As Figure 4.16, we propose an iterative successive re…nement mechanism to solve the original problem in the independent way. The main idea of the algorithm is to decide which frames to be encoded at the …rst place for MSE of di¤erent copy frames com-binations are huge; then we can allocate available bits among these chosen frames to encode and achieve the objective of total minimal distortion. Suppose that there is a R-D model which can estimate the needed coding bits, the rate control algorithm is the following:
Step 1 :
Use the r-d model to calculate the needed coding bits while encoding pre-selected frames at distortion=Dmax. If the required bits are smaller than available bits, go to Step 3, else go to Step 2.
Step 2 :
Use frame selection methodology to select a frame to be skipped with successive re…nement mechanism, and go to Step 1.
Chapter 4. Experiments and Analyses
FOOTBALL
K Bit
200 300 400 500 600 700
Total MSE
200 300 400 500 600 700
Total MSE
200 300 400 500 600 700
Total MSE
Figure 4.15: Comparison among proposed heuristic solution and its successive
re-…nement(a), methodology 1 and its successive re…nement(b), methodology 2 and its successive re…nement(c) in Football.
Start
Set # of Skipped Frame Snumber=0
Select Which Frames to be Encoded
Estimate Coding Bit Bestimateby R-D Model with Distortion=Dmax
If Bestimate<= Rt
Nskip=Nskip+1
No
Allocate Bit Budget Among Selected Frames to Minimize
Overall Distortion
Figure 4.16: Proposed algorithm ‡owchart. At the …rst stage to decide which frames to be encoded; to allocate bit among selected frames at the second stage.
Chapter 4. Experiments and Analyses
Step 3 :
Since skipped frames are out of the optimization target, we can simply allocate available bits among those selected coding frames and achieve the goal of minimum overall distortion.
CHAPTER 5
Conclusions and Future Works
In our work, we attempted to solve the quality- and rate-constrained problem and survey di¤erent constrained optimization problem methodologies. After comparing with related works and analyze our problem, we …nd out the best methodology for optimal solution is to use dynamic programming and the optimal path is a stairway-like curve, with huge complexity, the following lists our discoveries:
1. Constrained problems can be solved by dynamic programming. A simple algo-rithm for constrained optimization problem is to …nd the optimal solution among possible data set as integer programming; another commonly used mathematical tool for optimization problems is Lagrangian method, which turns the original constrained problem into unconstrained problem form.
2. For optmization problems with multiple constraints, each constraint correspond-ing to a Lagrangian multiplier, and the optimal solution should be obtained by iteratively adjusting each Lagrangian multiplier according to KKT conditions. As a result, the solution by constrained optimization problem like integer program-ming requires lower complexity than Lagrangian optimization; however, as for the single equality constrained problem, the Viterbi algorithm with Lagrangian
Chapter 5. Conclusions and Future Works
cost is commonly used owing to only one Lagrange multiplier variable to be solve, and the modern rate control apply this algorithm to real time system based on independency assumption.
3. According to optimal solution by integer programming for our problem, the op-timal path is a stairway-like curve, which means number of frames to be encoded and coding frame selection should be di¤erent to optimize our constrained prob-lem while the available bit budget changes. Furthermore, as long as more frame skipped, the MSE gap between each rate distortion line of di¤erent coding frame combination is larger; also, the interlacing part among coding bit range of di¤er-ent coding frame combination is getting smaller. From the above observation, it is a good choice to select another frame to be skipped while the available bit bud-get decreases in less frame skipped case for complexity issue, but it should choose another coding frame selection instead of skipping another frame immediately while more frame skipped.
4. In order to reduce complexity and to implement the proposed architecture in a real-time system, we try to develop a heuristic algorithm based on independent assumption and successive re…nement and devide the solution into two stages:
2.1) to …nd which frames to be encoded under rate constraint and distortion constraints;
2.2) to allocate available bit budget among these chosen frames to achieve the objective of minimize total distortion.
The experimental result shows this heuristic solution can reduce complexity ex-ponentially, though it does not achieve a good performance because the optimal path reveals that the encoder should choose di¤erent frames to encode when target rate changes.
Our work is still in its early stage, we plan to extend our investigation in several directions:
1. To survey other adaptive frame skipping methods and continue to research if there exits a better algorithm for our problem.
2. To replace the frame copy with temporal interpolation methodology and analyze the e¤ect.
3. To develop R-D models based on heuristic algorithm to allocate bits and minimize
Chapter 5. Conclusions and Future Works
total distortion for real-time systems.
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