# BandMathX - Band Math X¶

This application performs mathematical operations on several multiband images.

## Detailed description¶

This application performs a mathematical operation on several multi-band images and outputs the result into an image (multi- or mono-band, as opposed to the BandMath OTB-application). The mathematical formula is done by the muParserX libraries.

The list of features and the syntax of muParserX is available at [1].

As opposed to muParser (and thus the BandMath OTB-application [2]), muParserX supports vector expressions which allows outputting multi-band images.

Hereafter is a brief reference of the muParserX syntax

## Fundamentals¶

The formula can be written using:

- numerical values ( 2.3, -5, 3.1e4, ...)
- variables containing pixel values (please, note the indexing of inputs from 1 to N). Examples for the first input image:

- ‘im1’ a pixel from 1st input, made of n components (n bands)
- ‘im1b2’ the 2nd component of a pixel from 1st input (band index is 1-based)
- ‘im1b2N3x4’ a 3x4 pixels ‘N’eighbourhood of a pixel the 2nd component of a pixel from the 1st input
- ‘im1PhyX’ horizontal (X-axis) spacing of the 1st input.
- ‘im1PhyY’ vertical spacing of the 1st input input.
- ‘im1b2Mean’ mean of the 2nd component of the 1st input (global statistics)
- ‘im1b2Mini’ minimum of the 2nd component of the 1st input (global statistics)
- ‘im1b2Maxi’ maximum of the 2nd component of the 1st input (global statistics)
- ‘im1b2Sum’ sum of the 2nd component of the 1st input (global statistics)
- ‘im1b2Var’ variance of the 2nd component of the 1st input (global statistics)
- ‘idxX’ and ‘idxY’ are the indices of the current pixel (generic variables)
- binary operators:

- ‘+’ addition, ‘-‘ subtraction, ‘*’ multiplication, ‘/’ division
- ‘^’ raise x to the power of y
- ‘<’ less than, ‘>’ greater than, ‘<=’ less or equal, ‘>=’ greater or equal
- ‘==’ equal, ‘!=’ not equal
- logical operators: ‘or’, ‘and’, ‘xor’
- if-then-else operator: ‘(condition ? value_true : value_false)’
- functions : abs(), exp(), log(), sin(), cos(), min(), max(), ...

Always keep in mind that this application only addresses mathematically well-defined formulas. For instance, it is not possible to add vectors of different dimensions (e.g. addition of a row vector with a column vector), or a scalar to a vector or matrix, or divide two vectors, etc.

Thus, it is important to remember that a pixel of n components is always represented as a row vector.

- Example:
- im1 + im2 represents the addition of pixels from the 1st and 2nd inputs. This expression is consistent only if both inputs have the same number of bands.

Please, note that it is also possible to use the following expressions to obtain the same result:

- im1b1 + im2b1
- im1b2 + im2b2
- ...

Nevertheless, the first expression is by far much pleaseant. We call this new functionality the ‘batch mode’ (performing the same operation in a band-to-band fashion).

## Operations involving neighborhoods of pixels¶

Another new feature is the possibility to perform operations that involve neighborhoods of pixels. Variables related to such neighborhoods are always defined following the imIbJNKxP pattern, where:

- I is an number identifying the image input (remember, input #0 = im1, and so on)
- J is an number identifying the band (remember, first band is indexed by1)
- KxP are two numbers that represent the size of the neighborhood (first one is related to the horizontal direction)

NB: All neighborhood are centered, thus K and P must be odd numbers.

Many operators come with this new functionality:

- dotpr
- mean
- var
- median
- min
- max
- etc.

For instance, if im1 represents the pixel of 3 bands image:

```
im1 - mean( im1b1N5x5, im1b2N5x5, im1b3N5x5 )
```

could represent a high pass filter (note that by implying three neighborhoods, the operator mean returns a row vector of three components. It is a typical behaviour for many operators of this application).

In addition to the previous operators, other operators are available:

- existing operators/functions from muParserX, that were not originally defined for vectors and matrices (e.g. cos, sin). These new operators/functions keep the original names to which we added the prefix ‘v’ for vector (vcos, vsin, etc.)
- mult, div and pow operators, that perform element-wise multiplication, division or exponentiation of vector/matrices (e.g. im1 div im2).
- mlt, dv and pw operators, that perform multiplication, division or exponentiation of vector/matrices by a scalar (e.g. im1 dv 2.0).
- bands, which is a very useful operator. It allows selecting specific bands from an image, and/or to rearrange them in a new vector (e.g.bands( im1, { 1, 2, 1, 1 } ) produces a vector of 4 components made of band 1, band 2, band 1 and band 1 values from the first input.

Note that curly brackets must be used in order to select the desired bandindices.

## The application itself¶

The application can use an expression supplied with the ‘exp’ parameter. It can also use an input context file, that defines variables and expressions. An example of context file is given below:

```
#F expo 1.1
#M kernel1 { 0.1 , 0.2 , 0.3; 0.4 , 0.5 , 0.6; 0.7 , 0.8 , 0.9; 1 , 1.1, 1.2; 1.3 , 1.4 , 1.5 }
#E $dotpr( kernel1, im1b1N3x5 ); im2b1^expo$
```

As we can see, #I/#F allows the definition of an integer/float constant, whereas #M allows the definition of a vector/matrix. In the latter case, elements of a row must be separated by commas, and rows must be separated by semicolons. It is also possible to define expressions within the same txt file, with #E <expr> (see limitations, below). Finally, we strongly recommend to read the OTB Cookbook which can be found at: http://www.orfeo-toolbox.org/packages/OTBCookBook.pdf

## Parameters¶

This section describes in details the parameters available for this application. Table [1] presents a summary of these parameters and the parameters keys to be used in command-line and programming languages. Application key is *BandMathX* .

[1] | Table: Parameters table for Band Math X. |

Parameter Key | Parameter Name | Parameter Type |
---|---|---|

il | Input image-list | Input image list |

out | Output Image | Output image |

ram | Available RAM (Mb) | Int |

exp | Expressions | String |

incontext | Import context | Input File name |

outcontext | Export context | Output File name |

inxml | Load otb application from xml file | XML input parameters file |

outxml | Save otb application to xml file | XML output parameters file |

**Input image-list**: Image-list to perform computation on.**Output Image**: Output image.**Available RAM (Mb)**: Available memory for processing (in MB).**Expressions**: Mathematical expression to apply.**Import context**: A txt file containing user’s constants and expressions.**Export context**: A txt file where to save user’s constants and expressions.**Load otb application from xml file**: Load otb application from xml file.**Save otb application to xml file**: Save otb application to xml file.

## Example¶

To run this example in command-line, use the following:

```
otbcli_BandMathX -il verySmallFSATSW_r.tif verySmallFSATSW_nir.tif verySmallFSATSW.tif -out apTvUtBandMathOutput.tif -exp 'cos( im1b1 ) + im2b1 * im3b1 - im3b2 + ndvi( im3b3, im3b4 )'
```

To run this example from Python, use the following code snippet:

```
#!/usr/bin/python
# Import the otb applications package
import otbApplication
# The following line creates an instance of the BandMathX application
BandMathX = otbApplication.Registry.CreateApplication("BandMathX")
# The following lines set all the application parameters:
BandMathX.SetParameterStringList("il", ['verySmallFSATSW_r.tif', 'verySmallFSATSW_nir.tif', 'verySmallFSATSW.tif'])
BandMathX.SetParameterString("out", "apTvUtBandMathOutput.tif")
BandMathX.SetParameterString("exp", "'cos( im1b1 ) + im2b1 * im3b1 - im3b2 + ndvi( im3b3, im3b4 )'")
# The following line execute the application
BandMathX.ExecuteAndWriteOutput()
```

### Limitations¶

The application is currently unable to produce one output image per expression, contrary to otbBandMathXImageFilter.

Separating expressions by semi-colons ‘;’ will concatenate their results into a unique multiband output image.

### Authors¶

This application has been written by OTB-Team.

### See Also¶

- These additional resources can be useful for further information:
- [2] BandMath