Characterizing Generalized Rate-Distortion Performance of Video Coding: An Eigen Analysis Approach

TL;DR

This paper introduces a novel eigen analysis approach to model and estimate the generalized rate-distortion trade-off in video coding, enabling accurate predictions from limited data and improving codec comparison.

Contribution

It defines a mathematical framework for GRD functions, models them in a low-dimensional subspace, and develops an efficient eigen-based estimation method from sparse measurements.

Findings

The low-dimensional subspace effectively captures real-world GRD functions.

The eigen GRD method outperforms existing empirical estimation techniques.

The approach facilitates accurate video codec comparisons.

Abstract

Rate-distortion (RD) theory is at the heart of lossy data compression. Here we aim to model the generalized RD (GRD) trade-off between the visual quality of a compressed video and its encoding profiles (e.g., bitrate and spatial resolution). We first define the theoretical functional space $\mathcal{W}$ of the GRD function by analyzing its mathematical properties.We show that $\mathcal{W}$ is a convex set in a Hilbert space, inspiring a computational model of the GRD function, and a method of estimating model parameters from sparse measurements. To demonstrate the feasibility of our idea, we collect a large-scale database of real-world GRD functions, which turn out to live in a low-dimensional subspace of $\mathcal{W}$. Combining the GRD reconstruction framework and the learned low-dimensional space, we create a low-parameter eigen GRD method to accurately estimate the GRD function of a source video content from only a few queries. Experimental results on the database show that the learned GRD method significantly outperforms state-of-the-art empirical RD estimation methods both in accuracy and efficiency. Last, we demonstrate the promise of the proposed model in video codec comparison.