Normal HDR practice is to take a series of photos at different exposures - 
for example a 5 shot sequence could be at: EV -2, -1, 0, 1, 2.

These must be aligned and then merged into an HDR file.   If you have 
linear converted files, the merge becomes a weighed average of the files.  
Typical weights are the 2^EV, divided by the sum of 2^EV for the sequence.

Image averaging is where you take multiple shots at the same exposure, 
align and then average them.  Typical weighting is 1/N.

I am doing both together - meaning that I might have multiple shots at each 
EV level but I want to make one HDR out of it.

Surprisingly  to me, every HDR program I have tried so far - both free and 
commercial - refuses to do this - if you give the software more than one 
shot at each EV level, they assume you made a mistake and only look at 
one.     

The correct behavior is not difficult - you just average them all with a 
slightly different weighting that takes into account that you have more one 
than one frame at each EV.

I am new to Hugin, but it looks to me like Hugin would work for me.  I 
think I might need special settings for it.

This article describes a simple version of merging a bracketed sequence 
with Hugin https://pixls.us/articles/aligning-images-with-hugin/, but I 
need to know the answer to these questions, and I hope that a Hugin expert 
or developer could answer them:

1. If I give Hugin a set of shots with more than one frame at each EV, will 
it do the correct weighted average of all of them?

2. Is this true even if I have different numbers of shots at each EV ?

3. Is it possible to see, or set, what weighting factors Hugin hdrmerge 
uses?

4. Will merging work even if all of the shots are at the same EV (i.e. this 
is image averaging not HDR) ?

5. There is an anti-ghosting option on Hugin hdrmerge.  Ideally this would 
work for all of the cases above - i.e. pure image averaging, or an HDR 
bracketed sequence, or multiple copies of HDR bracketed sequence.    Will 
it? 

-- 
A list of frequently asked questions is available at: 
http://wiki.panotools.org/Hugin_FAQ
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