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.

中文翻译：

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表征视频编码的广义速率失真性能：一种特征分析方法

率失真 (RD) 理论是有损数据压缩的核心。在这里，我们旨在对压缩视频的视觉质量与其编码配置文件（例如，比特率和空间分辨率）之间的广义 RD (GRD) 权衡进行建模。我们首先通过分析其数学性质定义了 GRD 函数的理论函数空间 $\mathcal{W}$。 我们证明 $\mathcal{W}$ 是 Hilbert 空间中的凸集，启发了 GRD 的计算模型函数，以及一种从稀疏测量中估计模型参数的方法。为了证明我们想法的可行性，我们收集了真实世界 GRD 函数的大规模数据库，结果证明这些函数存在于 $\mathcal{W}$ 的低维子空间中。结合GRD重建框架和学习到的低维空间，我们创建了一种低参数特征 GRD 方法，以仅从几个查询中准确估计源视频内容的 GRD 函数。数据库上的实验结果表明，学习到的 GRD 方法在准确性和效率方面都明显优于最先进的经验 RD 估计方法。最后，我们证明了所提出模型在视频编解码器比较中的前景。