February 2000 1
School of Computing ScienceSchool of Computing ScienceSimon Fraser University, CanadaSimon Fraser University, Canada
Rate-Distortion Optimized Streaming of Fine-Grained Scalable Video Sequences
Mohamed Hefeeda & ChengHsin Hsu
2 February 2007
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MotivationsMotivations
Multimedia streaming over the Internet is becoming very popular- More multimedia content is continually created
- Users have higher network bandwidth and more powerful computers
Users request more multimedia content
And they look for the best quality that their resources can support
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Motivations (cont’d)Motivations (cont’d)
Users have quite heterogeneous resources (bandwidth)- Dialup, DSL, cable, wireless, …, high-speed LANs
To accommodate heterogeneity scalable video coding:
Layered coded stream- Few accumulative layers
- Partial layers are not decodable
Fine-Grained Scalable (FGS) coded stream- Stream can be truncated at bit level
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Motivations (cont’d)Motivations (cont’d)
Goal: Optimize quality for heterogeneous receivers
In general setting- FGS-coded streams
- Multiple senders with heterogeneous bandwidth and store different portions of the stream
Why multiple senders?- Required in P2P streaming:
• Limited peer capacity and Peer unreliability
- Desired in distributed streaming environment:• Disjoint network path Better streaming quality
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Our Optimization ProblemOur Optimization Problem
Assign to each sender a rate and bit range to transmit such that the best quality is achieved at the receiver.
Consider a simple example to illustrate the importance of this problem
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Example: Different Streaming SchemesExample: Different Streaming Schemes
Non-scalable Layered
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Example: Different Streaming SchemesExample: Different Streaming Schemes
FGS Scalable Optimal FGS Scalable
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Problem FormulationProblem Formulation
First: single-frame case- Optimize quality for individual frames
Then: multiple-frame case- Optimize quality for a block of frames
- More room for optimization
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Input ParametersInput Parameters
T : fixed frame period
n : number of senders
bi : outgoing bandwidth of sender i
bI : incoming bandwidth of receiver
si : length of (contiguous) bits held by sender i
Assume s1 <= s2 <= …… <= sn
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Allocation: A = {(Δi , ri) | i=1, 2, ……, n}
- Δi : number of bits assigned to i
- ri : streaming rate assigned to i
Specifies:
- Sender 1 sends range [0, Δ1 -1] at rate r1
- Sender 2 sends range [Δ1 , Δ1+Δ2 -1] at rate r2
- …
- Sender i sends range at rate ri
OutputsOutputs
]1,[1
1
1
i
tt
i
tt
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Integer Programming ProblemInteger Programming Problem
Minimize distortion
Subject to:
- on-time delivery
- assigned range is available
- assigned rate is feasible
- Aggregate rate not exceeds receiver’s incoming BW
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How do we Compute Distortion?How do we Compute Distortion?
Using Rate-Distortion (R-D) models- Map bit rates to perceived quality
- Optimize quality rather than number of bits
Approaches to construct R-D models- Empirical Models: Many empirical samples expensive
- Analytic Models: Quality is a non-linear function of bit rate, e.g., log model [Dai 06] and GGF model [Sun 05]
- Semi-analytic Models: A few carefully chosen samples, then interpolate, e.g., piecewise linear R-D model [Zhang 03]
Detailed analysis of R-D models in [Hsu 06]
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Within each bitplane, approximate R-D function by a line segment
Line segments of different bitplanes have different slopes
The Linear R-D ModelThe Linear R-D Model
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Visual Validation of Linear R-D ModelVisual Validation of Linear R-D Model
Mother & Daughter, frame 110
Foreman, frame 100
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Rigorous Validation of Linear R-D ModelRigorous Validation of Linear R-D Model
Average error is less than 2% in most cases
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Let yi be number of bits transmitted from bitplane i
Distortion is:
- d : base layer only distortion
- gi : slope of bitplane i
- z : total number of bitplanes
Using the Linear R-D ModelUsing the Linear R-D Model
z
hhh ygd
1
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Integer Linear Programming (ILP) ProblemInteger Linear Programming (ILP) Problem
Linear objective function
Additional constraints
- number of bits transmitted from bit plane h does not exceed its size lh
- bits assigned to senders are divided among bitplanes
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Solution of ILP is a Valid FGS StreamSolution of ILP is a Valid FGS Stream
Lemma 1: - An optimal solution for the integer linear program produces a
contiguous FGS-encoded bit stream with no bit gaps
Proof sketch- minimizing
- Since g1 < g2 < …… <gn<0 (line segment slopes),
- the ILP will never assign bits to yi+1 if yi is not full
z
hhh ygd
1
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Solving ILP problem is expensive
Solution: Transform it to Linear Programming (LP) problem - Relax variables to take on real values
Objective function and constraints remain the same
Linear Programming RelaxationLinear Programming Relaxation
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Solve LP
- Result is real values
Then, use the following rounding scheme for solution of the ILP
Efficient Rounding SchemeEfficient Rounding Scheme
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Correctness/Efficiency of Proposed RoundingCorrectness/Efficiency of Proposed Rounding
Lemma 2 (Correctness) - Rounding of the optimal solution of the relaxed
problem produces a feasible solution for the original problem
Lemma 3 (Efficiency: Size of Rounding Gap) - The rounding gap is at most nT + n, where n is the
number of senders and T is the frame period
- Example: T=30 fps, n=30, the gap is 32 bits
- Indeed negligible (frame sizes are in order of KBs)
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FGSAssign: Optimal Allocation AlgorithmFGSAssign: Optimal Allocation Algorithm
Solving LP (using Simplex method for example) may still be too much- Need to run in real-time on PCs (not servers)
Our solution: FGSAssign- Simple yet optimal allocation algorithm
- Greedy: Iteratively allocate bits to sender with smallest si (stored segment) first
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Pseudo Code of FGSAssignPseudo Code of FGSAssign
1. Sort senders based on si, s1 ≤ s2 ≤ …… ≤ sn;
2. x0 = …… = xn = 0; Δ1 = …… = Δn = 0; ragg = 0;
3. for i = 1 to n do
4. xi = min(xi−1 + biT, si);
5. ri = (xi − xi−1)/T ;
6. if (ragg + ri < bI ) then
7. ragg = ragg + ri;
8. Δi = xi − xi−1;
9. else
10. ri = bI − ragg;
11. Δi = T × ri;
12. return
13. endfor
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Optimality of FGSAssignOptimality of FGSAssign
Theorem 1- The FGSAssign algorithm produces an optimal
solution in O(n log n) steps, where n is the number of senders.
Proof: see paper
Experimentally validated as well.
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Multiple-Frame OptimizationMultiple-Frame Optimization
Solve the allocation problem for blocks of m frames each
Objective: minimize total distortion in block
Why consider multiple-frame optimization?- More room for optimization
- Less computation overhead: solve the problem less often
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Multiple-Frame Optimization: Why?Multiple-Frame Optimization: Why?
More room for optimization: higher quality and less quality fluctuation
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Multiple-Frame OptimizationMultiple-Frame Optimization
Formulation (in the paper): - Straightforward extension to single-frame with lager
number of variables and constraints
- Computationally expensive to solve
Our Solution: mFGSAssign algorithm - Heuristic (close to optimal results)
- Achieves two goals: • Minimize total distortion in a block
• Reduce quality fluctuations among successive frames
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mFGSAssign: High-Level DescriptionmFGSAssign: High-Level Description
1. Estimate a target distortion D that is feasible and achieves the two goals (binary search)
2. Compute for each frame f in the block its bit budget Bf
3. For each frame f, call FGSAssign to allocate Bf among senders
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Computing Target DistortionComputing Target Distortion
Is bit budget enough to transmit all frames at distortion level D ?
- Du : distortion upper bound
- Dl : distortion lower bound
- D : distortion estimate
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Efficiency of mFGSAssignEfficiency of mFGSAssign
Lemma 5- mFGSAssign terminates in O(m n log n) steps,
where n is the number of senders and m is the number of frames in a block
Much more efficient than linear programming approach
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Experimental SetupExperimental Setup
Software used - MPEG-4 Reference Software ver 2.5
• Augmented to extract R-D model parameters
Algorithms implemented (in Matlab)- LP solutions using Simplex for the single-frame and
multiple-frame problems
- FGSAssign algorithm
- mFGSAssign algorithm
- Nonscalable algorithm for baseline comparisons
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Experimental Setup (cont’d)Experimental Setup (cont’d)
Streaming scenarios- Four typical scenarios for Internet and corporate
environments
Testing video sequences - Akiyo, Mother, Foreman, Mobile (CIF)
- Sample results shown for Foreman and Mobile
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Single Frame: Quality (PSNR)Single Frame: Quality (PSNR)
Foreman, Scenario I Mobile, Scenario III
Quality Improvement: 1--8 dB
FGSAssign is optimal
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Multiple Frame: Quality (PSNR)Multiple Frame: Quality (PSNR)
Foreman, Scenario II Mobile, Scenario III
Scalable: higher improvement than single frame
mFGSAssign: almost optimal (< 1% gap)
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Fluctuation ReductionFluctuation Reduction
Foreman, Scenario II Mobile, Scenario III
Small quality fluctuations in successive frames
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Running TimeRunning Time
Foreman, Scenario I Foreman, Scenario IV
Small and stable running times for mFGSAssign, unlike mOPT (Simplex)
mFGSAssign can be used in real time
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Reconstructed PicturesReconstructed Pictures
Nonscalable
mFGSAssign
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ConclusionsConclusions
Formulated and solved the bit allocation problem for single and multiple frame cases
Nonlinear problem integer linear program- Using linear R-D model
Integer linear program linear program - Using simple rounding scheme
Efficient Algorithms - FGSAssign: Optimal and efficient
- mFGSAssign: close to optimal in terms of average distortion, reduces quality fluctuations, runs in real time
Significant quality improvements shown by our experiments
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Thank You!Thank You!
Questions??
All programs/scripts/videos are available:
http://www.cs.sfu.ca/~mhefeeda