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bjontegaard/bjontegaard_delta.py:49: UserWarning: Curves do not overlap. BD cannot be calculated.
warnings.warn("Curves do not overlap. BD cannot be calculated.")
BD-Rate=nan% | BD-PSNR=nan dB
Rationale
Consider a single test point $(R, D)$. Let its corresponding "fake" test curve be defined as $\{ (R, D), (R + \epsilon, D + \epsilon) \}$. As $\epsilon \to 0$, BD rate just becomes a distance measure between the test point and the interpolated point on the anchor curve with the same value of PSNR.
Request
Given:
Expected output:
Actual output:
Rationale
Consider a single test point$(R, D)$ . Let its corresponding "fake" test curve be defined as $\{ (R, D), (R + \epsilon, D + \epsilon) \}$ . As $\epsilon \to 0$ , BD rate just becomes a distance measure between the test point and the interpolated point on the anchor curve with the same value of PSNR.
Disclaimer: I didn't really check that the equation above makes sense. Also, pretend that$R \to \log R$ , if needed.
As a numerical example, consider the following method which fakes a test "curve" using a small epsilon deviation about the single test point:
Output:
Clearly, in the limit, the single point "curve" converges to a well-defined value of BD-Rate and BD-PSNR.
Other
I suppose a similar argument might also apply to single-point anchor "curves".
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