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.
The window is divided into 5 parts.
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.
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.
The third, the parameters field, allows the user to define parameters that are separated by
,
. For example, if you set parameters with the expressionfactor=0.8, K=0.2
, all the occurences offactor
andK
in the formula above will be replaced by 0.8 and 0.2 respectively.Ha * factor + OIII * K
would therefore evaluate toHa * 0.8 + OIII * 0.2
.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
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. Doubleclick on the formula to copy it to the right entry.
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.
Examples
Let's take a monochrome image of galaxies This is a linear data seen through the autostretch view.
The following expression:
iif(Image>med(Image)+3*noise(Image), 1, 0)
will produce a star mask.
Siril command line
pm "expression" [rescale [low] [high]] [nosum]
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).
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 ) 
Base10 logarithm of x. 
log10 
log10 ( x ) 
Base10 logarithm of x. 
log2 
log2 ( x ) 
Base2 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. 
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
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. 