  Many multimedia applications require precise understanding of the
rate-distortion characteristics measured by the function relating visual
quality to media attributes, for which we term it the generalized
rate-distortion (GRD) function. In this study, we explore the GRD behavior of
compressed digital videos in a three-dimensional space of bitrate, resolution,
and viewing device/condition. Our analysis on a large-scale video dataset
reveals that empirical parametric models are systematically biased while
exhaustive search methods require excessive computation time to depict the GRD
surfaces. By exploiting the properties that all GRD functions share, we develop
an Robust Axial-Monotonic Clough-Tocher (RAMCT) interpolation method to model
the GRD function. This model allows us to accurately reconstruct the complete
GRD function of a source video content from a moderate number of measurements.
To further reduce the computational cost, we present a novel sampling scheme
based on a probabilistic model and an information measure. The proposed
sampling method constructs a sequence of quality queries by minimizing the
overall informativeness in the remaining samples. Experimental results show
that the proposed algorithm significantly outperforms state-of-the-art
approaches in accuracy and efficiency. Finally, we demonstrate the usage of the
proposed model in three applications: rate-distortion curve prediction,
per-title encoding profile generation, and video encoder comparison.
