GaussClumps

This is based on the algorithm described by Stutzki & Gusten (1990, ApJ 356, 513). This algorithm proceeds by fitting a Gaussian profile to the brightest peak in the data. It then subtracts the fit from the data and iterates, fitting a new ellipse to the brightest peak in the residuals. This continues until any one of the ``termination criteria'' described below is satisfied. Each fitted ellipse is taken to be a single clump and is added to the output catalogue. In this algorithm, clumps may overlap, and for this reason each input pixel cannot simply be assigned to a single clump (as can be done for algorithms such as FellWalker or ClumpFind). Therefore, when using GassClumps, the primary output NDF from FINDCLUMPS does not hold the clump index at each input pixel. Instead it holds the sum of all the fitted Gaussian that contribute to each input pixel position.

Any input variance component is used to scale the weight associated with each pixel value when performing the Gaussian fit. The most significant configuration parameters for this algorithm are: GaussClumps.FwhmBeam and GaussClumps.VeloRes which determine the minimum clump size, and GaussClumps.Thresh which (together with the ADAM parameter RMS) determine the second of the above termination criteria.

Note, this implementation of the GaussClumps algorithm is a completely independent re-write, and includes some differences from other GaussClumps implementations. Specifically, these include the following modifications.

• The Gaussian fitting is based on the SUMSL module (algorithm 611) from the TOMS library available from http://www.netlib.org/.

• Any available variance information is used to weight the pixels when doing the Gaussian fit. This is in addition to the Gaussian weighting function implied by configuration parameters GaussClumps.Wwidth and GaussClumps.Wmin.

• The termination criteria are different. FINDCLUMPS stops finding further clumps if any one of the following criteria is met.
  1. the total data sum in the fitted Gaussians is equal to or exceeds the total data sum in the supplied input data (this is the original termination criterion used by Stutzki & Gusten).

  2. The number of clumps already found equals the value of configuration parameter GaussClumps.MaxClumps.

  3. The number of consecutive fitted peaks with peak value below the value of configuration parameter GaussClumps.Thresh reaches the value of configuration parameter GaussClumps.NPad (the final group of NPad clumps are not included in the returned list of usable clumps).

  4. The number of failed attempts to fit consecutive clumps reaches the value of configuration parameter GaussClumps.MaxSkip.

• A clump will be ignored if its fitted peak value is a long way above or below the peak value of the previously fitted clump. The definition of ``a long way'' is more than GaussClumps.NSigma times the standard deviation of the previous GaussClumps.NPeak fitted peaks. This restriction is only imposed once GaussClumps.NPeak peaks have been fitted.

• In certain situations the chi-squared value that is minimised when fitting a Gaussian clump to a peak in the data array may be dominated by pixels that are largely unaffected by changes in the parameters of the Gaussian clumps¹. This can result in a very poor fit to the clump. To avoid this at attempt is made to identify such pixels and to lower the weight associated with them.