仅使用一对PSNR和BitRate的Bjontegaard计算

Question

我想使用下面的python脚本来计算两种不同视频编码设置的BD率。

使用第四个点(R1和PSNR1是Video1的参考RD点，而R2和PSNR2是具有不同视频设置的Video2的新测试)，脚本工作得很好

from bjontegaard_metric import *    
R1 = np.array([686.76, 309.58, 157.11, 85.95])
PSNR1 = np.array([40.28, 37.18, 34.24, 31.42])
R2 = np.array([893.34, 407.8, 204.93, 112.75])
PSNR2 = np.array([40.39, 37.21, 34.17, 31.24])

print 'BD-PSNR: ', BD_PSNR(R1, PSNR1, R2, PSNR2)
print 'BD-RATE: ', BD_RATE(R1, PSNR1, R2, PSNR2)

但只有第一点

 from bjontegaard_metric import *
 R1 = np.array([686.76])
 PSNR1 = np.array([40.28])
 R2 = np.array([893.34])
 PSNR2 = np.array([40.39])
        
 print 'BD-PSNR: ', BD_PSNR(R1, PSNR1, R2, PSNR2)
 print 'BD-RATE: ', BD_RATE(R1, PSNR1, R2, PSNR2)

我收到一个警告：RankWarning: Polyfit可能是条件不良的。每个视频编码器运行，只返回一对PSNR和比特率作为结果。因此，我想比较两对PSNR/比特率(参考视频和修改视频)。有什么办法来修正这个警告吗？我只用第一点得到的结果是可靠的？

import numpy as np
import scipy.interpolate

def BD_PSNR(R1, PSNR1, R2, PSNR2, piecewise=0):
    lR1 = np.log(R1)
    lR2 = np.log(R2)

    PSNR1 = np.array(PSNR1)
    PSNR2 = np.array(PSNR2)

    p1 = np.polyfit(lR1, PSNR1, 3)
    p2 = np.polyfit(lR2, PSNR2, 3)

    # integration interval
    min_int = max(min(lR1), min(lR2))
    max_int = min(max(lR1), max(lR2))

    # find integral
    if piecewise == 0:
        p_int1 = np.polyint(p1)
        p_int2 = np.polyint(p2)

        int1 = np.polyval(p_int1, max_int) - np.polyval(p_int1, min_int)
        int2 = np.polyval(p_int2, max_int) - np.polyval(p_int2, min_int)
    else:
        # See https://chromium.googlesource.com/webm/contributor-guide/+/master/scripts/visual_metrics.py
        lin = np.linspace(min_int, max_int, num=100, retstep=True)
        interval = lin[1]
        samples = lin[0]
        v1 = scipy.interpolate.pchip_interpolate(np.sort(lR1), PSNR1[np.argsort(lR1)], samples)
        v2 = scipy.interpolate.pchip_interpolate(np.sort(lR2), PSNR2[np.argsort(lR2)], samples)
        # Calculate the integral using the trapezoid method on the samples.
        int1 = np.trapz(v1, dx=interval)
        int2 = np.trapz(v2, dx=interval)

    # find avg diff
    avg_diff = (int2-int1)/(max_int-min_int)

    return avg_diff


def BD_RATE(R1, PSNR1, R2, PSNR2, piecewise=0):
    lR1 = np.log(R1)
    lR2 = np.log(R2)

    # rate method
    p1 = np.polyfit(PSNR1, lR1, 3)
    p2 = np.polyfit(PSNR2, lR2, 3)

    # integration interval
    min_int = max(min(PSNR1), min(PSNR2))
    max_int = min(max(PSNR1), max(PSNR2))

    # find integral
    if piecewise == 0:
        p_int1 = np.polyint(p1)
        p_int2 = np.polyint(p2)

        int1 = np.polyval(p_int1, max_int) - np.polyval(p_int1, min_int)
        int2 = np.polyval(p_int2, max_int) - np.polyval(p_int2, min_int)
    else:
        lin = np.linspace(min_int, max_int, num=100, retstep=True)
        interval = lin[1]
        samples = lin[0]
        v1 = scipy.interpolate.pchip_interpolate(np.sort(PSNR1), lR1[np.argsort(PSNR1)], samples)
        v2 = scipy.interpolate.pchip_interpolate(np.sort(PSNR2), lR2[np.argsort(PSNR2)], samples)
        # Calculate the integral using the trapezoid method on the samples.
        int1 = np.trapz(v1, dx=interval)
        int2 = np.trapz(v2, dx=interval)

    # find avg diff
    avg_exp_diff = (int2-int1)/(max_int-min_int)
    avg_diff = (np.exp(avg_exp_diff)-1)*100
    return avg_diff

Answer 1

据https://tools.ietf.org/id/draft-ietf-netvc-testing-06.html#rfc.section.4.2 2号At least four points must be computed. These points should be the same quantizers when comparing two versions of the same codec的IETF表示。因此，任何小于4的点对于可靠的结果都是无效的。

1. Rate/distortion points are calculated for the reference and test codec.
2. At least four points must be computed. These points should be the same quantizers when comparing two versions of the same codec.
3. Additional points outside of the range should be discarded.
4. The rates are converted into log-rates.
5. A piecewise cubic hermite interpolating polynomial is fit to the points for each codec to produce functions of log-rate in terms of distortion.

Metric score ranges are computed:
1. If comparing two versions of the same codec, the overlap is the intersection of the two curves, bound by the chosen quantizer points.
2. If comparing dissimilar codecs, a third anchor codec’s metric scores at fixed quantizers are used directly as the bounds.
3. The log-rate is numerically integrated over the metric range for each curve, using at least 1000 samples and trapezoidal integration.
4. The resulting integrated log-rates are converted back into linear rate, and then the percent difference is calculated from the reference to the test codec.