# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# ImageTransformation

ImageTransformation[image,function]
gives an image in which each pixel at position p corresponds to the position function[p] in image.

ImageTransformation[image,function,size]
gives an image of the specified size.

## Details and OptionsDetails and Options

• In ImageTransformation[image,f], f is a function of form f[{x,y}] in 2D or f[{x,y,z}] in 3D that defines a backward transformation from points in the resulting image {x,y} or {x,y,z} into the input image image.
• The function f can also be specified with a TransformationFunction object.
• In 2D, the range of the coordinate system for the input image is assumed to be {{0,1},{0,a}}, where a is the aspect ratio. The bottom-left corner of the image corresponds to coordinates {0,0} by default.
• In 3D, the range of the coordinate system for the input image is assumed to be {{0,1},{0,d/w},{0,h/w}}, where {w,d,h} are the image dimensions. The bottom-left front corner of the image corresponds to coordinates {0,0,0} by default.
• Other coordinate systems can be specified by setting the DataRange option.
• ImageTransformation can take the following options:
•  Background 0 background color to use DataRange Automatic range of coordinates in the original image Masking Full region of interest to be transformed Padding 0 padding method PlotRange Automatic range of coordinates in the resulting image Resampling Automatic resampling method
• By default, ImageTransformation returns an image with the aspect ratio of the input image.
• Typical settings for DataRange include:
•  Automatic {{0,1},{0,h/w}} in 2D, {{0,1},{0,d/w},{0,h/w}} in 3D Full {{0,w},{0,h}} in 2D, {{0,1},{0,d},{0,h}} in 3D {{left,right},{bottom,top}} explicit coordinate ranges in 2D {{left,right},{front,back},{bottom,top}} explicit coordinate ranges in 3D
• The coordinate system of the resulting image is specified by the PlotRange option. Typical settings include:
•  Automatic same as DataRange settings All try to include all of the transformed pixels Full same ranges as the input image {{left,right},…} explicit coordinate ranges
• In ImageTransformation[image,function], the pixel dimensions of the resulting image are based on the dimensions of image and the ratio of PlotRange and DataRange.
• Masking option can be one of the following:
•  All input image only Full input image and padding mask any mask image
• For possible size specifications, see the reference page for ImageResize.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

Transformation of an image:

 In[1]:=
 Out[1]=

Transformation of a 3D image:

 In[1]:=
 Out[1]=

## See AlsoSee Also

Introduced in 2010
(8.0)
| Updated in 2014
(10.0)