Segment changes after publication (GNU Astronomy Utilities)

GNU Astronomy Utilities

7.3.1 Segment changes after publication

Segment’s main algorithm and working strategy were initially defined and introduced in Section 3.2 of Akhlaghi and Ichikawa [2015]. Prior to Gnuastro version 0.6 (released 2018), one program (NoiseChisel) was in charge of detection and segmentation. to increase creativity and modularity, NoiseChisel’s segmentation features were spun-off into a separate program (Segment). It is strongly recommended to read that paper for a good understanding of what Segment does, how it relates to detection, and how each parameter influences the output. That paper has a large number of figures showing every step on multiple mock and real examples.

However, the paper cannot be updated anymore, but Segment has evolved (and will continue to do so): better algorithms or steps have been (and will be) found. This book is thus the final and definitive guide to Segment. The aim of this section is to make the transition from the paper to your installed version, as smooth as possible through the list below. For a more detailed list of changes in previous Gnuastro releases/versions, please follow the NEWS file¹³⁴.

Since the spin-off from NoiseChisel, the default kernel to smooth the input for convolution has a FWHM of 1.5 pixels (still a Gaussian). This is slightly less than NoiseChisel’s default kernel (which has a FWHM of 2 pixels). This enables the better detection of sharp clumps: as the kernel gets wider, the lower signal-to-noise (but sharp/small) clumps will be washed away into the noise. You can use MakeProfiles to build your own kernel if this is too sharp/wide for your purpose. For more, see the --kernel option in Segment input.

The ability to use a different convolution kernel for detection and segmentation is one example of how separating detection from segmentation into separate programs can increase creativity. In detection, you want to detect the diffuse and extended emission, but in segmentation, you want to detect sharp peaks.

The criteria to select true from false clumps is the peak significance. It is defined to be the difference between the clump’s peak value ($C_c$) and the highest valued river pixel around that clump ($R_c$). Both are calculated on the convolved image (signified by the $c$ subscript). To avoid absolute values (differing from dataset to dataset), $C_c-R_c$ is then divided by the Sky standard deviation under the river pixel used ($\sigma_r$) as shown below:

$$C_c-R_c\over \sigma_r$$

When --minima is given, the nominator becomes $R_c-C_c$.

The input Sky standard deviation dataset (--std) is assumed to be for the unconvolved image. Therefore a constant factor (related to the convolution kernel) is necessary to convert this into an absolute peak significance¹³⁵. As far as Segment is concerned, the absolute value of this correction factor is irrelevant: because it uses the ambient noise (undetected regions) to find the numerical threshold of this fraction and applies that over the detected regions.

A distribution’s extremum (maximum or minimum) values, used in the new criteria, are strongly affected by scatter. On the other hand, the convolved image has much less scatter¹³⁶. Therefore $C_c-R_c$ is a more reliable (with less scatter) measure to identify signal than $C-R$ (on the unconvolved image).

Initially, the total clump signal-to-noise ratio of each clump was used, see Section 3.2.1 of Akhlaghi and Ichikawa [2015]. Therefore its completeness decreased dramatically when clumps were present on gradients. In tests, this measure proved to be more successful in detecting clumps on gradients and on flatter regions simultaneously.

With the new --minima option, it is now possible to detect inverse clumps (for example absorption features). In such cases, the clump should be built from its smallest value.

Footnotes

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The NEWS file is present in the released Gnuastro tarball, see Release tarball.

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To get an estimate of the standard deviation correction factor between the input and convolved images, you can take the following steps: 1) Mask (set to NaN) all detections on the convolved image with the where operator or Arithmetic. 2) Calculate the standard deviation of the undetected (non-masked) pixels of the convolved image with the --sky option of Statistics (which also calculates the Sky standard deviation). Just make sure the tessellation settings of Statistics and NoiseChisel are the same (you can check with the -P option). 3) Divide the two standard deviation datasets to get the correction factor.

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For more on the effect of convolution on a distribution, see Section 3.1.1 of Akhlaghi and Ichikawa [2015].