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The Bjøntegaard Delta (BD) rate is a metric to compare lossy compression method efficiency, specifically for image and video. The metric expresses (in percentage) the average bitrate savings of one method over another, at fixed distortion values[1]. It obtains the average difference between two rate-distortion (RD) curves by integrating fitted polynomials to the curves and computing their difference.
Definition
editThe original BD rate document[2] proposes fitting a third-degree polynomial to a RD curve and computing the difference between the integrals divided by the length of the integration interval.
The steps to compute the BD rate are[1]:
- Fit two cubic polynomials to the RD curves corresponding to the two methods, each to 4 data points.
- Integrate the curve.
- The BD rate is the difference between the integral results divided by the integration interval.
Implementation
editThere exist several publicly available implementations of the BD rate. They are widely used, as they provide a common benchmark for new methods. There are different versions for the most commonly used tools, such as Excel[3], MATLAB[4] or Python[5].
References
edit- ^ a b Barman, Nabajeet; Martini, Maria G.; Reznik, Yuriy (2024-01-08), Bj{\o}ntegaard Delta (BD): A Tutorial Overview of the Metric, Evolution, Challenges, and Recommendations, arXiv:2401.04039
- ^ Bjøntegaard, Gisle (April 2001). "Calculation of average PSNR differences between RD-curves". Itu-T Sg16/Q6 (Input Document VCEG-M33).
- ^ Bruylants, Tim (2024-11-10), tbr/bjontegaard_etro, retrieved 2024-11-22
- ^ Valenzise, Giuseppe. "Bjontegaard metric". Mathworks file exchange. Archived from the original on 2024-09-14. Retrieved 2024-11-22.
- ^ Anserw (2024-11-19), Anserw/Bjontegaard_metric, retrieved 2024-11-22