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Overview of JPEG

• RGB YUV
• Down sample UV
• Original data is 8 bits per pixel, all positive
  0,255. Shift to -128, 127.
• Divide image into 8x8 blocks
• DCT on each block
• Use quantization table to quantize values in each
  block Reducing high freq content
• Use zig-zag scanning to order values in each
  block
• Organize data into bands DC, low f, mid f, high
  f
• Run length encoding
• Huffman encoding

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Reference

• G. K. Wallace, The JPEG Still Picture
  Compression Standard, Communications of the ACM,
  April 1991, vol 34, No. 4, pp 30 - 44

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