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


gives an image of the specified size.

Details and Options

  • In ImageTransformation[image,f], the value of every pixel at position {x,y} in the output image is obtained from the position f[{x,y}] in the input image. This is known as a backward transformation.
  • ImageTransformation works with arbitrary 2D and 3D images.
  • Possible settings for size are:
  • Automaticautomatic image size
    Allsame as input image size
    widthexplicit width, automatic height
    {width,height}explicit width and height
    {width,depth,height}explicit width, depth and height in 3D
  • For possible width, depth and height specifications, see the reference page for ImageResize.
  • In 2D, the range of the coordinate system for the input image is assumed to be , where is the aspect ratio. The bottom-left corner of the image corresponds to coordinates by default.
  • In 3D, the range of the coordinate system for the input image is assumed to be , where are the image dimensions. The bottom-left front corner of the image corresponds to coordinates by default.
  • Other coordinate systems can be specified by setting the DataRange option.
  • ImageTransformation can take the following options:
  • Background0background color to use
    DataRangeAutomaticrange of coordinates in the original image
    MaskingFullregion of interest to be transformed
    Padding0padding method
    PlotRangeAutomaticrange of coordinates in the resulting image
    ResamplingAutomaticresampling method
  • By default, ImageTransformation returns an image with the aspect ratio of the input image.
  • Typical settings for DataRange include:
  • Automatic in 2D, in 3D
    Full in 2D, 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:
  • Automaticsame as DataRange settings
    Alltry to include all of the transformed pixels
    Fullsame ranges as the input image
    {{left,right},}explicit coordinate ranges
  • In ImageTransformation[image,f], the pixel dimensions of the resulting image are based on the dimensions of image and the ratio of PlotRange and DataRange.
  • The Masking option can be one of the following:
  • Allinput image only
    Fullinput image and padding
    maskany mask image


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Basic Examples  (2)

Transformation of an image:

Click for copyable input

Transformation of a 3D image:

Click for copyable input

Scope  (10)

Options  (7)

Applications  (5)

Properties & Relations  (2)

Possible Issues  (1)

Interactive Examples  (1)

Neat Examples  (6)

Introduced in 2010
Updated in 2014