Operational R-D optimal vertex-based shape coding using enhanced Bezier curves

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Operational R-D optimal vertex-based shape coding
using enhanced Bezier curves

• Ferdous Ahmed Sohel

Supervisors Professor Laurence S. Dooley Dr.
Gour C. Karmakar
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Presentation Outline

• Introduction
• ORD optimal shape coding Background
• Enhanced Bezier curves (EBC)
• Shape coding using EBC
• Results
• Conclusion

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Introduction
Shape Coding
Encoder
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Applications

• Communication Mobile multimedia communication,
  low bit rate coding.
• Storage and retrieval Digital library, indexing,
  digital archiving.
• Interactive editing Cartoons, digital films.

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Background 1

• Katsaggelos et al proposed
• Polygonal and
• B-spline based

Wmax is a constant
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Background 1
DAG
State diagram for quadratic B-splines (with 5
admissible control points).
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Background 1
Rate-distortion optimisation (quadratic curve)
Number of bits required to encode the control
point , given and .
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Background 2
To measure the distortion, they used -- The
shortest absolute distance or -- A
distortion band
Piecewise polygon
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Background 2
The admissible distortion can be

• Fixed (Dadm)
• Variable (depending on the image-gradient/
  shape-cornerity Tj for the j-th boundary
  point).

The admissible control point band should be of
variable width to utilise the variable adm. dist.
Mini-max width for polygonal case
Maximal width for quadratic B-spline case
Be submitted to IEEE Trans. on Image Proc.
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Background 1

• Katsaggelos et al. shown
• A higher degree curve based encoding is efficient
  in bit-rate sense.
• i.e. the quadratic B-spline is efficient over
  polygonal encoding.

The computational complexity depends on -
Degree of the curve employed. - Width of the
admissible control point band.
The higher these values are, the higher the
complexity is.
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Enhanced Bezier curve

• Enhanced Bezier curve
• Reduces the gap between the Bezier curve and the
  control polygon.

B-spline curves are piecewise Bezier curve.
EBC can be fitted well into the B-spline
replacing Bezier.
(ICASSP 05)
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Motivation
EBC

• Gives better approximation than Bezier so as
  than B-splines.
• Will improve the RD performance.
• Will have lower maximal width for admissible
  control point band.
• So, will be faster.
• Also maintain geometric continuity at the knots.

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EBC-based shape coding

• EBC is used instead of the B-splines.

EBC has the End-point interpolation property like
the Bezier.
To ensure the curve passes through the ends
The boundary end-points are duplicated.
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Results
Smaller Maximal Band width (Computationally
efficient)
Maximal band width (EBC)
Maximal band width (B-spline)
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Results
EBC
BS
Tmax2 Tmin1 pel
Polygon
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Results
Bit-requirements and mean-square distortion.
Tmax2, Tmin 1 Tmax3, Tmin 1 Tmax3, Tmin 2
Polygon 76, 0.82 62, 1.2 55, 1.80
B-spline 62, 0.50 46, 1.5 44, 1.70
EBC 59, 0.50 41, 0.9 36, 1.45
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Conclusion

• Provides better RD performance than B-splines.
• Has lower maximal width of admissible control
  point band.
• Computationally efficient.
• Measures the distortions accurately.

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• Thank you