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.


transforms frames of a video.

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.
  • The transformation function f can be one of the following:
  • fan arbitrary function f
    TransformationFunction[]a transformation function
  • 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


open allclose all

Basic Examples  (2)

Transformation of an image:

Transformation of a 3D image:

Scope  (11)

Data  (4)

Transform a grayscale image:

Transform a color image:

Transform frames of a video:

Transform a 3D image:

Transformation  (5)

Use any function for the transformation:

Operate explicitly on and pixel positions:

Operate on the vertical dimension only:

Perform a matrix transformation:

Use a TransformationFunction to specify the transformation:

Use a 3D transformation function:

Size  (2)

By default, the output image is of the same size as the input image:

Specify the size of the resulting image:

Specify width and height explicitly:

Use a scaled value:

Use a named size:

Use All to obtain an image of the same size as the original:

Make a 3D image narrow and tall:

Options  (7)

Background  (1)

By default, a black background is used:

Use a specific color for the background:

Use a transparent background:

Images with an alpha channel use a transparent background by default:

DataRange  (2)

By default, the Automatic DataRange is used:

Use DataRangeFull when defining translation in pixel coordinates:

Specify a custom DataRange:

Choose a data range symmetric on the axis to show a vertical reflection:

Vertical reflection transform applied to a 3D image:

Masking  (1)

By default, Masking->Full is used; padding is used for pixels outside of the original image:

With Masking->All, the Background option value is used for pixels outside of the original image:

Use an arbitrary mask:

PlotRange  (1)

By default, the output image retains the plot range of the input image:

Use PlotRange->All to view all transformed image pixels:

Use explicit plot range values:

Rotate image around its center:

Use pixel coordinates with PlotRangeFull option:

Padding  (1)

By default, Padding0 is used:

Use a named color:

Using fixed padding for values beyond the image:

Using a periodic padding:

Use transparent padding:

Resampling  (1)

By default, the resampling method is selected automatically, but any of the available methods may be used:

Applications  (6)

Reverse an unknown geometric transformation by determining the transformation function from a pair of images:

Apply the transformation function to the transformed image:

Make a photo mosaic:

Create a rain effect:

Create a tiling effect:

Warp a line of text along the vertical axis:

Use padding to extend the region of the image:

Mirror an image:

Properties & Relations  (2)

By default, the returned image retains the size and aspect ratio of the original:

Doing a transformation with a function and its inverse gives back the original image with some blurring due to interpolation:

Possible Issues  (1)

PlotRange->All cannot be used with functions that are not invertible:

Use an automatic or explicit plot range instead:

Interactive Examples  (1)

Interactive fisheye effect:

Neat Examples  (6)

Do mathematical transformations on images:

Create a caricature:

Fisheye effect:

Spiral mirror effect:

Distort a portrait image:

A curvy distortion:

Wolfram Research (2010), ImageTransformation, Wolfram Language function, (updated 2021).


Wolfram Research (2010), ImageTransformation, Wolfram Language function, (updated 2021).


Wolfram Language. 2010. "ImageTransformation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021.


Wolfram Language. (2010). ImageTransformation. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2022_imagetransformation, author="Wolfram Research", title="{ImageTransformation}", year="2021", howpublished="\url{}", note=[Accessed: 06-July-2022 ]}


@online{reference.wolfram_2022_imagetransformation, organization={Wolfram Research}, title={ImageTransformation}, year={2021}, url={}, note=[Accessed: 06-July-2022 ]}