# Image stretching

Image are stored as pixel values that come from the camera following a quasi-linear law, meaning that for areas of the sky that show no visible feature, the pixel value will be close to zero, but for bright objects like stars it will be close to a maximum value depending on exposure and gain. In between, if a nebula has a surface magnitude half of a star, it will have pixel values half of those of the star and so on. This is what we call the linear pixel mode.

The human eye doesn't quite see photons like that. It amplifies dark areas, so that an object maybe a tenth as bright as another would look half as bright. For astronomy images, we usually display images with a similar pixel value scaling (see display modes from the GUI).

But it is only a display trick, using a screen transfer function, to render the pixel values of the untouched image to better looking images.

Image stretching is about doing something similar but by modifying the pixel values of images instead of just altering their rendering. Siril has three main tools to achieve this.

## Asinh transformation

The asinh, or inverse hyperbolic sine, transformation will modify image pixel values in a way similar to what can be seen with the asinh display pixel scaling function, which is parametrized by the low and high values cut-off cursors. Here the parameters are the stretch factor and the black point value.

For monochrome images, pixel values are modified using the following function:

$\text{pixel} = \frac{(\text{original} - \text{blackpoint})\times\text{asinh}(\text{original}\times\text{stretch})}{\text{original}\times\text{asinh}(\text{stretch})}$

For color images, the function becomes:

$\text{pixel} = \frac{(\text{original} - \text{blackpoint})\times\text{asinh}(\text{rgb}\_\text{original}\times\text{stretch})}{\text{rgb}\_\text{original}\times\text{asinh}(\text{stretch})}$

where rgb_original is computed using the pixel values of the three channels.

Note

As rgb_original is an average of the 3 channels, one or two channel values will be greater than rgb_original and can therefore clip. This can cause color artefacts when bright, strongly-colored regions are stretched. In order to avoid this problem the RGB blend clipping algorithm is used. This was devised by the same authors as the Generalised Hyperbolic Stretch transforms. The $$(r, g, b)$$ values are stretched first based on the luminance value rgb_original to give $$(r', g', b')$$. Then the original $$(r, g, b)$$ values are independently stretched to give $$(r", g", b")$$. Finally the largest value of $$k$$ is identified such that

$$k * r' + ( 1 - k ) * r" ≤ 1$$;

$$k * g' + ( 1 - k ) * g" ≤ 1$$;

and

$$k * b' + ( 1 - k ) * b" ≤ 1$$

Then the transformed values are calculated as

$$( k * r' + ( 1 - k ) * r", k * g' + ( 1 - k ) * g", k * b' + ( 1 - k ) * b")$$

This RGB blend clipping algorithm is also used for the Generalised Hyperbolic Stretch transforms described below.

When the Use RGB working space option is not ticked, rgb_original is the mean between the three pixel values; when it is set, ponderation changes to 0.2126 for the red value, 0.7152 for the green value and 0.0722 for the blue value, which gets results closer to color balance.

Siril command line

asinh [-human] stretch [offset]

Stretches the image to show faint objects using an hyperbolic arcsin transformation. The mandatory argument stretch, typically between 1 and 1000, will give the strength of the stretch. The black point can be offset by providing an optional offset argument in the normalized pixel value of [0, 1]. Finally the option -human enables using human eye luminous efficiency weights to compute the luminance used to compute the stretch value for each pixel, instead of the simple mean of the channels pixel values. This stretch method preserves lightness from the L*a*b* color space

## Midtone Transfer Function Transformation (MTF)

MTF is one of the most powerful tools for stretching the image. It can be easily automated and that's why the auto-stretched view uses it.

The tool is presented in the form of a histogram with 3 sliders (in the form of a triangle placed underneath) that we must move to transform the image. The triangle on the left represents the shadow signal, the one on the right the highlights and finally, the one in the middle the midtone balance parameter. The values of these sliders are displayed below the histogram, on the left, and can be changed directly by hand. Opposite is the percentage of pixels that are clipped by the transformation: it is important not to clip too many pixels. If only the midtones parameter is changed, then no pixel can be clipped.

The new pixel values are then computed with this function:

(1)$\begin{split}\text{MTF}(x_p) = \frac{(m - 1)x_p}{(2m - 1)x_p - m} \\\end{split}$
• For $$x_p=0$$, $$\text{MTF} = 0$$.

• For $$x_p=m$$, $$\text{MTF} = 0.5$$.

• For $$x_p=1$$, $$\text{MTF} = 1$$.

where $$x_p$$ is the pixel value defined as follow

(2)$x_p=\frac{\text{original}-\text{shadows}}{\text{highlights}-\text{shadows}}$

Note

It is generally not recommended to change the value of the highlights, otherwise they will become saturated and information will be lost.

The toolbar contains many buttons that affect the visualization of the histogram. You can choose to display the input histogram, the output histogram, the transfer curve and the grid. The button allows you to apply the same transformation as the autostretch algorithm. It is rarely advisable to use this button as is. Adjustments are usually necessary to avoid losing information. At the top of the histogram it is also possible to choose to display the histogram in logarithmic view, as in the illustration. This behavior can be made default as explained here. Finally a zoom in X is available. This is very useful when all the signal is concentrated on the left of the histogram.

Siril command line

mtf low mid high [channels]

Applies midtones transfer function to the current loaded image.

Three parameters are needed, low, midtones and high where midtones balance parameter defines a nonlinear histogram stretch in the [0,1] range. For an automatic determination of the parameters, see AUTOSTRETCH.
Optionally the parameter [channels] may be used to specify the channels to apply the stretch to: this may be R, G, B, RG, RB or GB. The default is all channels

Note

mtf is also a function that can be used in the PixelMath tool.

Siril command line

autostretch [-linked] [shadowsclip [targetbg]]

Auto-stretches the currently loaded image, with different parameters for each channel (unlinked) unless -linked is passed. Arguments are optional, shadowclip is the shadows clipping point, measured in sigma units from the main histogram peak (default is -2.8), targetbg is the target background value, giving a final brightness to the image, range [0, 1], default is 0.25. The default values are those used in the Auto-stretch rendering from the GUI.

Do not use the unlinked version after color calibration, it will alter the white balance

Applying transformation to the sequence

This transformation can easily be applied to a sequence. You just have to define the transformation on the loaded image (with a sequence already loaded), then check the Apply to sequence button and define the output prefix of the new sequence (stretch_ by default), or use the following command:

Siril command line

seqmtf sequencename low mid high [channels] [-prefix=]

Same command as MTF but for the sequence sequencename.

The output sequence name starts with the prefix "mtf_" unless otherwise specified with -prefix= option

## Generalised Hyperbolic Stretch transformations (GHS)

This is the most capable and modern tool of Siril, also the most complex to learn. A very detailed tutorial for this tool in Siril was written by the authors of this algorithm: https://siril.org/tutorials/ghs. Here, we will just summarize here the basic operation of this tool.

Simply put, the GHS is able to improve the contrast of a range of brightness levels in an image. For example, if one wanted to better view the details in the medium to high brightness part of a nebula (which is in general very faint in an astronomy image), it would be possible to only select this range for stretching. It is very good at improving the contrast of main objects without making stars too big. The tool is very much based on iterative use, so stretching all the different ranges of brightnses in the image one after the other, by small touches.

To achieve this, the tool relies heavily on histogram display and interaction, for each color channel. The transformation function, shaped like a hyperbole or an 'S', can be altered by moving its center (the SP - symmetry point parameter), by flattening either of its ends (with shadow and highlight protections), and of course its twist (stretch D and local stretch b factors). Manipulating these parameters on a small (for speed) image with an SP value of 0.5 will help you understanding their effect.

There are two main operations to do on each iteration: selecting the range of lights to modify, and actually modifying it. Selecting the range is quite easy, it's a matter of finding a representative value (SP) and defining the width of the range (b). Setting SP can be done in three ways:

• selecting an area of similar brightness in the image and clicking on the picker button

• clicking on the histogram itself with a single left click (it is possible to zoom in the histogram using the + button at the top left)

• using the cursor or its associated plus and minus buttons or direct value.

The width of the range depends on the local stretch. A high value of b will make a small range, and increase contrast over a small range of brightnesses in the image.

Modifying the histogram once the location of the change has been set is a more complex operation. One goal given by the algorithm's authors is to make the logarithmic view of the histogram (enabled by checking the box) as close as possible to a decreasing line. To do this, bumps need to be carved out and valleys to be filled. Here is a quick guide of values to use depending on what needs to be achieved:

• initial stretch from linear: set SP slightly to the left of the main peak, moderate b value from 6 and up, increase D slightly only to start to see the main object. Do not stretch too much at this point like an autostretch would do, otherwise the stars would grow too big (main tutorial section for this).

• improving contrast of a range, or filling a valley: set SP to the centre of the valley in the histogram, set b as high as how narrow the range or valley is, decrease HP to preserve stars, increase D slowly until the improvement appears.

• decreasing contrast of a range, or flattening a peak: decreasing a peak is not easy to do but will happen as a side effect of valleys being filled. For example, creating a peak, or filling a valley, will decrease what is on the left of SP. Another possibility is to use the inverse transformation, from the Type of stretch combo box, and a high LP value, and HP at 1.

• move curve to the left, making the image darker: often if we stretched the entire histogram, the peak will move to the right, making the background too bright. There is a simple way to just move everything to the left, select in the Type of stretch combo box the last entry, Linear stretch (BP shift). There's only one cursor to move now, controlling how much it will shift.

Some operations are also common for color images, where we often want to have a similar shape of curve for the three channels, working on each channel independently by unselecting them with the three colored circles below the histogram view:

• moving the peak to the right: a simple strech with a SP value left of the peak will do that in general, so this should be done as part of a stretch.

• spreading a peak: to stretch a channel a bit more and it give it more importance in the final result, without changing the location of the peak too much, set SP near the peak or slightly to its right, set b depending on how the contribution is expected throughout the channel, between a negative value if the impact shall be felt up to the stars levels (to change their color) and a high value if this is only for a nebula, increase D to obtain the target width of the peak, and then offset the peak to the left by increasing HP.

• moving all channels together: an alternative luminance mapping stretch exists, see the Color stretch model combo box at the top right of the GHS window, using either luminance stretch values will stretch the luminance and reapply colors on it instead of stretching directly the three channels. The luminance modes can be better at preserving colours in the image. These modes use the same RGB blend clipping mode described above to prevent color channel clipping artefacts.

• remapping image saturation: the GHS transforms can be applied to the image saturation channel by selecting the Saturation option from the Color stretch model combo box. When this mode is selected the pre- and post- stretch saturation histograms will be shown in yellow. All the GHS options are available and this mode can provide highly targeted adjustment of the image saturation channel. A simple method of increasing the saturation in relatively unsaturated regions while preventing oversaturation is to use an Inverse generalised hyperbolic transform stretch with SP set to around 0.5, and HP brought down low enough to flatten the upper end of the saturation histogram. The image above shows how applying the GHS tool to the saturation channel gives an easy way of strongly enhancing saturation in a low-saturation image while still retaining control of the upper end of the saturation histogram, here used to create a 'Mineral Moon' image highlighting the differing mineral composition of different regions of the lunar surface.

Siril command line

ght -D= [-B=] [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels]

Generalised hyperbolic stretch based on the work of the ghsastro.co.uk team.

The argument -D= defines the strength of the stretch, between 0 and 10. This is the only mandatory argument. The following optional arguments further tailor the stretch:
B defines the intensity of the stretch near the focal point, between -5 and 15;
LP defines a shadow preserving range between 0 and SP where the stretch will be linear, preserving shadow detail;
SP defines the symmetry point of the stretch, between 0 and 1, which is the point at which the stretch will be most intense;
HP defines a region between HP and 1 where the stretch is linear, preserving highlight details and preventing star bloat.
If omitted B, LP and SP default to 0.0 ad HP defaults to 1.0.
An optional argument (either -human, -even or -independent) can be passed to select either human-weighted or even-weighted luminance or independent colour channels for colour stretches. The argument is ignored for mono images. Alternatively, the argument -sat specifies that the stretch is performed on image saturation - the image must be color and all channels must be selected for this to work.
Optionally the parameter [channels] may be used to specify the channels to apply the stretch to: this may be R, G, B, RG, RB or GB. The default is all channels

Siril command line

invght -D= [-B=] [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels]

Inverts a generalised hyperbolic stretch. It provides the inverse transformation of GHT, if provided with the same parameters, undoes a GHT command, possibly returning to a linear image. It can also work the same way as GHT but for images in negative

Siril command line

modasinh -D= [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels]

Modified arcsinh stretch based on the work of the ghsastro.co.uk team.

The argument -D= defines the strength of the stretch, between 0 and 10. This is the only mandatory argument. The following optional arguments further tailor the stretch:
LP defines a shadow preserving range between 0 and SP where the stretch will be linear, preserving shadow detail;
SP defines the symmetry point of the stretch, between 0 and 1, which is the point at which the stretch will be most intense;
HP defines a region between HP and 1 where the stretch is linear, preserving highlight details and preventing star bloat.
If omitted LP and SP default to 0.0 ad HP defaults to 1.0.
An optional argument (either -human, -even or -independent) can be passed to select either human-weighted or even-weighted luminance or independent colour channels for colour stretches. The argument is ignored for mono images. Alternatively, the argument -sat specifies that the stretch is performed on image saturation - the image must be color and all channels must be selected for this to work.
Optionally the parameter [channels] may be used to specify the channels to apply the stretch to: this may be R, G, B, RG, RB or GB. The default is all channels

Siril command line

invmodasinh -D= [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels]

Inverts a modified arcsinh stretch. It provides the inverse transformation of MODASINH, if provided with the same parameters, undoes a MODASINH command, possibly returning to a linear image. It can also work the same way as MODASINH but for images in negative

Siril command line

linstretch -BP= [-sat] [channels]

Stretches the image linearly to a new black point BP.
The argument [channels] may optionally be used to specify the channels to apply the stretch to: this may be R, G, B, RG, RB or GB. The default is all channels.
Optionally the parameter -sat may be used to apply the linear stretch to the image saturation channel. This argument only works if all channels are selected

Applying transformation to the sequence

This transformation can easily be applied to a sequence. You just have to define the transformation on the loaded image (with a sequence already loaded), then check the Apply to sequence button and define the output prefix of the new sequence (stretch_ by default). All of the commands have a sequence processing form too. Each sequence stretching command starts with seq and the first argument must be the sequence name, but they are otherwise the same.

Siril command line

seqght sequence -D= [-B=] [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels] [-prefix=]

Same command as GHT but the sequence must be specified as the first argument. In addition, the optional argument -prefix= can be used to set a custom prefix

Siril command line

seqinvght sequence -D= [-B=] [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels] [-prefix=]

Same command as INVGHT but the sequence must be specified as the first argument. In addition, the optional argument -prefix= can be used to set a custom prefix

Siril command line

seqmodasinh sequence -D= [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels] [-prefix=]

Same command as MODASINH but the sequence must be specified as the first argument. In addition, the optional argument -prefix= can be used to set a custom prefix

Siril command line

seqinvmodasinh sequence -D= [-LP=] [-SP=] [-HP=] [-human | -even | -independent | -sat] [channels] [-prefix=]

Same command as INVMODASINH but the sequence must be specified as the first argument. In addition, the optional argument -prefix= can be used to set a custom prefix

Siril command line

seqlinstretch sequence -BP= [channels] [-sat] [-prefix=]

Same command as LINSTRETCH but the sequence must be specified as the first argument. In addition, the optional argument -prefix= can be used to set a custom prefix