Improvements of the BD-Rate Metrics Using Monotonic Curve-Fitting Methods

The Bj⊘ntegaard Delta rate (BD-rate) measurements have been used as the primary metrics to evaluate performance of video codecs. However, current BD-rate calculation methods are only applicable under the condition that the rate-distortion (R-D) values maintain a monotonic relationship, as this prerequisite is essential for computing integral along the distortion axis. To address this limitation, we propose a curve-fitting based BD-rate solution that guarantees the reconstructed R-D curve to be monotonic. Considering different use cases, we provide a four parameters logistic curve and a constraint cubic curve to approximate the underlying R-D curve. Computation of BD-rate and BD-metric using fitted R-D curve are elaborated in detail. Experimental results indicate that the proposed solutions work well on non-monotonic data. Furthermore, we verified through quantitative analysis that curve-fitting solutions provide more precise measurements of coding efficiency compared to interpolation methods. This improved accuracy contributed by the proposed methods is attributed to the higher resilience to the inherent randomness present in observed data. The proposed method has been adopted by the MPEG WG4 VCM study group for standardization activities. The source code was released at https://multimedia.tencent.com/resources/tvd.