Radial Basis Functions (Geostatisical Analyst)

Summary

Uses one of five basis functions to process each measured sample value, thus creating an exact interpolation surface.

How_Radial_Basis_Functions work

Usage

• The smooth search neighborhood is only available for the Inverse multiquadric function.

• For all methods except the Inverse multiquadric function, the higher the parameter value, the smoother the surface. The opposite is true for the Inverse multiquadric function.

Syntax

RadialBasisFunctions_ga (in_features, z_field, {cell_size}, out_ga_layer, {out_raster}, {cell_size}, {search_neighborhood}, {radial_basis_functions}, {small_scale_parameter})

Parameter	Explanation	Data Type
in_features	The input features containing the z-values to be interpolated.	Feature Layer
z_field	Field that holds a height or magnitude value for each point. This can be a numeric field or the Shape field if the input features contain z-values or m-values.	Field
cell_size (Optional)	The cell size at which the output raster will be created. This value can be explicitly set under Raster Analysis from the Environment Settings. If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.	Analysis Cell Size
out_ga_layer	The geostatistical layer produced. This layer is required output only if no output raster is requested.	Geostatistical Layer
out_raster (Optional)	The output raster. This raster is required output only if no output geostatistical layer is requested.	Raster Dataset
cell_size (Optional)	The cell size at which the output raster will be created. This value can be explicitly set under Raster Analysis from the Environment Settings. If not set, it is the shorter of the width or the height of the extent of the input point features, in the input spatial reference, divided by 250.	Analysis Cell Size
search_neighborhood (Optional)	Defines which surrounding points will be used to control the output. There are two options: Standard and Smooth. Standard is the default. This is a Search Neighborhood class (SearchNeighborhoodStandard and SearchNeighborhoodSmooth). Standard Major semiaxis — The major semi-axis value of the searching neighborhood. Minor semiaxis — The minor semi-axis value of the searching neighborhood. Angle — The angle of rotation for the axis (circle) or semi-major axis (ellipse) of the moving window. Maximum neighbors — The maximum number of neighbors that will be used to estimate the value at the unknown location. Minimum neighbors — The minimum number of neighbors that will be used to estimate the value at the unknown location. Sector type — The geometry of the neighborhood. One sector - Single ellipse Four sectors - Ellipse divided in four sectors. Four sectors shifted - Ellipse divided in four sectors and shifted 45 degrees. Eight sectors - Ellipse divided into eight sectors. Smooth Major semiaxis — The major semi-axis value of the searching neighborhood. Minor semiaxis — The minor semi-axis value of the searching neighborhood. Angle — The angle of rotation for the axis (circle) or semi-major axis (ellipse) of the moving window. Smoothing factor — The Smooth Interpolation option creates an outer ellipse and an inner ellipse at a distance equal to the Major Semiaxis multiplied by the Smoothing factor. The points that fall outside the smaller ellipse but inside the largest ellipse are weighted using a sigmoidal function with a value between zero and one.	Geostatistical Search Neighborhood
radial_basis_functions (Optional)	Available Radial basis functions. THIN_PLATE_SPLINE —Thin-plate spline SPLINE_WITH_TENSION — Spline with tension COMPLETELY_REGULARIZED_SPLINE — Completely regularized spline MULTIQUADRIC_FUNCTION — Multiquadric function INVERSE_MULTIQUADRIC_ FUNCTION —Inverse multiquadric function	String
small_scale_parameter (Optional)	Used to calculate the weights assigned to the points located in the moving window. Each of the radial basis functions has a parameter that controls the degree of small-scale variation of the surface. The (optimal) parameter is determined by finding the value that minimizes the root mean square prediction error (RMSPE).	Double

Code Sample

RadialBasisFunctions example 1 (Python window)

Interpolate point features onto a rectangular raster.

import arcpy
arcpy.env.workspace = "C:/gapyexamples/data"
arcpy.RadialBasisFunctions_ga(
    "ca_ozone_pts", "OZONE", "outRBF", "C:/gapyexamples/output/rbfout", "2000", 
    arcpy.SearchNeighborhoodStandard(300000, 300000, 0, 15, 10, "ONE_SECTOR"),
    "THIN_PLATE_SPLINE", "")

RadialBasisFunctions example 2 (stand-alone script)

Interpolate point features onto a rectangular raster.

# Name: RadialBasisFunctions_Example_02.py
# Description: RBF methods are a series of exact interpolation techniques;
#              that is, the surface must go through each measured sample value.
# Requirements: Geostatistical Analyst Extension

# Import system modules
import arcpy

# Set environment settings
arcpy.env.workspace = "C:/gapyexamples/data"

# Set local variables
inPointFeatures = "ca_ozone_pts.shp"
zField = "OZONE"
outLayer = "outRBF"
outRaster = "C:/gapyexamples/output/rbfout"
cellSize = 2000.0
rbf = "THIN_PLATE_SPLINE"
smallscaleParam = ""

# Set variables for search neighborhood
majSemiaxis = 300000
minSemiaxis = 300000
angle = 0
maxNeighbors = 15
minNeighbors = 10
sectorType = "ONE_SECTOR"
searchNeighbourhood = arcpy.SearchNeighborhoodStandard(majSemiaxis, minSemiaxis, 
                                                       angle, maxNeighbors, 
                                                       minNeighbors, sectorType)

# Check out the ArcGIS Geostatistical Analyst extension license
arcpy.CheckOutExtension("GeoStats")

# Execute RadialBasisFunctions
arcpy.RadialBasisFunctions_ga(inPointFeatures, zField, outLayer, outRaster, 
                              cellSize, searchNeighbourhood, rbf, smallscaleParam)

Environments

Cell Size, Current Workspace, Output Coordinate System, Extent, Scratch Workspace, Snap Raster, Coincident Points

Licensing Information

ArcView: Requires Geostatistical Analyst

ArcEditor: Requires Geostatistical Analyst

ArcInfo: Requires Geostatistical Analyst