Graph-based construction and assessment of motion-adaptive transforms

In this paper, we propose two algorithms to construct motion-adaptive transforms that are based on vertex-weighted graphs. The graphs are constructed by motion vector information. The weights of the vertices are given by scale factors that are used to accommodate proper concentration of energy in transforms. The vertex-weighted graph defines a one dimensional linear subspace. Thus, our transform basis is subspace constrained. We propose two algorithms. The first is based on the Gram-Schmidt orthonormalization of the discrete cosine transform (DCT) basis. The second combines the rotation of the DCT basis and the Gram-Schmidt orthonormalization. We assess both algorithms in terms of energy compaction. Moreover, we compare to prior work on graph-based rotation of the DCT basis and on so-called motion-compensated orthogonal transforms (MCOT). In our experiments, both algorithms outperform MCOT in terms of energy compaction. However, their performance is similar to that of graph-based rotation of the DCT basis.