Explorations in Image Partition Encoding

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Explorations in Image Partition Encoding

• Sameer Agarwal
• Department of Computer Science and Engineering
• University of California, San Diego

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Background

• Multiple Raster Content Specification
• Three layered image structure
• Aimed at documents with a distinct text layer.
• Layer specific compression algorithms for better
  compression
• DjVu from AtT is a working system which
  implements a scheme like this.

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Generalization to natural images

• Implement the MRC idea to natural scenes/ video.
• Use a robust image segmentation method (e.g.
  N-Cut) to break the image into pieces.
• Compress each segment separately.
• Many different ways of compressing the segments
  possible including, texture modelling and wavelet
  based compression.

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How do you reassemble an image from partitions ?

• Besides the individuals segments a image
  partition map needs to be stored for re-assembly
  of the image.
• How do you efficiently store the image partition
  map ?

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The shape coding problem

1. Shape descriptors like a fourier transform of the
   curve.
2. Chain-coding of the boundary.
3. Bitmap compression
4. Label each region with a small integer and
   compress the resulting low bitrate image.

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The Naïve solution

• Label each segment by its segment number.
• Problem
• The number of bits per pixel depends on the
  number of segments.
• (Press Enter for the smart solution)

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The four color theorem
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The smart solution

• The four color theorem allows you to encode an
  image partition with just 4 colors.
• A strict upper bound of 2 bpp.
• Problem
• How to four color ?
• How to find the most compressible 4-coloring ?

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Explorations in Four-coloring

• Polynomial time algorithms exist but are quite
  useless
• Alternate solutions
• Integer -gt Linear programming based solutions
• Heuristic based coloring
• Backtracking
• First two methods do not guarantee a 4 coloring.
• Backtracking is exponential.
• None of them solve the most-compressible
  4-coloring problem.

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Four-coloring

• Our attempts
• Greedy backtracking
• Greedy on color use, hence tries to minimize
  color-entropy
• Inefficient and does not get the best coloring,
  random does better sometimes.

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Attempts (contd.)

• Spectral coloring
• Approximate coloring method, based on using the
  top two eigenvectors of the laplacian.
• Gives approximate coloring, but makes mistakes.
  Probably these mistakes can be repaired.
• work still in progress..

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Attempts (contd.)

• Balkanization
• Coloring becomes difficult with increasing
  connectivity of the graph.
• Break segments with very high degree into pieces
  with lower degree.
• The size of the graph increases too fast for the
  backtracking based methods.
• The spectral methods do not show any difference.

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Acknowledgements

• Serge for all the hours.
• Pam Cosman and Yan Ye for their JBIG2 encoder.
• and the music of Nickelback for keeping me
  company.