[FFmpeg-devel] apsnr's PSNR formula is different from Wikipedia's formula

[Anton Khirnov]

Quoting Shawn Singh via ffmpeg-devel (2024-10-07 19:22:29)
> On Tue, Oct 1, 2024 at 3:41 PM Jing Lu <lujin at google.com> wrote:
> 
> > Hi ffmpeg-devel@,
> >
> > I recently came across the apnsr filter
> > <https://github.com/FFmpeg/FFmpeg/blob/master/libavfilter/af_asdr.c#L238>,
> > and the formula for PSNR it uses:
> >
> > 2.0 * log(s->max) - log(s->nb_samples / s->chs[ch].uv)
> >
> >
> > which is different from the formula given by Wikipedia's PSNR
> > <https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio>:
> >
> > 20 * log_10(MAX) - 10 * log_10(MSE)
> >
> >
> > Some differences I noticed:
> > - the forms of the formulae are very different
> > - natural number (e) as its log base v.s. 10 as the log base.
> > - the choice of s->max
> > <https://github.com/FFmpeg/FFmpeg/blob/master/libavfilter/af_asdr.c#L213> as
> > FLT_MAX or DBL_MAX v.s. 1.0 or 2.0 in popular implementations of
> > Wikipedia's formula, for floating point sample formats.
> >
> > These differences yield significantly different ranges of PSNR values:
> > 600+ v.s. mostly around 0 - 100 dB.
> >
> > I'm wondering:
> >
> >    - What's the context of apsnr's formula?
> >    - If we could change apsnr's implementation to use Wikipedia's formula
> >    or add a switch to use Wikipedia's formula?
> >
> > Thanks,
> > Jing
> >
> 
> 
> Dear all, does anyone else have opinions about this?    Here are some
> additional thoughts I have:
> 
> - All definitions of decibels that I am aware of use log base 10, including
> textbooks and online course materials.  Both Wikipedia and ITU-R V.574-5
> cite two standards in particular, ISO 80000-2 (or the upcoming ISO
> 80000-15) and IEC 60027-3 as measurement standards that define decibels
> with base 10.  (I have not seen the ISO or IEC documents myself)
> -  The expression (nb_samples / s->chs[ch].uv) is the inverse of MSE.
> Therefore, when the error is larger, the final logarithm result will be
> lower.  This is backwards from the usual interpretation that more error has
> a lower signal-to-noise ratio.
> 
> Is there interest in changing the apsnr implementation, if we can provide a
> patch?

Fixing the formula sounds reasonable to me.

Some tests for this filter would be great as well.

-- 
Anton Khirnov