# Re: efficient kernel or masking algorithm ? UPDATE

```"John-David Smith" <jdsmith@astro.cornell.edu> wrote in message
3A99C6B4.10549265@astro.cornell.edu">news:3A99C6B4.10549265@astro.cornell.edu...
>
> P.S. I think I originally got the idea from sigma_filter.pro, a NASA
library
> routine, dating back to 1991.  It's chock-full of other good tidbits too.
> Thanks Frank and Wayne!

Hi John,
Just checked the file SIGMA_FILTER.pro at
http://idlastro.gsfc.nasa.gov/ftp/pro/image/?N=D
I really must spend more time browsing these great sites.
The code is similar, however it does not calculate the true variance under
they calculate for a box width of n, (ignoring centre pixel removal):
--------------------------------------
mean_im=(smooth(image, n) )
dev_im = (image - mean_im)^2
var_im = smooth(dev_im, n)/(n-1)
-------------------------------------
This is not the true variance of the pixels under the box mask, as each
pixel in the mask is having a different mean subtracted.
i.e (read this as a formula if you can!)
Pseudo_Variance = SUM ij ( ( I(x+i,y+j) - MEAN(x+i,y+j)^2) /(n-1)

Variance = SUM ij ( ( I(x+i,y+j) - MEANxy)^2) /(n-1)
which can be reduced to :  {(SUM ij ( ( I(x+i,y+j)^2 ) - (SUM ij
I(x+i,y+j) ) ^2)/n }/(n-1)
hence the non loop method we use below:
---------------------------
; calc box mean
mean_im = smooth(image, n)
; calc box mean of squares
msq_im = smooth(image^2, n)
; hence variance
var_im = ( msq_im - mean_im^2) * (n/(n-1.0))
----------------------------------

cheers

Martin

PS: Sorry about my before-and-after-coffee postings this morning, outlook
decided to post my replies whilst I was still pondering - how kind -  I've
killed that *feature* now :)

```