fx

Fx allows general arithmetic operations to be performed on an arbitrary number of input cubes. Fx loads whatever input files are specified, applies a user defined equation to those files and writes the results to an output file. The input file can be a single band or multiple band cube file. If the band number is not specified for the multiple band cube file, then the equation is applied to all the bands within the file.

Five files or fewer can be entered for parameters F1 to F5 under the "Input Cube Files" section to specify the input data. A second method to specify data is to include an arbitrary number of files in a file list and enter the list name in the fromlist parameter that is only visible upon selecting the MODE list located under "File I/O Mode." If the user selects "OUPUTONLY" under "File I/O Mode" then an output file is created based on an equation provided by the user. The user will also need to specify the number of lines, samples, and bands of the output file.

The command line parsing has been improved to handle escape sequences and support arrays better. The equation parser is case insensitive, ignores whitespace, and converts all braces to parentheses. Parameter values, when quoted, no longer need the quotes escaped.

The command line syntax changes are as follows (with TCSH/BASH examples):

TCSH/BASH
Before: crop from=\"some file.cub\" to=\"output file.cub\"
Now: crop from="some file.cub" to="output file.cub"

Please note that the dollar sign ($) still requires a backslash for batchlist variables. Array values, for programs such as spiceinit, will be the same.

TCSH
Before: spiceinit from=input.cub ck='(file1.bc,file2.bc)'
Now: spiceinit from=input.cub ck='(file1.bc,file2.bc)'

BASH
Before: spiceinit from=input.cub ck='(file1.bc,file2.bc)'
Now: spiceinit from=input.cub ck='(file1.bc,file2.bc)'

An escape character "\" has been added to differentiate a first parenthesis from the beginning of an array sequence.

TCSH
Before: fx equation='"(1+2)/2"'
Now: fx equation='\(1+2)/2'

BASH
Before: fx equation='"(1+2)/2"'
Now: fx equation=\(1+2)/2

The equation string entered within a GUI interface may not work if the entire string is copied, pasted, and executed at the command line. If the first character in the equation is a "(" then it must be prefixed by a "\" when executing as a command line, but the remaining parentheses do not need to be prefixed with a backslash.

Example:

This equation string works inside the fx GUI:
fx f1=BIFQF23N004_D218_T069S02_V02_I3.cub to=tt.cub equation=(f1*(f1>.004))

These equation strings fail on the command line:
fx f1=BIFQF23N004_D218_T069S02_V02_I3.cub to=tt.cub equation=(f1*(f1>.004))

fx f1=BIFQF23N004_D218_T069S02_V02_I3.cub to=tt.cub equation="(f1*(f1>.004))"

This equation string works on the command line:
fx f1=BIFQF23N004_D218_T069S02_V02_I3.cub to=tt.cub equation="\(f1*(f1>.004))"

Note: The use of negative numbers within an equation could cause problems in the latest version of ISIS. The "--" or "neg" operators are specifically designed to handle negative numbers within an equation. If an equation includes a negative number, prefix the value with a "--" instead of "-" in the equation.

Example:

equation="f1*(--0.018*sec*(f3*pi/180)^2+f2+4.4234)"

or

equation="f1*(neg(0.018)*sec*(f3*pi/180)^2+f2+4.4234)"

For additional information see Command Line Usage under the User Documentation web pages for ISIS.
Note: Some instructions may be outdated.

The equation parser is case insensitive and all braces, such as "[{[{ }]}]" are converted to parentheses "(((( ))))" first. Whitespace is ignored. Currently, you must explicitly state all multiplication operations (e.g. 2pi will not work, but 2*pi will). The modulus (%), AND, and OR operators are not implemented yet. Functions such as pha, ina, ema, lat, lon, radius, and resolution require a Level1 input file with SPICE information in the image labels. That is, the program spiceinit should be executed on the input files before using these functions. For Level2 images, the backplanes containing the photometric and spatial information must be present. This is normally performed with the program phocube before the image is projected to a map projection.

Requirements and result of operators

The following operators return a "0" or "1" DN value when they are used in the equations:

< , >, <=, >=, ==, !=

The following operators are used to shift pixels left or right, and move the entire image to different sample and line positions:

<<, >>

Example:

Some pixels are set to NULL depending on whether the left or right pixel shift operation is used. For example, the left image below is the input file, and the right image is the result of "equation = f1 << 10", which shows a 10 pixel shift to the left.

Sample 1 line 1 of the left image maps outside the image area of the right image; therefore, sample 11 line 1 of the left image maps to sample 1 line 1 of the right image, and sample 12 line 1 of the left image maps to sample 2 line 1 of the right image. The remaining pixels that do not have an assigned pixel value are set to NULL.

The following operators use the input image statistics to apply the equations:

linemin, linemax, cubemin, cubemax, cubeavg, cubestd

The min and max operators are used to compare two pixel values. The pixel values can be obtained from input files or manually entered by the user. The two values are compared against each other and the one that meets the equation criteria is used.

min, max

In order to use the camera operators, images must be processed through spiceinit so that the NAIF camera model information is stored in the image labels. These operators calculate values on a band-by-band basis so that band-dependent images have correctly calculated camera-related values.

pha, phal, phac, ina, inal, inac, ema, emal, emac
lat, lon, radius, resolution

The following operators are used to convert between degrees and radians:

rads, degs

All trigonometric functions expect angles in radians, not degrees. However, all camera functions return angles in degrees and therefore should be converted to radians.

The following table shows all currently supported scalars and special tokens:

SCALARS
Scalar	Description	Example
F#	File operator	f3 denotes third file
# or #.# or .#	Any integer or double	12, 3.14, .007 are all valid
band	Current band number	f1 * band
line	Current line number	line + f1
sample	Current sample number	sample / line + f1
pi	Pi (3.14159...)	f1 > (e^pi)
e	Euler's number (2.71828...)	f1 == ln(e)

The following table shows all currently supported operators sorted by precedence (0 = highest precedence). All examples are valid equations that assume one or more files (F1, F2, etc.) are loaded:

OPERATORS
Precedence Level	Operator	Description	Example
0	{ [ ( ) ] }	Parentheses, brackets, or braces	f2*(f1+[30-{line/pi}])
1	-- or neg	Negative sign	--f1 + f2 or neg(f1) + f2
1	abs	Absolute value	abs(f2 - f1)
1	min	Minimum of two DNs	f1 + min(5, f2) + min(f2, f3)
1	max	Maximum of two DNs	20 * max(f1,f2)
1	linemin	Minimum of DNs on the current line	f1 + linemin(f2)
1	linemax	Maximum of DNs on the current line	f1 + linemax(f2)
1	cubemin	Minimum of a cube	f1 + cubemin(f2)
1	cubemax	Maximum of a cube	f1 + cubemax(f2)
1	cubeavg	Average of a cube	f1 / cubeavg(f1)
1	cubestd	Standard deviation of a cube	f1 * (abs(f1-cubeavg(f1)) < 2*cubestd(f1))
1	sin	Sine	f1 * sin(123/321)
1	cos	Cosine	cos(.02*50)
1	tan	Tangent	tan(f1/f2)
1	csc	Cosecant	12.3 + csc(f1)
1	sec	Secant	sin(pi/60) + (sec(f2))^2
1	cot	Cotangent	line + cot(f1) - 42
1	asin	Arcsine	0.006 ^ asin(f1*5)
1	acos	Arccosine	acos(1/[2*pi])
1	atan	Arctangent	atan(f1/e)
1	atan2	Arctangent2	atan2(--10 5.5)
1	sinh	Hyperbolic sine	55 + sinh(f2)
1	cosh	Hyperbolic cosine	cosh(sample^pi)
1	tanh	Hyperbolic tangent	tanh(f1)
1	log or ln	Natural log	ln(abs(1/[f2-f1]))
1	log10	Log base 10	99 + log10(f1-160)
1	sqrt	Square root	sqrt(abs[1000 - f2])
1	pha	Phase angle on the ellipsoid	pha(f1)
1	ina	Incidence angle on the ellipsoid	ina(f1)
1	ema	Emission angle on the ellipsoid	ema(f1)
1	phal	Local phase angle on DTM	phal(f1)
1	inal	Local incidence angle on DTM	inal(f1)
1	emal	Local emission angle on DTM	emal(f1)
1	phac	Phase angle on the ellipsoid at image center	phac(f1)
1	inac	Incidence angle on the ellipsoid at image center	inac(f1)
1	emac	Emission angle on the ellipsoid at image center	emac(f1)
1	rads	Convert degrees to radians	f1 / cos(rads(pha(f1)))
1	degs	Convert radians to degrees	degs(acos(f1))
1	lat	Latitude	lat(f1)
1	lon	Longitude	lon(f1)
1	radius	Radius of DTM in meters	radius(f1)
1	res	Pixel resolution in meters	res(f1)
2	^	Exponent	f1 ^ 3
3	*	Multiplication	10 * f1
3	/	Division	f2 / f1
4	<<	Left shift (Note: pixel shift, not bitwise)	f1 << 250
4	>>	Right shift (Note: pixel shift, not bitwise)	f2 + (f1 >> 500)
5	+	Addition	123 + 0.004 + f1
5	-	Subtraction	10 - (--f1)
6	>	Greater than (Note: result is 0 or 1)	f1 > f2
6	<	Less than (Note: result is 0 or 1)	f1 * (f1 < cubeavg(f1))
6	<=	Less than or equal (Note: result is 0 or 1)	f1 <= 0.505
6	>=	Greater than or equal (Note: result is 0 or 1)	f1 * (f1 >= 101)
6	==	Equal to (Note: result is 0 or 1)	f1 == (f2/2)
6	!=	Not equal to (Note: result is 0 or 1)	f1 != f2

In this example, two images with the same filename but have two different bands will be added to each other.

fx f1=../isisTruth.cub+1 f2=../isisTruth.cub+2 to=../result.cub equation=f1+ f2

fx GUI

Example GUI Screenshot of GUI with parameters filled in to perform a calculation on the input image.

Input image	Input file band 1 Parameter Name: F1 This is the first input image for the fx example.
Input image	Input file band 2 Parameter Name: F2 This is the second input image for the fx example.

Output image

Output file Parameter Name: TO This is the 500 by 500 output image containing the results. Parameter Name: EQUATION "f1+ f2"

In this example, an output file that is 360 samples by 360 lines is created by converting the line number to radians, and then calculating the cosine of the calculated value using the following equation:

cos(rads(line))

The line number is input as degrees and converted to radians first in order to output the correct cosine values.

fx to=cosine_of_line.cub equation="cos(rads(line))" mode=outputonly lines=360 samples=360

fx GUI

Example GUI Screenshot of GUI with parameters filled in to perform a calculation to create an output image.

Output image

Output file Parameter Name: TO This is the output file created based on a user defined equation without specifying input filenames. Parameter Name: EQUATION "cos(rads(line))"

The example below demonstrates how easily one can get an incorrect product if angles are not converted to radians before calculating the cosine of a line number when the line number represents angles in degrees. In this example, the output file has 360 samples by 360 lines.

fx to=cosine_of_line_deg.cub equation="cos(line)" mode=outputonly lines=360 samples=360

fx GUI

Example GUI Screenshot of GUI with parameters filled in to perform a calculation to create an output image.

Output image

Output file Parameter Name: TO This is the output file created based on a user defined equation without specifying input filenames. Parameter Name: EQUATION "cos(line)"

In this example, a gamma stretch is applied to a CTX image. The image statistics are determined and used as part of the equation to calculate new DN values.

fx f1=B10_013516_1520_XN_28S285W_eo_reduced.cub to=B10_013516_1520_XN_28S285W_gammast2.cub equation="{[cubemax(f1)-abs(cubemin(f1))]*{[f1-abs(cubemin(f1))]/[cubemax(f1)-abs(cubemin(f1))]}^(1.0/1.8)}"

fx GUI

Example GUI Screenshot of GUI with parameters filled in to perform a calculation on the input image.

Input image

Input file Parameter Name: F1 This is the input image for the fx example.

Output image

Output file Parameter Name: TO This is the output image where the bright and dark tones in the input image are adjusted based on the input image statistics that are incorporated into the equation that is applied to calculate new output values. Parameter Name: EQUATION "{[cubemax(f1)-abs(cubemin(f1))]*{[f1-abs(cubemin(f1))]/[cubemax(f1)-abs(cubemin(f1))]}^(1.0/1.8)}"

In this example, all input DN values greater than 0.11 is set to "1.0" and all other pixels set to "0.0".

fx f1=B10_013516_1520_XN_28S285W_eo_reduced.cub to=B10_013516_1520_XN_28S285W_mask.cub equation="f1>0.11"

fx GUI

Example GUI Screenshot of GUI with parameters filled in to perform a calculation on the input image.

Input image

Input file Parameter Name: F1 This is the input image for the fx example.

Output image

Output file Parameter Name: TO This is an image consisting of "0" and "1" DN values based on the equation provided. Parameter Name: EQUATION "f1>0.11"

In this example, all DN values less than 0.11 will be set to "0.0" and all other DN values will retain the original input value.

fx f1=B10_013516_1520_XN_28S285W_eo_reduced.cub to=B10_013516_1520_XN_28S285W_extract.cub equation="f1*(f1>0.11)"

fx GUI

Example GUI Screenshot of GUI with parameters filled in to perform a calculation on the input image.

Input image

Input file Parameter Name: F1 This is the input image for the fx example.

Output image

Output file Parameter Name: TO The pink areas in this image were set to "0.0" based on the equation entered. All other values retained the original values because the input value was multiplied by 1.0 when the calculations were performed. Parameter Name: EQUATION "f1*(f1>0.11)"