EBCOT in JPEG2000

1
EBCOT in JPEG2000

• Chi-Wen Lo
• January 7, 2005

2
Agenda

• Overview
• Embedded Block Coding
• Rate Distortion Optimization
• Conclusion

3
Overview

• What is Embedded Block Coding with Optimized
  Truncation (EBCOT) ?
• Highly scalable bit-stream
• Independent embedded blocks
• Post-compression rate-distortion (PCRD)
  optimization
• Layered bit-stream organization
• Input of EBCOT
• Subband samples generated using a wavelet
  transform, like EZW and SPIHT

4
High Scalable Compression

• Resolution Scalable
• Containing distinct subsets representing
  successive resolution levels
• SNR Scalable
• Containing distinct subsets successively
  augmenting the quality
• Advantage of scalable compression
• Taget bit rate or reconstruction SNR/resolution
  need not know at compression time
• Abstract Quality Layers

5
Independent Embedded Blocks

• Division of subbands into code-blocks with the
  same size
• Random Access
• Identify the region within each subband
• code-blocks which are required to correctly
  reconstruct the region of interest

6
Two-Tiered Coding Structure of EBCOT
7
Embedded Block Coding
8
Bit-Plane Coding

• Quantization
• Scalar quantizer (SQ)
• Embedded deadzone quantizers
• Bit-plane coding procedure
• Ensure a sufficiently fine embedding.

9
Conditional Coding of Bit-Planes

• Four coding primitives
• Zero coding (ZC)
• Run-length coding (RLC)
• Sign coding (SC)
• Magnitude refinement (MR)
• Three coding pass
• Significance propagation Pass
• Magnitude Refinement Pass
• Cleanup Pass

10
Scan Order
11
Zero Coding (ZC) - 9

• Markov Significance of sample depends only upon
  the values of its immediate 8 neighbors

12
Run-Length Coding (RLC) - 1

• Invoked in ZC when sample and its neighbors are
  all insignificant
• Four consecutive samples must all be
  insignificant
• Samples must have insignificant neighbors
• Samples must reside in the same blocks
• The horizontal index of the first sample must be
  even

13
Sign Coding - 5

• Used at most once when found significant in ZC

14
Magnitude Refinement - 3

• Code magnitude bit is already significant

15
Significance propagation Pass

• Pixel is insignificant, but has significant
  neighbor (ZC)
• RLC will never be satisfied in this pass
• SC is invoked after sample becomes significant

16
Magnitude Refinement Pass

• code magnitude bit which was already significant
  in the previous bit-lane

17
Cleanup Pass

• Samples has not already been coded
• Samples in this pass must be insignificant
• RLC occur in this pass
• Use RLC to identify the first if any samples
  becomes significant in bit-plane p

18
Rate Distortion Optimization
19
Rate Distortion Optimization

• Post-Compression Rate-Distortion (PCRD)
  Optimization
• Truncate each code-block bit-stream in an optimal
  way so as to minimize distortion subject to the
  bit-rate constraint.
• The rate-distortion algorithm is applied after
  all the subband samples have been compressed.

20
Rate Distortion Optimization

• Select ni truncated to Lini with distortion Dini
  for code-block Bi.
• Optimal selection of the truncation points, ni
  , so as to minimize overall distortion, D,
  subject to an overall length constraint, Lmax .
• D ? Dini
• Lmax ? L ? Lini

21
Rate Distortion Optimization

• ? ni? , which minimizes
• ? is optimal that D cannot be reduced without
  also increasing L and vice-versa.
• Optimization of ni? in for given ?

Initialization ni? 0 Loop For j 1,2,
?, Zi (Zi is the last
truncation point) Set ?L Lij ?
Li ni? and ?D Di ni? ? Dij
IF ?D/?L gt ?, THEN ni? j.
22
Feasible Truncation Point

• Set of Feasible Truncation Points, Pi , for
  code-block
• Distortion-rate slope of a truncation point
• Property of the slopes
• Convex Hull Interpretation

An enumeration of points in Pi, 0 hi0 lt hi1 lt ?
lt hiPi-1.
?i(hin) (Di hin-1 ? Di hin)/(Li hin ? Li
hin-1), ? n ? 1.
?i(hi0) gt ?i(hi1) gt ?i(hi2) gt ? gt ?i(hiPi-1).
(Strictly decreasing.)
23
Fractional Bit-Plane

• To result in largest reduction in distortion
  relative to increase in code length
• Pass 0 yield the longest code length to reduce
  distortion
• Pass 2 slope is expected to be smallest
• Pass 0 though pass 2 represent all information
  for bit-plane p

24
Quality Layer

• Interleave the coding passes from each code-block
• Truncation distortion of each code-block should
  degrade gracefully

25
Conclusion

• State-of-the-art Compression Performance
• Embedded Block Coding
• High Scalability
• Resolution scalability
• Distortion/SNR/quality/rate scalability
• Spatial scalability (Random access capability)
• Enabling
• Use of Post-Compression Rate-Distortion
  Optimization