Gaussian kernel ISO 16610-21/-61

[dhueser]

Dear Frederic,

• in filter.py line 46 you have the conversion from cut off wavelength to sigma

46: return cutoff / (2 * np.sqrt(2 * np.log(2)))

• kernel according to ISO 16610-21 and -61 $s(u) \propto \exp(-\pi (\frac{u}{\alpha \lambda_c})^2)$ where $\alpha = \sqrt{\frac{\log(2)}{\pi}}$
• Gaussian as of ndimage: $g(u) \propto \exp(-\frac{1}{2} (\frac{u}{\sigma})^2 )$
• i.e. $\frac{1}{2 \sigma^2} = \frac{\pi}{(\alpha \lambda_c)^2}$
• inserting $\alpha = \sqrt{\frac{\log(2)}{\pi}}$ we obtain $\frac{1}{2 \sigma^2} = \frac{\pi^2}{\log(2) \lambda_c^2}$
• i.e. $2 \sigma^2 = \log(2) (\frac{\lambda_c}{\pi} )^2$
• i.e. $\sigma = \sqrt{\frac{\log(2)}{2}} \frac{\lambda_c}{\pi}$
• therefore, could it be that in line 46 of filter.py you might have ment?

46: return (cutoff/np.pi) * (np.sqrt(np.log(2)/2))

Best wishes - Dorothee

[fredericjs]

Thanks Dorothee,

I'm not sure anymore how I arrived at the current implementation for sigma, but there is definitely an error. Your implement is correct, at least it's what I obtain for the standard deviation when I equate a general Gaussian kernel with the kernel function proposed by ISO 16610.

Thanks alot for correcting this mistake. I have published a fix in v0.8.2

Best
Frederic