Graph-based lifting transform for intra-predicted video coding

Abstract

In this paper, we propose a graph-based lifting transform for intrapredicted video sequences. The transform can approximate the performance of a Graph Fourier Transform (GFT) for a given graph, but does not require computing eigenvectors. A predict-update bipartition is designed based on a Gaussian Markov Random Field (GMRF) model with the goal to minimize the energy in the prediction set. Additionally, a novel re-connection method is applied for multi-level graphs, leading to significant gain for the proposed bipartition method and for the conventional MaxCut based bipartition. Experiments on intra-predicted video sequences show that the proposed method, even considering the extra overhead for edge information, outperforms the Discrete Cosine Transform (DCT) and approximates the performance of the higher complexity GFT.

Graph-based transforms for inter predicted video coding

“…2) Obtain two N × N sample covariances, S row and S col , from rows and columns of size N , respectively, obtained from residual blocks in the dataset. 3) Solve instances of the problem in (18), GGL(S row , A line ) and GGL(S col , A line ), by using the GGL estimation algorithm [23] to learn Laplacians L row and L col representing line graphs, respectively. 4) Perform eigendecomposition on L row and L col to obtain GBTs, U row and U col , which define the GBST as in (5).…”

“…In these figures, sample variances of residuals and corresponding graph-based models are illustrated. Both grid and line graphs (with normalized edge and vertex weights) are estimated from residual data by solving the GGL estimation problem in (18) used for GBNT and GBST construction.…”

Steerable Discrete Cosine Transform

“…A novel graph-based method for intra-frame video coding has been presented in [23], which introduces a new generalized graph Fourier transform optimized for intra-prediction residues. Instead, in [24] the authors propose a block-based lifting transform on graphs for intra-predicted video coding. Moreover, a graph-based method for inter-predicted video coding has been introduced in [25], where the authors design a set of simplified graph templates capturing basic statistical characteristics of interpredicted residual blocks.…”

Steerable Discrete Cosine Transform

“…A novel graph-based method for intra-frame video coding has been presented in [23], which introduces a new generalized graph Fourier transform optimized for intra-prediction residues. Instead, in [24] the authors propose a block-based lifting transform on graphs for intra-predicted video coding. Moreover, a graph-based method for inter-predicted video coding has been introduced in [25], where the authors design a set of simplified graph templates capturing basic sta-tistical characteristics of inter-predicted residual blocks.…”