Formulas¶

The formula should be a mathematical expression containing: band names, operators and functions. Available bands for supported data blocks are listed in supported blocks section.

Basic arithmetics¶

Available bands can be referenced by their name. You can add, subtract, multiply and divide. Example:

"((BAND1 + BAND2 - BAND3) / 2) * 5"

Functions¶

The following functions are available in formulas:

Rounding¶

round(x)
ceil(x)
floor(x)

Trigonometric¶

sin(x)
cos(x)
tan(x)
sinh(x)
cosh(x)
tanh(x)
arcsin(x)
arccos(x)
arctan(x)

Logarithm and exponentiation¶

sqrt(x)
log(x)
log2(x)
log10(x)
exp(x)
relu(x) - rectified linear unit
sigmoid(x)
expit(x) - alias for sigmoid

Summary statistics¶

min(x) - the minimum value of the entire band in the current image
max(x)- the maximum value of the entire band in the current image
std(x) - the standard deviation of values in the band in the current image
var(x) - the variance of values in the band in the current image
mean(x) - the mean value of the entire band in the current image
median(x) - the median value of the entire band in the current image

Miscellaneous¶

abs(x)
threshold(x, t) - returns 1 for x >= t and 0 otherwise

Example:

"threshold(abs(BAND1 - BAND2), 12.5) * 255"

Convolution¶

Use @ operator or convolve function with an array of constant values to apply a convolutional filter to a band.

There are also several predefined filters:

box_blur(x) - uses [[1, 1, 1], [1, 1, 1], [1, 1, 1]] / 9 kernel
gauss_blur(x) - uses [[1, 2, 1], [2, 4, 2], [1, 2, 1]] / 16 kernel
edges(x) - uses [[-1, -1, -1], [-1, 8, -1], [-1, -1, -1]] kernel
sobel_x(x) - uses [[1, 0, -1], [2, 0, -2], [1, 0, -1]] kernel
sobel_y(x) - uses [[1, 2, 1], [0, 0, 0], [-1, -2, -1]] kernel

Examples:

"(BAND1 @ [[1, 2, 1], [2, 4, 2], [1, 2, 1]]) / 16"
"(convolve(BAND1, [[1, 2, 1], [2, 4, 2], [1, 2, 1]]) / 16)"
"gauss_blur(BAND1)"

Operator Precedence¶

Priority	Operator	Associativity
0	`-` (unary)	right to left
1	`*` `/`	left to right
2	`+` `-`	left to right
3	`@`	left to right