[gnuastro-devel] [task #14140] Using Gaussian sigma instead of quantile for initial thresholds

[Mohammad Akhlaghi]

URL:
  <http://savannah.gnu.org/task/?14140>

                 Summary: Using Gaussian sigma instead of quantile for initial
thresholds
                 Project: GNU Astronomy Utilities
            Submitted by: makhlaghi
            Submitted on: Mon 29 Aug 2016 06:28:28 PM JST
         Should Start On: Mon 29 Aug 2016 12:00:00 AM JST
   Should be Finished on: Mon 29 Aug 2016 12:00:00 AM JST
                Category: NoiseChisel
                Priority: 5 - Normal
              Item Group: Enhancement
                  Status: Need Info
                 Privacy: Public
        Percent Complete: 0%
             Assigned to: makhlaghi
             Open/Closed: Open
         Discussion Lock: Any
                  Effort: 0.00

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Details:

The user specifies the threshold values that are applied to the convolved
image in NoiseChisel as quantiles <https://en.wikipedia.org/wiki/Quantile>.
Quantiles are a non-parametric (model-agnostic) measures to specify a point in
a distribution. Once you assume a distribution, then the quantile can be
translated to the distribution parameters through the inverse of the
cumulative distribution function
<https://en.wikipedia.org/wiki/Cumulative_distribution_function>, or the
Quantile function <https://en.wikipedia.org/wiki/Quantile_function>. This was
one of the main reason we adopted this low-level, non-parametric scale for the
user to specify the threshold.

However, the threshold is only found when the median and mode of the
distribtuion are approximately equal (signal has not skewed the noise
distribtion significantly). In the context of observational noise, the only
relevant distribution (that I can think of right now) that has this property
is the Gaussian distribution
<https://en.wikipedia.org/wiki/Normal_distribution>.

Since astronomers are more accustommed to think parametrically (and most
commonly with a Gaussian distribution), it might be better to specify these
initial thresholds in units of the Gaussian sigma and not quantile. 

I am still considering which one to choose and I might be missing some points,
so I am opening this task as a discussion point to find the best way forward.




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