Within an image, pixels have both a position and a value. In the sections above all the measurements involved position (see Position measurements in pixels or Position measurements in WCS). The measurements in this section only deal with pixel values and ignore the pixel positions completely. In other words, for the options of this section each labeled region within the input is just a group of values (and their associated error values if necessary), and they let you do various types of measurements on the resulting distribution of values.

`--sum`The sum of all pixel values associated to this label (object or clump). Note that if a sky value or image has been given, it will be subtracted before any column measurement. For clumps, the ambient values (average of river pixels around the clump, multiplied by the area of the clump) is subtracted, see

`--river-mean`. So the sum of all the clump-sums in the clump catalog of one object will be smaller than the`--clumps-sum`column of the objects catalog.If no usable pixels are present over the clump or object (for example, they are all blank), the returned value will be NaN (note that zero is meaningful).

`--sum-error`The (\(1\sigma\)) error in measuring the sum of values of a label (objects or clumps).

The returned value will be NaN when the label covers only NaN pixels in the values image, or a pixel is NaN in the

`--instd`image, but non-NaN in the values image. The latter situation usually happens when there is a bug in the previous steps of your analysis, and is important because those pixels with a NaN in the`--instd`image may contribute significantly to the final error. If you want to ignore those pixels in the error measurement, set them to zero (which is a meaningful number in such scenarios).`--clumps-sum`[Objects] The total sum of the pixels covered by clumps (before subtracting the river) within each object. This is simply the sum of

`--sum-no-river`in the clumps catalog (see below). If no usable pixels are present over the clump or object (for example, they are all blank), the stored value will be NaN (note that zero is meaningful).`--sum-no-river`[Clumps] The sum of Sky (not river) subtracted clump pixel values. By definition, for the clumps, the average value of the rivers surrounding it are subtracted from it for a first order accounting for contamination by neighbors.

If no usable pixels are present over the clump or object (for example, they are all blank), the stored value will be NaN (note that zero is meaningful).

`--mean`The mean sky subtracted value of pixels within the object or clump. For clumps, the average river flux is subtracted from the sky subtracted mean.

`--std`The standard deviation of the pixels within the object or clump. For clumps, the river pixels are not subtracted because that is a constant (per pixel) value and should not affect the standard deviation.

`--median`The median sky subtracted value of pixels within the object or clump. For clumps, the average river flux is subtracted from the sky subtracted median.

`--maximum`The maximum value of pixels within the object or clump. When the label (object or clump) is larger than three pixels, the maximum is actually derived by the mean of the brightest three pixels, not the largest pixel value of the same label. This is because noise fluctuations can be very strong in the extreme values of the objects/clumps due to Poisson noise (which gets stronger as the mean gets higher). Simply using the maximum pixel value will create a strong scatter in results that depend on the maximum (for example, the

`--fwhm`option also uses this value internally).`--sigclip-number`The number of elements/pixels in the dataset after sigma-clipping the object or clump. The sigma-clipping parameters can be set with the

`--sigmaclip`option described in MakeCatalog inputs and basic settings. For more on Sigma-clipping, see Sigma clipping.`--sigclip-median`The sigma-clipped median value of the object of clump’s pixel distribution. For more on sigma-clipping and how to define it, see

`--sigclip-number`.`--sigclip-mean`The sigma-clipped mean value of the object of clump’s pixel distribution. For more on sigma-clipping and how to define it, see

`--sigclip-number`.`--sigclip-std`The sigma-clipped standard deviation of the object of clump’s pixel distribution. For more on sigma-clipping and how to define it, see

`--sigclip-number`.`-m``--magnitude`The magnitude of clumps or objects, see

`--sum`.`--magnitude-error`The magnitude error of clumps or objects. The magnitude error is calculated from the signal-to-noise ratio (see

`--sn`and Quantifying measurement limits). Note that until now this error assumes uncorrelated pixel values and also does not include the error in estimating the aperture (or error in generating the labeled image).For now these factors have to be found by other means. Task 14124 has been defined for work on adding these sources of error too.

The returned value will be NaN when the label covers only NaN pixels in the values image, or a pixel is NaN in the

`--instd`image, but non-NaN in the values image. The latter situation usually happens when there is a bug in the previous steps of your analysis, and is important because those pixels with a NaN in the`--instd`image may contribute significantly to the final error. If you want to ignore those pixels in the error measurement, set them to zero (which is a meaningful number in such scenarios).`--clumps-magnitude`[Objects] The magnitude of all clumps in this object, see

`--clumps-sum`.`--upperlimit`The upper limit value (in units of the input image) for this object or clump. This is the sigma-clipped standard deviation of the random distribution, multiplied by the value of

`--upnsigma`). See Quantifying measurement limits and Upper-limit settings for a complete explanation. This is very important for the fainter and smaller objects in the image where the measured magnitudes are not reliable.`--upperlimit-mag`The upper limit magnitude for this object or clump. See Quantifying measurement limits and Upper-limit settings for a complete explanation. This is very important for the fainter and smaller objects in the image where the measured magnitudes are not reliable.

`--upperlimit-onesigma`The \(1\sigma\) upper limit value (in units of the input image) for this object or clump. See Quantifying measurement limits and Upper-limit settings for a complete explanation. When

`--upnsigma=1`, this column’s values will be the same as`--upperlimit`.`--upperlimit-sigma`The position of the label’s sum measured within the distribution of randomly placed upperlimit measurements in units of the distribution’s \(\sigma\) or standard deviation. See Quantifying measurement limits and Upper-limit settings for a complete explanation.

`--upperlimit-quantile`The position of the label’s sum within the distribution of randomly placed upperlimit measurements as a quantile (value between 0 or 1). See Quantifying measurement limits and Upper-limit settings for a complete explanation. If the object is brighter than the brightest randomly placed profile, a value of

`inf`

is returned. If it is less than the minimum, a value of`-inf`

is reported.`--upperlimit-skew`¶This column contains the non-parametric skew of the \(\sigma\)-clipped random distribution that was used to estimate the upper-limit magnitude. Taking \(\mu\) as the mean, \(\nu\) as the median and \(\sigma\) as the standard deviation, the traditional definition of skewness is defined as: \((\mu-\nu)/\sigma\).

This can be a good measure to see how much you can trust the random measurements, or in other words, how accurately the regions with signal have been masked/detected. If the skewness is strong (and to the positive), then you can tell that you have a lot of undetected signal in the dataset, and therefore that the upper-limit measurement (and other measurements) are not reliable.

`--river-mean`[Clumps] The average of the river pixel values around this clump. River pixels were defined in Akhlaghi and Ichikawa 2015. In short they are the pixels immediately outside of the clumps. This value is used internally to find the sum (or magnitude) and signal to noise ratio of the clumps. It can generally also be used as a scale to gauge the base (ambient) flux surrounding the clump. In case there was no river pixels, then this column will have the value of the Sky under the clump. So note that this value is

*not*sky subtracted.`--river-num`[Clumps] The number of river pixels around this clump, see

`--river-mean`.`--river-min`[Clumps] Minimum river value around this clump, see

`--river-mean`.`--river-max`[Clumps] Maximum river value around this clump, see

`--river-mean`.`--sn`The Signal to noise ratio (S/N) of all clumps or objects. See Akhlaghi and Ichikawa (2015) for the exact equations used.

The returned value will be NaN when the label covers only NaN pixels in the values image, or a pixel is NaN in the

`--instd`image, but non-NaN in the values image. The latter situation usually happens when there is a bug in the previous steps of your analysis, and is important because those pixels with a NaN in the`--instd`image may contribute significantly to the final error. If you want to ignore those pixels in the error measurement, set them to zero (which is a meaningful number).`--sky`The sky flux (per pixel) value under this object or clump. This is actually the mean value of all the pixels in the sky image that lie on the same position as the object or clump.

`--sky-std`The sky value standard deviation (per pixel) for this clump or object. This is the square root of the mean variance under the object, or the root mean square.

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GNU Astronomy Utilities 0.21 manual, October 2023.