The Image and Video Coding Group is very active in optimizing the operational encoder control for video coding standards. The Lagrangian encoder control has become an integral part of the reference encoders for the video coding standards H.264/MPEG-4 AVC and HEVC.
Lagrange Optimization in Image and Video Encoding
The task of the encoder control is to determine the values of the syntax elements, and thus the bitstream, for a given input sequence. For that purpose, the distortion between the input sequence and its reconstruction is to be minimized under a rate constraint. Due to the huge parameter space of this optimization problem, this minimization is done on a block-by-block basis. For a block k and its set of coding options Pk , the optimal coding decision p shall be found, such that the distortion Dk (p) is minimized under a constraint Rc for the bit rate Rk (p).
This constrained minimization problem can be reformulated as an unconstrained minimization,
Application of Lagrange Optimization in Video Encoding
The approach of Lagrange optimization has been applied to different aspects of the video encoder control:
- Determination of coding modes (intra or inter)
- Determination of block partitionings
- Determination of motion vectors and reference indices for motion-compensated blocks
- Determination of intra prediction modes
- Determination of transform coefficient levels
The R-D optimized encoder control has been applied for the following video coding standards:
- H.262/MPEG-2 Video
- MPEG-4 Visual
- H.264/MPEG-4 AVC
For H.263, the encoder control design led to the creation of a new test model TMN-10. For H.264/MPEG 4 AVC, some aspects of the Lagrangian encoder control were already included in the first Test Model, the complete Lagrangian encoder control has been included during the development process. The Lagragian encoder control was used from the beginning for the development of the SVC and MVC extension of H.264/MPEG-4 AVC and for the HEVC development.
Furthermore, the rate-distortion optimized encoder control has been used as basis for:
- Optimizing encoders for error-prone environments 
- Developing a multi-layer encoder for SVC 
- Developing an optimized encoder for lapped transforms 
- G. J. Sullivan and T. Wiegand, Rate-Distortion Optimization for Video Compression, IEEE Signal Processing Magazine, Nov. 1998.
- T. Wiegand, H. Schwarz, A. Joch, F. Kossentini, and G. J. Sullivan, Rate-constrained coder control and comparison of video coding standards, IEEE Transactionc on Circuits and Systems for Video Technology, July 2003.
- J.-R. Ohm, G. J. Sullivan, H. Schwarz, T. K. Tan, and T. Wiegand, Comparison of the Coding Efficiency of Video Coding Standards, IEEE Transactions on Circuits and Systems for Video Technology, December 2012.
- T. Stockhammer, D. Kontopodis, and T. Wiegand, Rate-distortion optimization for JVT/H.26L Video Coding in Packet Loss Environments, Packet Video Workshop, April 2002.
- H. Schwarz and T. Wiegand, R-D optimized multi-layer encoder control for SVC, IEEE Conf. on Image Processing, 2007.
- M. Winken, D. Marpe, and T. Wiegand, Global and local rate-distortion optimization for Lapped Biorthogonal Transform Coding, IEEE International Conference on Image Processing, Sept. 2010.