Rate-Distortion Optimized Streaming of. Mohamed Hefeeda & ChengHsin Hsu

Transcription

1 School of Computing Science Simon Fraser University, Canada Rate-Distortion Optimized Streaming of Fine-Grained Scalable Video Sequences Mohamed Hefeeda & ChengHsin Hsu MMCN January

2 Motivations Multimedia streaming over the Internet is becoming very popular - More multimedia content is continually created - Users have higher h network bandwidth and more powerful computers Users request more multimedia content And they look kfor the best quality that t their resources can support 2

3 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 3

4 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 4

5 Our Optimization Problem Assign to each sender a rate and bit range to transmit such that the best quality is achieved at tthe receiver. Consider a simple example to illustrate the importance of this problem 5

6 Example: Different Streaming Schemes Non-scalable Layered 6

7 Example: Different Streaming Schemes FGS Scalable Optimal FGS Scalable 1. FGS enables us to get the best quality from senders 2. However, there too many allocation options, and we need to carefully choose the optimal one 7

8 Problem Formulation First: single-frame case - Optimize i quality for individual id frames Then: multiple-frame case - Optimize quality for a block of frames - More room for optimization - Details are presented in the extended version of the paper 8

9 Input Parameters T : fixed frame period n : number of senders b i : outgoing gbandwidth of sender i b I : incoming bandwidth of receiver s i : length of f( (contiguous) )bits held ldby sender i Assume w.l.g. s 1 <= s 2 <= <= s n 9

10 Outputs Allocation: A = {(Δ i, r i ) i = 1, 2,, n} - Δ i : number of bits assigned to i - r i : streaming rate assigned to i Specifies: - Sender 1 sends range [0, Δ 1-1] at rate r 1 - Sender 2 sends range [Δ 1, Δ 1 +Δ 2-1] at rate r 2 - i 1 i - Sender i sends range [ Δt, Δt 1] at rate r i t= 1 t= 1 10

11 Integer 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 min D( Δ ) t A t =1 s.t. Δ i r i T 0 n i Δ t =1 t r b i i n r t =1 t s i b I Δi,,r N; ; i = 1,2,L,,n. i i 11

12 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 i lmodels: Many empirical i 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 our previous work [Hsu 06] 12

13 The Linear R-D Model Within each bitplane, approximate R-D function by a line segment Line segments of different bitplanes have different slopes 13

14 Visual Validation of Linear R-D Model Mother & Daughter, frame 110 Foreman, frame

15 Rigorous Validation of Linear R-D Model Average error is less than 2% in most cases 15

16 Using the Linear R-D Model Let y i be number of bits transmitted from bitplane i Distortion is: d + z h=1 g y h h - d : base layer only distortion - g i : slope of bitplane i - z : total number of bitplanes 16

17 Integer Linear Programming (ILP) Problem Linear objective function min Additional constraints - number of bits transmitted from bit plane h does not exceed dits size l h - bits assigned to senders are divided among bitplanes n z D( Δ t ) = d + g A t=1 v y v=1 v s.t. Δ i r i T 0 i Δ t =1 t r i b i n r t =1 t s i b I y h l h n Δt z y v t =1 v=1 Δ i,r i,y h N; i = 1, 2,L,n; h = 1, 2,L,z. 17

18 Solution 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 z h=1 - minimizing i i i d + g h y h - Since g 1 < g 2 < <g n <0 (line segment slopes), - the ILP will never assign bits to y i+1 if y i is not full 18

19 Linear Programming Relaxation Solving ILP problem is expensive Solution: Transform it to Linear Programming (LP) problem - Relax variables to take on real values Δ + i,r i, y h R U{0}; i = 1,2,L,n; h = 1,2,L,z. Objective function and constraints remain the same 19

20 Efficient Rounding Scheme Solve LP - Result is real values  = {( ˆΔ i, ˆr i ) i = 1, 2,L,n} Then, use the following rounding scheme for solution of the ILP r i = rˆr i, ˆΔ ˆr i 1 i, r ˆr > 1 Δ i = Δ ˆr i 0, 0 rˆr 1 20

21 Correctness/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 - (Extreme) e) Example: n = 30 senders, s, T = 30 fps ==> gap is 32 bits - Indeed negligible (frame sizes are in order of KBs) 21

22 FGSAssign: 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 s i (stored segment) first 22

23 Pseudo Code of FGSAssign 1. Sort senders based on s i, s 1 s 2 s n ; 2. x 0 = = x n = 0; Δ 1 = = Δ n = 0; r agg = 0; 3. for i = 1 to n do 4. x i = min(x i 1 + b i T, s i ); 5. r i = (x i x i 1 )/T ; 6. if (r agg + r i < b I ) then 7. r agg = r agg + r i ; 8. Δ i = x i x i 1 ; 9. else 10. r i = b I r agg ; 11. Δ i = T r i ; 12. return 13. endfor 23

24 Optimality 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. 24

25 Multiple-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 - Solve the problem less often 25

26 Multiple-Frame Optimization: Why? Distortion (MSE) Bit rate More room for optimization: higher quality and less quality fluctuation 26

27 Multiple-Frame Optimization Formulation (in extended version of the paper): - Straightforward extension to single-frame with hlager 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 of frames Reduce quality fluctuations among successive frames - Pseudo code and analysis: see extended version of the paper 27

28 Experimental 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 28

29 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 29

30 Single Frame: Quality (PSNR) Foreman, Scenario I Mobile, Scenario III Quality Improvement: 1--8 db FGSAssign is optimal 30

31 Multiple Frame: Quality (PSNR) Foreman, Scenario II Mobile, Scenario III Scalable: higher improvement than single frame mfgsassign: almost optimal (< 1% gap) 31

32 Fluctuation Reduction Foreman, Scenario II Mobile, Scenario III Small quality fluctuations in successive frames 32

33 Conclusions Formulated and solved the bit allocation problem to optimize quality for receivers in general settings - Multiple l heterogeneous senders Considered single and multiple frame cases Approach - Nonlinear problem integer linear program Using linear R-D model - Integer linear program linear program Using simple rounding scheme Proposed 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 33

34 Thank You! Questions?? All programs/scripts/videos are available: 34