The Bjøntegaard Bible -- Why your Way of Comparing Video Codecs May Be Wrong

In this paper, we provide an in-depth assessment on the Bj{\o}ntegaard Delta. We construct a large data set of video compression performance comparisons using a diverse set of metrics including PSNR, VMAF, bitrate, and processing energies. These metrics are evaluated for visual data types such as classic perspective video, 360{\deg} video, point clouds, and screen content. As compression technology, we consider multiple hybrid video codecs as well as state-of-the-art neural network based compression methods. Using additional performance points inbetween standard points defined by parameters such as the quantization parameter, we assess the interpolation error of the Bj{\o}ntegaard-Delta (BD) calculus and its impact on the final BD value. Performing an in-depth analysis, we find that the BD calculus is most accurate in the standard application of rate-distortion comparisons with mean errors below 0.5 percentage points. For other applications, the errors are higher (up to 10 percentage points), but can be reduced by a higher number of performance points. We finally come up with recommendations on how to use the BD calculus such that the validity of the resulting BD-values is maximized. Main recommendations include the use of Akima interpolation, the interpretation of relative difference curves, and the use of the logarithmic domain for saturating metrics such as SSIM and VMAF.