Add missing sqrt to magSpectrum().

[yo1990]

resolves #20100

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Add some std::sqrt() to magSpectrum().
#20100

force_builders=ARMv7,Custom
build_image:Custom=centos:7
buildworker:Custom=linux-1,linux-4,linux-6

[llschloesser]

For phase correlation, the | | in DFT' (F G* / |F G*|) means absolute value and not magnitude, right? Is magSpectrums() the wrong operation to use for phase correlation?

[llschloesser]

For phase correlation, the | | in DFT' (F G* / |F G*|) means absolute value and not magnitude, right? Is magSpectrums() the wrong operation to use for phase correlation?

In my code I replaced:
magnitude_of_spectrums(cross_power_, cross_power_magnitude_);
with
cv::absdiff(cross_power_, cv::Scalar::all(0), cross_power_magnitude_);
and observed no loss of accuracy/quality. Same good results as before. What am I not understanding?

[llschloesser]

For phase correlation, the | | in DFT' (F G* / |F G*|) means absolute value and not magnitude, right? Is magSpectrums() the wrong operation to use for phase correlation?

In my code I replaced:
magnitude_of_spectrums(cross_power_, cross_power_magnitude_);
with
cv::absdiff(cross_power_, cv::Scalar::all(0), cross_power_magnitude_);
and observed no loss of accuracy/quality. Same good results as before. What am I not understanding?

In the book Image Processing, Analysis, and Machine Vision, the magnitude function | F(u,v) | is defined as sqrt(R(u,v)^2 + I(u,v)^2). So it seems that the magnitude function on a spectrum is indeed the right operation and is denoted with single bars rather than double?

[vpisarev]

👍

[yo1990]

Thank you.
I agree with your corrections; absolute value is more appropriate, not magnitude.