Pixel Math

One of the most powerful tools in Siril is the Pixel Math. It allows you to manipulate the pixels of the images using mathematical functions. From simple addition or subtraction, to more advanced functions, like MTF, Pixel Math is a perfect tool for astronomical image processing.

This page aims to describe the tool entirely, to see detailed examples, please refer to the excellent tutorial on the site.

Pixel Math dialog box as shown at opening

The window is divided into 5 parts.

1. The first one, including 3 text zones receiving the mathematical formulas. Only the first one is used if you want to produce a monochrome image. Uncheck the Use single RGB/K expression button to produce RGB output.

2. The second is the variables area with the selection of Functions and Operators. Each variable is an image that must be loaded beforehand with the + button. You can click on the desired function and/or operator to make it appear in the formula entry to make it appear in the formula entry.

3. The third, the parameters field, allows the user to define parameters that are separated by ,. For example, if you set parameters with the expression factor=0.8, K=0.2, all the occurences of factor and K in the formula above will be replaced by 0.8 and 0.2 respectively. Ha * factor + OIII * K would therefore evaluate to Ha * 0.8 + OIII * 0.2.

   

   Pixel Math parameters box

4. The output field is reserved for scaling the image within a given range and to enable or not the Sum exposure time. This last option gives the user the option of summing or not the exposures of individual images, storing the result in the FITS header. One need to expand the frame before using it.

   

   Pixel Math rescale box

5. Finally, the presets area allows the user to reuse previously saved formulas with the button to the right of the formula areas. One need to expand the frame before using it. Double-click on the formula to copy it to the right entry.

   

   Pixel Math presets

Usage

Name of variables

By default it is possible to load 10 images simultaneously. Each image is given a variable name starting with I followed by a number from 1 to 10. However, if the loaded image contains the keyword FILTER, then the value of the latter becomes the default variable name. Of course it is always possible to change it by double clicking on it.

It is possible to change the name of the variable.

Examples

Let's take a monochrome image of galaxies This is a linear data seen through the autostretch view.

Original image.

The following expression:

iif(Image>med(Image)+3*noise(Image), 1, 0)

will produce a star mask.

After the formula above.

Siril command line

pm "expression" [-rescale [low] [high]] [-nosum]

This command evaluates the expression given in argument as in PixelMath tool. The full expression must be between double quotes and variables (that are image names, without extension, located in the working directory in that case) must be surrounded by the token $, e.g. "$image1$ * 0.5 + $image2$ * 0.5". A maximum of 10 images can be used in the expression.

Image can be rescaled with the option -rescale followed by low and high values in the range [0, 1]. If no low and high values are provided, default values are set to 0 and 1. Another optional argument, -nosum tells Siril not to sum exposure times. This impacts FITS keywords such as LIVETIME and STACKCNT

Functions

There are two types of functions. Those that apply directly to the pixels and those that apply to the entire image (such as the statistics functions).

Pixel oriented functions

Function	Use case	Definition
abs	abs ( x )	Absolute value of x.
acos	acos ( x )	Arc cosine of x.
acosh	acosh ( x )	Hyperbolic arc cosine of x.
asin	asin ( x )	Arc sine of x.
asinh	asinh ( x )	Hyperbolic arc sine of x.
atan	atan ( x )	Arc tangent of x.
atan2	atan2 ( y, x )	Arc tangent of y/x.
atanh	atanh ( x )	Hyperbolic arc tangent of x.
ceil	ceil ( x )	Round x upwards to the nearest integer.
cos	cos ( x )	Cosine of x.
cosh	cosh ( x )	Hyperbolic cosine of x.
e	e	The constant e=2.718282...
exp	exp ( x )	Exponential function.
fac	fac( x )	Factorial function.
iif	iif( cond, expr_true, expr_false )	Conditional function (or inline if function). Returns expr_true if cond evaluates to nonzero. Returns expr_false if cond evaluates to zero.
floor	floor ( x )	Highest integer less than or equal to x.
ln	ln ( x )	Natural logarithm of x.
log	log ( x )	Base-10 logarithm of x.
log10	log10 ( x )	Base-10 logarithm of x.
log2	log2 ( x )	Base-2 logarithm of x.
max	max ( x, y )	Maximum function.
min	min ( x, y )	Minimum function.
mtf	mtf ( m, x )	Midtones Transfer Function (MTF) of x for a midtones balance parameter m in the [0, 1] range.
ncr	ncr ( x, y )	Combinations function.
npr	npr ( x, y )	Permutations function.
pi	pi	The constant π=3.141592...
pow	pow ( x, y )	Exponentiation function.
sign	sign ( x )	Sign of x: \(+1\) if \(x > 0\) \(−1\) if \(x < 0\) \(\;0\) if \(x = 0\).
sin	sin ( x )	Sine of x.
sinh	sinh ( x )	Hyperbolic sine of x.
sqrt	sqrt ( x )	Square root of x.
tan	tan ( x )	Tangent of x.
tanh	tanh ( x )	Hyperbolic tangent of x.
trunc	trunc ( x )	Truncated integer part of x.

Statistics functions

Function	Use case	Definition
adev	adev ( Image )	Average absolute deviation of the image.
bwmv	bwmv ( Image )	Biweight midvariance of the image.
height	height ( Image )	Height in pixels of the specified image.
mad	mad ( Image )	Median absolute deviation of the image. The use of mdev is also possible.
max	max ( Image )	Pixel maximum of the image.
mean	mean ( Image )	Mean of the image.
med	med ( Image )	Median of the image. The use of median is also possible.
min	min ( Image )	Pixel minimum of the image.
noise	noise ( Image )	Estimation of Gaussian noise in the image.
sdev	sdev ( Image )	Standard deviation of the image.
width	width ( Image )	Width in pixels of the specified image.

Operators

Operators

Operator	Use case	Definition
~	~x	Pixel Inversion operator.
-	-x	Unary Minus operator (sign change).
+	+x	Unary Plus operator.
!	!x	Logical NOT operator.
^	x ^ y	Exponentiation operator.
*	x * y	Multiplication operator.
/	x / y	Division operator.
%	x % y	Modulus operator.
+	x + y	Addition operator.
-	x - y	Subtraction operator.
<	x < y	Less Than relational operator.
<=	x <= y	Less Than Or Equal relational operator.
>	x > y	Greater Than relational operator.
>=	x >= y	Greater Than Or Equal relational operator.
==	x == y	Equal To relational operator.
!=	x != y	Not Equal To relational operator.
&&	x && y	Logical AND operator.
||	x || y	Logical OR operator.