Motion-Adaptive Transforms Based on Vertex-Weighted Graphs

Motion information in image sequences connects pixels that are highly correlated. In this paper, we consider vertex-weighted graphs that are formed by motion vector information. The vertex weights are defined by scale factors which are introduced to improve the energy compaction of motion-adaptive transforms. Further, we relate the vertex-weighted graph to a subspace constraint of the transform. Finally, we propose a subspace-constrained transform (SCT) that achieves optimal energy compaction for the given constraint. The subspace constraint is derived from the underlying motion information only and requires no additional information. Experimental results on energy compaction confirm that the motion-adaptive SCT outperforms motion-compensated orthogonal transforms while approaching the theoretical performance of the Karhunen Loeve Transform (KLT) along given motion trajectories.