Filter optimization and complexity reduction for video coding using graph-based transforms

Abstract

The basis functions of lifting transform on graphs are completely determined by finding a bipartition of the graph and defining the prediction and update filters to be used. In this work we consider the design of prediction filters that minimize the quadratic prediction error and therefore the energy of the detail coefficients, which will give rise to higher energy compaction. Then, to determine the graph bipartition, we propose a distributed maximum-cut algorithm that significantly reduces the computational cost with respect to the centralized version used in our previous work. The proposed techniques show improvements in coding performance and computational cost as compared to our previous work.

Directional Transforms for Video Coding Based on Lifting on Graphs

“…The mean number of spatial neighbors per node greatly varies among sequences, being lower in sequences with high texture or big number of contours (1.42 in Mobile) and vice-versa (4.36 in Carphone). Although we employ the distributed approach of [35] and the subgraph approach of [34] for performing the U /P assignment, which greatly reduce the encoder complexity, this complexity can be further reduced by limiting the size of the subgraphs, or using parallel processing (e.g., the U /P assignment for different blocks can be parallelized).…”

“…In order to obtain an improved complete encoder, we propose a reordering method and a new entropy coder, significantl improving previous versions of the encoder. Finally, we extend the results in [33]- [35] by including a comparison of the proposed encoder with MCTF and H.264/AVC video encoders for QCIF and CIF sequences.…”

“…Previous work was presented by the authors in [33]- [35]. In this paper we formalize and solve analytically some of the underlying problems that arise from the transform design, describing and optimizing the complete scheme.…”

Optimized Update/Prediction Assignment for Lifting Transforms on Graphs

“…In previous works we proposed UPAs that aim at minimizing the energy of detail coefficients in a lifting-based video encoder [35]- [37]. To this end, given a weighted graph that represents the video signal, we find the UPA that solves the WMC problem which, intuitively, maximizes the correlation between the P and the U sets (Figure 2(f)).…”

“…In Section III we formally define the UPA problem and describe our proposed general solution. In Section IV we analyze and 1 The topology is given by the geometry and the physics of the problem at hand (e.g., sensor networks or community graphs) or selected based on signal characteristics [35]- [37], [40]- [43], and the weights capture similarity between samples and can be defined, for example, as the inverse of the distance, using a Gaussian kernel weighting function [2], or inferred from the data [36], [37].…”