Distortion Measurement Using Arc-Length-Parameterisation within Vertex-Based Shape Coding Framework (DMALP)

1
Distortion Measurement Using Arc-Length-Parameteri
sation within Vertex-Based Shape Coding Framework
(DMALP)

• Authors
• Dr. Ferdous Sohel
• Prof. Mohammed Bennamoun
• Speaker
• Prof. M. Kaykobad

2
Presentation outline

• Shape coding
• Geometric distortion
• Distortion metrics
• Distortion measurement techniques
• Proposed DMALP
• Experimental results
• Summary

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Shape coding
Object Segmentation
Grey Scale Foreground Object
Natural Image/ Video Frame
Grey to binary
Object Shape/
Binary alpha-plane of the object
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Shape coding (cont.)
Bit-map based coding (encodes all pixels in a
shape) e.g., Context-based Arithmetic Encoder
(CAE) Group 4 (G4)
Modified Modified Read (MMR)
Contour based coding (only encodes the outline of
a shape) e.g.,
Polygon-based coding

Polynomial-based coding
Base-line based coding
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Contour-based Shape Coding
Polynomial-based coding
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Distortion metrics

• Distortion and the metrics have an important role
  in these algorithms
• Some metrics
• Peak signal to noise ratio (PSNR)
• Dn metric

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Distortion metrics
Problem with Dn Butterfly shape with the same
Dn with the antenna lost and with the antenna
preserved.
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Distortion metrics

• Lp norms
• peak distortion ( p8 Dmax), average distortion
  (p1), Mean-square (p2 Dms)

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Distortion measurement techniques

• The shortest absolute distance (SAD)
• at an arbitrary contour point bt with respect to
  an approximating polygon edge with endpoints
  sk-1 and sk is given by

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SAD
segments GK, IM and HJ correspond to the
respective SAD of line EF from contour points G,
I and H
An arbitrary shaped object and (b) approximated
contour (solid line) from the encoded data by the
basic vertex-based ORD optimal shape coding
framework using SAD with Dmax 1 pixel.
Computational complexity Polygon O(N) splines
O(N2)
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Distortion measurement techniques

• Distortion band/ tolerance band
• A band of width equal to the admissible
  distortion (Dmax) is drawn around the original
  contour, so it is then only required to detect
  whether either a candidate approximating
  polygon-edge or BS curve resides completely
  inside the band.

Distortion measurement failed for 2 pixel,
tolerance band.
Computational complexity both polygon and
splines O(N2)
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Distortion measurement techniques

• Accurate distortion measurement for shape coding
  (ADMSC)

Solves the inaccuracy problem of SAD and
distortion band.
Computational complexity Polygon O(N) splines
O(N2)
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Distortion measurement techniques

• All these techniques require
• Fast distortion measurement technique using
  chord-length-parameterisation (DMCLP)
• Takes O(N) for splines but uses a relaxed
  measurement.

Computational complexity of O(N2) for
splines. Splines are efficient in a bit-rate
sense.
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Distortion measurement techniques
Does not consider the orientation of the contour
points. Some may be horizontal, some are vertical
while the others may be diagonal. So the
parameterisation in DMCLP is not efficient.
The control point positions only play the role in
spine point concentration and hence the amount
of relaxation in distortion calculation.
We propose an arc-length parameterisation so
unit speed between spline points which is
consistent with the contour points so a better
distortion measurement.
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Distortion Measurement Using Arc-Length-Parameteri
sation within Vertex-Based Shape Coding Framework
(DMALP)

• Perform the arc-length parameterisation
• Use the parameters in spline point generation
• Calculate the distortion

It is computationally efficient and as well as
accurate.
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Results

• Table 1 Test sequence specifications.
• Video sequence Format Spatial resolution
  (pixels) Number of frames
• MissAmerica.qcif QCIF 176, 144 100
• Akiyo.qcif QCIF 176, 144 300
• Bream.qcif QCIF 176, 144 300
• Kids.sif SIF 352, 240 100
• Stefan.sif SIF 352, 240 450
• Kids.sdtv SDTV 720, 486 300
• Stefan.sdtv SDTV 720, 480 300

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Results

• Table 2 Average bit-rate (bits per frame)
  requirements (with the obtained distortion in
  parenthesis whenever it is different from the
  admissible peak) for the various test sequences
  with Dmax2 and Dmin1 pixels using various
  combinations of polygon-based algorithms.
• Algorithms? SAD TB ADMSC DMCLP DMALP
• Video sequence? Bit-rate Bit-rate Bit-rate Bit-ra
  te Bit-rate
• MissAmerica.qcif 343 (3.0) 338 (3.0) 348 355 350
• Akiyo.qcif 312 (2.8) 310 (3.0) 313 320 314
• Bream.qcif 421 (3.0) 415 (3.0) 421 430 422
• Kids.sif 1592 (4.0) 1593 (4.0) 1593 1600 1595
• Stefan.sif 580 (4.0) 582 (4.0) 585 589 587
• Kids.sdtv 4500 (5.0) 4499 (5.0) 4507 4512 4510
• Stefan.sdtv 1080 (5.0) 1080 (5.0) 1085 1092 1090 
  

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Results

• Table 3 Computational time (seconds) required
  for the Neck region of the 31th frame of the
  MissAmerica.qcif by different ORD optimal shape
  coding algorithms for various AD pairs ( Dmax,
  Dmin in pixels) (distortion values produced using
  SAD/TB also shown in parentheses).
• Admissible ? Dmax 1 Dmax2 Dmax2 Dmax3 Dmax
  3
• distortion Dmin 1 Dmin1 Dmin2
  Dmin1 Dmin2
• Algorithms ? Time Time Time Time Time
• PolygonSAD 1.59 (1.42) 1.80 (2.24) 1.90
  (2.23) 2.0 2.0
• PolygonTB 4.26 (2.24) 6.03(2.24) 7.73
  (4.0) 11.35 (5.0) 12.66 (5.0)
• PolygonADMSC 1.63 1.89 2.01 2.15 2.25
• PolygonDMCLP 1.61 1.83 1.92 1.97 2.02
• PolygonDMALP 1.62 1.83 1.93 1.98 2.03
• B-splineSAD 120 (2.0) 550 (2.45) 560 (5.65) 565
  (7.0) 570 (8.0)
• B-splineTB 90.60 (2.0) 510.50 (3.6) 545.50
  (2.8) 620.30 (6.0) 680.40 (6.0)
• B-splineADMSC 554.20 575.00 582.10 587.80 591.60
• B-splineDMCLP 270.20 290.30 297.00 312.50 314.30
• B-splineDMALP 271.05 291.20 297.50 313.00 315.20

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Results
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Results
Figure 4 Time-distortion performance comparison.
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Summary

• This paper has presented a novel distortion
  measurement technique based on arc-length-paramete
  risation (DMALP).
• This can be seamlessly embedded into the
  classical vertex-based rate-distortion optimal
  shape coding framework to improve the RD
  performance without increasing the computational
  time complexity.
• DMALP always maintain the admissible distortion.
• Experimental results have shown that among the
  existing distortion measurement techniques DMALP
  is the best next to DMCLP in terms of
  computational time requirement.
• It has outperformed DMCLP in terms of RD with a
  much larger margin while it is comparable with
  the others.
• Orthogonal least square fitting would be a next
  step forward.

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References

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• 6 F. A. Sohel, G. C. Karmakar, and L. S.
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Contacts

• Dr. Sohel Ferdous.Sohel_at_csse.uwa.edu.au
• Prof. M Bennamoun m.bennamoun_at_csse.uwa.edu.au