domain Modeling for Rate Estimation

1
?-domain Modeling for Rate Estimation

• Carri Chan and Yuki Konda
• EE398 Project Presentation
• 3/14/06

2
Outline

• ?-domain Model
• Overview of Model
• Our Estimation Results
• Observations
• Rate Control
• Transmission Model
• Optimization
• Results
• Conclusion

3
Explanation of ?-domain model
Quantized matrix
Original matrix
Transformed matrix

• ? of zero coefficients
• Different quantization levels correspond to
  different ?s

Zhihai He, Sanjit Mitra, "A Unified
Rate-Distortion Analysis Framework for Transform
Coding," IEEE Trans. on Circuits and Systems for
Video Technology, vol. 11, no. 12, pp. 1221-1236,
December 2001.
4
Using ? values to calculate RD

• Relationship between transform coefficients and ?
  very similar for different images
• Linear model to approximate R(?) ?(1- ?)
• R hits 0 at ? 1.
• Calculate ? by linear regression of observed
  behavior in ? domain
• estimate D based on transform coefficients to
  obtain RD curve

q domain
? domain
5
Our RD results for SPIHT codec

• Dots indicate estimated RD
• Solid line indicates empirical RD

6
Benefits and limitations of ?-domain model

• Simple allows for accurate RD model based on
  easy to calculate image/frame statistics
• Fast encoding at many rates is very time
  consuming
• Model improves if training set has similar
  statistics to the actual images to estimate
• Best estimates at low rates high ?

7
Variable Bit Rate Channel

• Lagrangian optimization gives best performance
• The buffer constraint may not make this policy
  possible
• Lets optimize given the buffer constraint and RD
  estimation of each frame

8
Dynamic Programming Optimization (1) State

• i channel state Discrete Markov Chain,
  transition probability qij
• Rc(i) channel rate given channel state
• b amount of bits in the buffer
• T total amount of bits availablenecessary to
  maintain average bit constraint

9
Dynamic Programming Optimization

• minimum Cost-to-Go
• Then
• Terminal Costs
• Based on Training Data

Future cost
Immediate cost
10
Use Estimation!
Identical Expected Cost-to-Go from n1
Estimated Distortion using ?-domain modeling
11
Frame Estimation
Blue dots Estimated (R,D) Red line Empirical
(R,D)
12
Results
13
Summary Results

• We get much better performance than no-control
• For large buffer sizes we approach Lagrangian
  optimal
• For estimation to help more, we need video frames
  that vary more

14
Conclusion

• ?-domain model allows fast/effective
  Rate-Distortion Estimation
• We can use this estimate to perform
  fast/effective Rate Control

15
Thank you!
16
Calculation of ?(reference)

• Qnz pseudo bit rate to describe non-zero
  coefficients
• Qnz (1/M) ? S(x) S(x) floor(log2x) 2
• M coefficients in matrix, x is value of
  coefficient
• Qz pseudo bit rate to describe zero
  coefficients
• Qz Ai? Bi
• ? Qnz(qo)/(1- ?(qo))
• A and B are obtained from linear regression

17
Calculation of ? contd (reference)

• R (?i) A(?i) Qnz(?i) B(?i) Qz(?i) C(?i)
  
• A 1.1018 0.8825 0.5780 0.6078 1.0325
  0.4176
• B 1.2431 1.0448 0.9718 1.2732 1.2802
  0.6390
• C 0.0503 0.0469 0.1398 0.0111 -0.1167
  4.9123e-005
• ? 0.7207 0.8047 0.8957 0.9550 0.9791
  0.9985
• ? (? ?i ? R(?i) - n ? ?iR(?i) ) /
• (n ? ?i 2 (? ?i )2)
• n number of estimate points (6 in above
  example)

18
CBR Channel

• We also looked at a Constant Bit Rate Channel
• No room for improvement over Lagrangian Optimal!

19
Using Empirical Data to Calculate PSNR

• Interpolated Values and Actual Values are very
  close