Available with Spatial Analyst license.

## Summary

Defines a Gaussian transformation function which is determined from the midpoint and spread shapeâ€“controlling parameters as well as the lower and upper threshold that identify the range within which to apply the function.

Learn more about how the parameters affect this transformation function

## Discussion

The tool that uses the TfGaussian object is Rescale by Function.

The equation for the Gaussian transformation function is:

The inputs to the equation are *f*1, the spread, and *f*2, the midpoint.

The function values range from 0 to 1, which are then transformed to the evaluation scale.

The spread determines how rapidly the transformation function values decrease from the midpoint. If the midpoint is within the lower and upper thresholds, then the spread determines how rapidly the function values decrease from the toScale to the fromScale. The larger the spread, the steeper the function will be around the midpoint. Said another way, as the spread gets smaller, the transformation function approaches the midpoint more slowly.

The selection of an appropriate spread value is a subjective process that is dependent on the range of the input values. The default value of 0.1 is a good starting point. Typically, the values vary within the ranges of 0.01 to 1 or 0.001 to 1, respectively. A default spread is calculated to fit the function to the minimum and maximum of the input dataset.

The Gaussian function is useful when the highest preference is near a specific value.

The Gaussian function is similar to the Near function, except the Near function has a narrower spread and therefore is steeper around the midpoint.

## Syntax

TfGaussian ({midpoint}, {spread}, {lowerThreshold}, {valueBelowThreshold}, {upperThreshold}, {valueAboveThreshold})

Parameter | Explanation | Data Type |

midpoint |
The user-defined value that defines the highest point of the Gaussian transformation function curve. If the midpoint value is between the lower and upper threshold, input cell locations with the corresponding value will receive the toScale evaluation scale value on the output raster. (The default value is None) | Double |

spread | Defines the spread of the Gaussian function that controls the steepness of the decay of the function from the midpoint. The spread generally ranges from 0.01 to 1; the larger the value results in a steeper decay from the midpoint. (The default value is None) | Double |

lowerThreshold | Defines the starting value at which to begin applying the specified transformation function. The input value corresponding to the lowerThreshold is assigned to the fromScale evaluation scale value on the output raster. Input values below the lowerThreshold are assigned to the valueBelowThreshold and are not considered in the function value range. The lowerThreshold must be less than the upperThreshold. (The default value is None) | Double |

valueBelowThreshold | A user-specified value to assign output cell locations with input values below the lowerThreshold. The value for valueBelowThreshold can be float, integer, or NoData. In the tool dialog box, no quotation marks are used around NoData; however, quotation marks are required around "NoData" when scripting. (The default value is None) | Variant |

upperThreshold | Defines the ending value at which to stop applying the specified transformation function. The input value corresponding to the upperThreshold is assigned to the toScale evaluation scale value on the output raster. Input values above the upperThreshold are assigned to the valueAboveThreshold and are not considered in the function value range. The lowerThreshold must be less than the upperThreshold. (The default value is None) | Double |

valueAboveThreshold | A user-specified value to assign output cell locations with input values above the upperThreshold. The value for valueAboveThreshold can be float, integer, or NoData. In the tool dialog box, no quotation marks are used around NoData; however, quotation marks are required around "NoData" when scripting. (The default value is None) | Variant |

## Properties

Property | Explanation | Data Type |

midpoint (Read and Write) | The value of the midpoint for the transformation function which defines the highest point of the function curve. | Double |

spread (Read and Write) |
The value of the spread for the transformation function which controls the steepness of the decay of the function from the midpoint. | Double |

lowerThreshold (Read and Write) |
The value of the lowerThreshold for the transformation function which defines the starting value at which to begin applying the specified transformation function. | Double |

valueBelowThreshold (Read and Write) |
The value that will be assigned to the output cells whose input values are below the lowerThreshold. | Variant |

upperThreshold (Read and Write) |
The value of the upperThreshold for the transformation function which defines the ending value at which to stop applying the specified function. | Double |

valueAboveThreshold (Read and Write) | The value that will be assigned to the output cells whose input values are above the upperThreshold. | Variant |

## Code sample

##### Transformation function Gaussian example 1 (Python window)

Demonstrates how to create a TfGaussian class and use it in the RescaleByFunction tool within the Python window.

```
import arcpy
from arcpy.sa import *
from arcpy import env
env.workspace = "c:/sapyexamples/data"
outRescale = RescaleByFunction("solar", TfGaussian(180, 0.0004, "#", "#", "#", "#"), 1, 10)
outRescale.save("c:/sapyexamples/rescaletfga1")
```

##### Transformation function Gaussian example 2 (stand-alone script)

Demonstrates how to transform the input data with the RescaleByFunction tool using the TfGaussian class.

```
# Name: TfGaussian_Ex_02.py
# Description: Rescales input raster data using a Gaussian function and
# transforms the function values onto a specified evaluation scale.
# Requirements: Spatial Analyst Extension
# Author: esri
# Import system modules
import arcpy
from arcpy import env
from arcpy.sa import *
# Set environment settings
env.workspace = "C:/sapyexamples/data"
# Set local variables
inRaster = "solar"
# Create the TfGaussian object
midpoint = 180
spread = 0.0004
lowerthresh = "#"
valbelowthresh = "#"
upperthresh = "#"
valabovethresh = "#"
myTfFunction = TfGaussian(midpoint, spread, lowerthresh, valbelowthresh, upperthresh, valabovethresh)
# Set evaluation scale
fromscale = 1
toscale = 10
# Check out the ArcGIS Spatial Analyst extension license
arcpy.CheckOutExtension("Spatial")
# Execute RescaleByFunction
outRescale = RescaleByFunction(inRaster, myTfFunction, fromscale, toscale)
# Save the output
outRescale.save("c:/sapyexamples/rescaletfga2")
```