1. Reji Mathew and David S. Taubman CSVT 2010

2.  Introduction  Quad-tree representation  Quad-tree motion modeling  Motion vector prediction strategies  Pruning algorithm  Merging principle  Motion signaling  R-D performance results  Hierarchical and polynomial motion modeling  Scalable motion modeling  Conclusion

3.  Image modeling  Image to be recursively divided into smaller regions, each region represented by a suitable model.  Sub-optimal: dependency between neighboring leaf nodes with different parents is not exploited

4.  Image modeling  Rate-distortion optimization, allowing a Lagrangian cost function( D+ λ R ) to be minimized using tree pruning with leaf merging step. [1] R. Shukla, P. Dragotti, M. Do, and M. Vetterli, “Rate-distortion optimized tree structure compression algorithms for piecewise polynomial images,” IEEE Trans. Image Process., vol. 14, no. 3, pp. 343–359, Mar. 2005.

5.  Motion model  forward-only, backward only or bi-directional motion with two reference frames.  Motion vector prediction strategies  Hierarchical motion coding  H.264 spatial motion vector prediction strategy Motion models

6.  Pruning Algorithm  Produce a quad-tree structure that minimizes the Lagrangian cost objective D f + λ R f  Given a parent node p, the four children c i, 1 ≤ i ≤ 4, are pruned away if  When pruning occurs, and Otherwise, and = R p in hierarchical coding =0 at all times in spatial coding R-D optimally pruned quad-tree: Tree pruning yields a globally minimal value for D f + λR f for hierarchical coding; while it is somewhat greedy for spatially predictive coding. R-D optimally pruned quad-tree: Tree pruning yields a globally minimal value for D f + λR f for hierarchical coding; while it is somewhat greedy for spatially predictive coding.

7.  Merging principle  possibility of jointly coding and optimizing neighboring nodes that belong to different parents.  Merge target contains nieghboring node located at a higher level or at the same level.  Merging is allowed to take place only if it reduces the overall Lagrangian cost. The same parent

8.  Motion signaling  Anchor node:  Hierarchical: the only member node of the region that is not signaled as being merged  Spatial: the first node in the region that is encountered during decoding.(the top-left block)

9.  R-D performance results 35% 25% 45% 35% once merging is included the performance of hierarchical motion representation can be brought close to that achieved by spatial prediction with merging.

10.  Further improve the performance of hierarchical motion representation by polynomial motion models.  Formation of larger regions during merging process  Smoother motion representations  Motion models  The parameters of the motion model are obtained by a weighted least squares fitting procedure.  Pruning phase  Merging phase : mv belonging to node b at level k : motion corresponding to translation, linear and affine flows : mv belonging to node b at level k : motion corresponding to translation, linear and affine flows

11.  Motion compensation  Generate a set of MVs for each descendants at level K (4*4 block)  R-D performance with motion models depend on the motion model and the central location of block b’

12.  Scalability objective  Modified Lagrangian cost function  When terminating decoding at an intermediate resolution level, motion compensation is performed using leaf nodes that may already be available; in those cases where leaf nodes are not available, information contained in branch nodes is utilized. : The costs for each level k of the quad-tree : The weights assigned to each level, and Leaf node b Branch node b Contribution to : The total distortion of all nodes for which motion compensation is performed Level k : terminate

13.  Scalability performance  α 0 = α 1 = α 2 =0.1, α 3 =0.7

14.  Residual coding  JPEG2000: full resolution motion compensated residual frames  Total rate for coding motion and residual frames

15.  Wavelet-based video encoding results  integrate the quad-tree motion model with the wavelet- based scalable interactive video (SIV) codec[9] [9] A. Secker and D. S. Taubman, “Lifting-based invertible motion adaptive transform framework for highly scalable video compression,” IEEE Trans. Image Process., vol. 12, no. 12, pp. 1530–1542, Dec. 2003.

16.  The merging step can be incorporated into quad-tree motion representations for a range of motion modeling contexts.  R-D performance that can be gained by introducing merging for the two cases of hierarchical and spatially predictive motion coding (such as that employed by H.264).  Report on the benefits of polynomial modeling and hierarchical coding, once merging has been incorporated into the conventional quad-tree approach.