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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
[edit]The 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
[edit]There 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, doi:10.48550/arXiv.2401.04039, retrieved 2024-11-21
- ^ 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