The PSNR/VMAF BD-rate is a measure of coding efficiency in the terms of the average change in bitrate for a fixed PSNR or VMAF quality between two video compression methods. Additional information on BD-Rate is present here (“Bjontegaard Delta-Rate Metric” by Maxim Sharabayko)
For example, if PSNR BD-rate is -10% between codec A and codec B , this means that the given same PSNR quality the codec A in average gets a bit-rate saving of 10%, i.e. the codec A is more code efficient.
How to compute BD-Rate?
There is a free python script bjontegaard_metric.py, to clone the script use:
git clone https://github.com/Anserw/Bjontegaard_metric.git
actually the code in bjontegaard_metric.py is a replica of the corresponding Matlab code for BD-rate calculation. So, we can trust this code.
You need at least four points (Qualit, Rate) to compute BD-Rate. Piecewise cubic interpolation is commonly used to join all data points.
For example i ran x264 and x265 on same ‘evil’ testing sequence with an aligned settings and obtained the following results:
x264:
target bitrates (Mbps) 10 15 20 25
bitrates (Mbps): 9.525, 14.270, 19.113, 24.393
psnr: 37.73, 39.07, 40.07, 40.95
x265:
target bitrates (Mbps) 10 15 20 25
bitrates (Mbps): 8.914, 13.330, 17.880, 22.990
psnr: 37.02, 38.37, 39.42, 40.35
The python code to apply bjontegaard_metric function BD_RATE and get PSNR BD-Rate:
from bjontegaard_metric import *
ratesx264 = np.array([9.525,14.27,19.113,24.393])
psnrx264 = np.array([37.73,39.07,40.07,40.95])
ratesx265 = np.array([8.914,13.330,17.880,22.990])
psnrx265=np.array([37.02,38.37,39.42,40.35])
BD_RATE(ratesx265, psnrx265, ratesx264, psnrx264)
-12.098
Note:
- Originally a cubic interpolation is used for computation of BD-Rate. But the cubic interpolation method was found to be not always stable and more advanced curve fitting methods proposed and accepted (e.g. the piecewise cubic interpolation), for details pls. look at the paper “Revisiting Bjontegaard Delta Bitrate (BD-BR) Computation for Codec Compression Efficiency Comparison” by Nabajeet Barman et al.
- Choice of metric can change BD-Rate results, it’s not uncommon that in PSNR metric codec A is better than codec B and in VMAF metric codec B is better than codec A:
23+ years’ programming and theoretical experience in the computer science fields such as video compression, media streaming and artificial intelligence (co-author of several papers and patents).
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