Image weighting

[MeyGray3833]

Hi.

I was following a tutorial last night by Light Vortex Astronomy (very good, mind you) and I have seen it before and tried to get my head around "weighting". 

http://www.lightvortexastronomy.com/tutorial-pre-processing-calibrating-and-stacking-images-in-pixinsight.html

My question, specifically is what is image weighting and how does it work, what does it effect and should I use it? I do not seem to get a good answer with internet searching.

Cheers!

[Skipper Billy]

Does this help - its an extract from this full document - http://trappedphotons.com/blog/?p=693

David.

SubframeSelector’s use is fairly straight forward.  You give it a list of images (Figure 15, Target Subframes), put in some information about your camera (Figure 15, System Parameters), tell it what restrictions you want to use for approving images and how you want to weight the combination of that data with ImageIntegration (Figure 15, Expressions) and then measure and output your approved frames.  As you can see from Figure 15, I’ve am limiting the approved images to frames that have a FWHM less than 4 arc-seconds.  FWHM is the full with at half maximum of a point spread function (PSF) and in astronomy since stars are true point sources their FWHM can be used to understand what is actually resolveable in the image.  Smaller FWHM values are better.  I’ve also restricted the list by the Eccentricity and Noise metrics.  Noise is fairly straight forward, the higher the noise level the more difficult it is to discern your target, so again, lower values are better.  Eccentricity is a measure of how far from round a star is.  If a star is very elongated it will have a higher Eccentricity value, so it is also better to have lower values here.

The weighting is more complicated.  Here is the full equation I used in Figure 15:
(35*(1-(FWHM-3.008)/(4.003-3.008)) + 5*(1-(Eccentricity-0.3663)/(0.5712-0.3663)) + 10*(1-(Noise-107.6)/(117.5-107.6)))+50

It looks like a bit of a mess, but if we break it down it’s not difficult to understand.  The first term is: (FWHM-3.008)/(4.003-3.008).  Really all I’m doing is normalizing the FWHM values to a range of 0 to 1.  I subtract the FWHM for a given image by the minimum value and the divide by the range of values.  So, when FHWM is the maximum value I get (4.003-3.008)/(4.003-3.008) or 1.0.  You can see I do this for all the terms I’m interested in.  Unfortunately, SubframeSelector doesn’t currently have a FWHMmax or FWHMmin variable so you have to sort the list and manually enter the min/max values for each term.  The next thing I do is invert those terms, which is where the 1-x comes from.  This simply takes each term which are now ranging from 0 to 1 and makes them range from 1 to 0.  This way if I have a large FWHM image it will have a lower weighting value, since larger FWHM values are worse.  If I was using the SNRWeighting term I wouldn’t include a 1-x term since larger values are  better.  Next I weight each term by its importance to me.  For example, I’m more interested in getting the highest resolution possible so I increase the FWHM terms resulting value relative to the other terms.  This is what the 35, 5 & 10 values are for.  If you were less concerned with resolution and wanted rounder stars with a better SNR then you might weight FWHM lower and Eccentricity and Noise higher.  I’ve chosen the weighting values so that my result will be in the range of 0 to 50 and then I add 50 to the entire expression so that the final range is 50 to 100.  I could have used a 0 to 5 or 0.5 range and it wouldn’t really matter, but the offset is important.  By forcing the weighting range to be 50 to 100 I make sure that even the worst frame still has a reasonable contribution to the final ImageIntegration result since its weight is never less than half the maximum value.  If I left the range as 0 to 50 then the worst frame would not contribute to the final image at all.

Now that we’ve approved and weighted our images, we want to annotate them with that information and output them so we can use them for registration and integration.  In the output panel (see figure 16) select the directory where you want your images to go, how you want them tagged and define what the Weight keyword will be (I chose SFSWEIGHT for Sub Frame Selector Weight).  We will use the weight keyword later on in ImageIntegration.  Click the Output Subframes button and you’ll now have a directory full of calibrated, defect corrected and weighted light frames.

[MeyGray3833]

Thanks, I'll check the whole thing out!

[wimvb]

Image integration can use a weight factor based on either signal strength or noise, among others. The first frame in the stack is a reference, and all other images are compared to this.

To simplify, lets say that the ref frame has a snr of 100, and that another frame has the same snr. Both frames will then count equal when calculating the average. If a third frame has a snr of 50, it will contribute only 50 % of it's value to the stack. The average of these 3 frames would then be

(F1 + F2 + 0.5xF3)/2.5

You use an appropriate weighting property when doing image integration. Choosing the best property (snr, fwhm, signal, etc) will let you maximise snr in the integrated image. That's why the (PixInsight) docs tell you to do the integration manually, and not to use BPP script for this. Here is an article where the author used the noise evaluation script to optimise the process, and increase snr. It's a time consuming enterprise.

http://www.astrosurf.com/jordigallego/articles.html

[MeyGray3833]

Thanks, that make sense. I'll do some more reading on that link. Cheers.