Scalable Geometric Flow Representation for Image Compression with Directional Lifting

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Scalable Geometric Flow Representation for Image
Compression with Directional Lifting

• Tao Xu
• Jad Naous

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Outline

• Background
• Goal
• Previous work
• Our work
• Results
• Conclusion

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Background and Goal

• DWT works horizontally and vertically gt Not
  efficient on other directions
• Solution Directional lifting to adapt directions
  to geometric flow.
• Side information Directions have to be signaled
  to the decoder.
• Project goals
• Explore better compression techniques
• Find a scalable representation of side
  information to get lower distortion at low
  bitrates.

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Previous Work and Improvements

• Directions losslessly encoded and sent using
  predictive coding.gt Improved coder
• Scalable methods for video motion vector
  compression exist.gt Adapted for geometric flows

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Methods Adapted for Geometric Flow

• SPIHT encoding of geometric flowsgt results not
  satisfactory
• Quality layer approach
• Choose coarser directions for lower bitrates, and
  enhance through quality layers.
• Use stages within a single layer corresponding to
  each level of the wavelet transform to provide
  more quality layers where the scalable bitstream
  can be cutoff

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Quality layers
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Quality Layer ordering

• Line by line (best)
• Column by column
• Zigzag

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Interpolation methods

• Hierarchical interpolation (upsample from lower
  stages)
• Cross-layer interpolation (map from coarser
  directions)

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Best layer organization

• Use brute force search
• Find the number of stages and the quality layer
  that achieves the maximum PSNR at each bitrate
  such that the the side information bitrate is
  nondecreasing as the quality improves
• the quality layers are nondecreasing
  (lambda is nonincreasing)
• the number of stages are nondecreasing
  in the same layer

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Best layer organization (cont.)
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Best layer organization (cont.)
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Best layer organization (cont.)
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Results
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Rate0.04 bpp optimal scalable
scheme non-scalable scheme optimal
scalable scheme non-scalable scheme
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Rate0.06 bppoptimal
scalable scheme non-scalable scheme
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Rate0.1
bppoptimal scalable scheme
non-scalable scheme
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SPIHT coding of the direction scheme, rate0.1 bpp
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Rate 0.6 bpp optimal scalable scheme
non-scalable scheme
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SPIHT coding of the direction scheme, rate0.6 bpp
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Conclusion

• Improved the predictor for predictive coding of
  geometric flow
• Found a scalable geometric flow representation
  that achieves significant improvement in both
  objective and subjective quality at low bitrates
• Performance at high bitrates very similar to the
  nonscalable representation.
• Due to the very small prediction errors, better
  compression techniques (instead of VLC) could
  still be found.