## GNU Astronomy Utilities

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#### 7.1.3.2 Sky value misconceptions

As defined in Sky value, the sky value is only accurately defined when the detection algorithm is not significantly reliant on the sky value. In particular its detection threshold. However, most signal-based detection tools122 use the sky value as a reference to define the detection threshold. So these old techniques had to rely on approximations based on other assumptions about the data. A review of those other techniques can be seen in Appendix A of Akhlaghi and Ichikawa (2015)123. Since they were extensively used in astronomical data analysis for several decades, such approximations have given rise to a lot of misconceptions, ambiguities and disagreements about the sky value and how to measure it. As a summary, the major methods used until now were an approximation of the mode of the image pixel distribution and $$\sigma$$-clipping.

• To find the mode of a distribution those methods would either have to assume (or find) a certain probability density function (PDF) or use the histogram. But astronomical datasets can have any distribution, making it almost impossible to define a generic function. Also, histogram-based results are very inaccurate (there is a large dispersion) and it depends on the histogram bin-widths.
• Another approach was to iteratively clip the brightest pixels in the image (which is known as $$\sigma$$-clipping, since the reference was found from the image mean and its standard deviation or $$\sigma$$). See Sigma clipping for a complete explanation. The problem with $$\sigma$$-clipping was that real astronomical objects have diffuse and faint wings that penetrate deeply into the noise. So only removing their brightest parts is completely useless in removing the systematic bias an object’s fainter parts cause in the sky value.

As discussed in Sky value, the sky value can only be correctly defined as the average of undetected pixels. Therefore all such approaches that try to approximate the sky value prior to detection are ultimately poor approximations.

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According to Akhlaghi and Ichikawa (2015), signal-based detection is a detection process that relies heavily on assumptions about the to-be-detected objects. This method was the most heavily used technique prior to the introduction of NoiseChisel in that paper.

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Akhlaghi M., Ichikawa. T. (2015). Astrophysical Journal Supplement Series.

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