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ImagePerspectiveTransformation
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ImagePerspectiveTransformation

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applies a linear fractional transform specified by a matrix m to the positions of each pixel in image.

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uses the TransformationFunction given by tf.

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gives an image of the specified size.

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transforms frames of a video.

Details and Options

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Transform an image using a perspective transformation:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-c4c98w
Out[1]=1

Perspective transformation of a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-8776w9
Out[1]=1

Scope  (13)Survey of the scope of standard use cases

Data  (4)

Transform a grayscale image by scaling with a factor of :

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-gfrv9x
Out[1]=1

Transform a color image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-igkr4a
Out[1]=1

Transform frames of a video:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-zvje5z
Out[1]=1

Transform a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bnijgx
Out[1]=1

Transformations  (8)

2D Images  (4)

A pure rescaling:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-w47th6
Out[1]=1

A clockwise rotation of an image:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-godd3
Out[2]=2

A shearing transformation:

In[3]:=3
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bkddyx
Out[3]=3

A pure translation:

In[4]:=4
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-jxb25j
Out[4]=4

A general affine transformation:

In[5]:=5
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-ccx3zx
Out[5]=5

A perspective transformation:

In[6]:=6
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-0n8nfp
Out[6]=6

Use a geometric transformation function to rotate an image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-ze985
Out[1]=1

Rotate about the opposite image corner:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-jd1lg
Out[2]=2

Rotate about the image center:

In[3]:=3
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-ircwt8
Out[3]=3

Shear an image using ShearingTransform:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-geh2ft
Out[1]=1

Transform an image using a general TransformationFunction object:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-5cgmx
Out[1]=1

3D Images  (4)

A pure rescaling of a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bk0kbf
Out[1]=1

Rotate a 3D image around the axis:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-iswiu7
Out[2]=2

A pure translation of a 3D image in the vertical direction only:

In[3]:=3
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-xtttx
Out[3]=3

Rotate a 3D image using RotationTransform:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-c9b142
Out[1]=1

An affine transformation of a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-mhsrcz
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-dzg4y7
Out[2]=2

A linear fractional transformation of a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-hiaats
Out[1]=1

Size  (1)

The size value Automatic usually returns images of the same size as the original:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-m7ukfc
In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-6y5wv5
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-h59h6
Out[3]=3

When PlotRange is specified, the returned image size is derived from the original size and plot range:

In[3]:=3
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-480iua
Out[3]=3

Using the value All always returns an image of the same size as the original:

In[4]:=4
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-i11vz0
Out[4]=4

Specify the width of the resulting image:

In[4]:=4
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-cbpc4w
Out[4]=4

Specify the width and height of the resulting image:

In[5]:=5
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-l6nrsi
Out[5]=5

Use a scaled value:

In[12]:=12
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-czw4x3
Out[12]=12

Use a predefined named size value:

In[6]:=6
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-v8x0nk
Out[6]=6

Options  (7)Common values & functionality for each option

Background  (1)

By default, a black background is used:

In[3]:=3
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-4b21fy
Out[4]=4

Use a specific color for the background:

In[5]:=5
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-21p0fd
Out[5]=5

Use a transparent background:

In[6]:=6
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-ese0ag
Out[6]=6

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

In[7]:=7
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-i9dskb
Out[7]=7

DataRange  (2)

By default, the Automatic DataRange is used:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bfgcxm
Out[3]=3

Use DataRangeFull when defining translation in pixel coordinates:

In[4]:=4
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bev4iv
Out[4]=4

Specify a custom DataRange:

In[5]:=5
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bu5hl4
Out[5]=5

Use a custom DataRange setting in translating a 3D image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-gocoyy
Out[1]=1

Masking  (1)

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

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-pwhgmk
Out[2]=2

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

In[5]:=5
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-lhq9jp
Out[5]=5

Use an arbitrary mask:

In[6]:=6
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-hi9sbz
Out[6]=6

Padding  (1)

By default, the Padding0 is used:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-lia0ff
Out[2]=2

Use a named color:

In[3]:=3
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-eexluk
Out[3]=3

Use reflected padding:

In[4]:=4
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-b77u3s
Out[4]=4

PlotRange  (1)

By default, PlotRangeAutomatic is used:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-d0u0uu
Out[2]=2

Use the PlotRangeAll option to show all the transformed pixels from the original image:

In[11]:=11
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-eoml1x
Out[11]=11

Use a custom PlotRange setting:

In[15]:=15
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-fypkcm
Out[15]=15

Use pixel coordinates with PlotRangeFull option:

In[4]:=4
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-f5ph3
Out[4]=4

Resampling  (1)

A cubic interpolant is used by default:

In[7]:=7
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-biriiu
Out[7]=7

Use a different resampling method:

In[8]:=8
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-ewnw3
Out[8]=8

Applications  (4)Sample problems that can be solved with this function

Use a perspective transformation to modify camera position in an image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-nvvop

Obtain the geometric transformation that maps the four corners of the book to their desired positions:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-cmgjku
Out[4]=4
In[17]:=17
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-f4javk
Out[17]=17

Apply the transformation function to the image:

In[16]:=16
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-gdkh8w
Out[16]=16

Remove the perspective distortion of the road:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bml634
Out[1]=1

Enhance the perspective effect:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bvrqf5
Out[1]=1

Segment out the building in an image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-jpvm3i
Out[1]=1

Shear the image to straighten up the building:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-dknwe
Out[2]=2

Properties & Relations  (2)Properties of the function, and connections to other functions

ImagePerspectiveTransformation[image,{a,b}] applies AffineTransform[{a,b}] to image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-cx45gk
Out[4]=4

ImagePerspectiveTransformation[image,{a,b,c,d}] applies LinearFractionalTransform[{a,b,c,d}] to image:

In[1]:=1
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-mt1ww8
Out[1]=1

Possible Issues  (2)Common pitfalls and unexpected behavior

When the function maps some coordinates to infinity, truncated output is displayed:

In[2]:=2
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https://wolfram.com/xid/0bzqwlfvllpiv6kdy-b28sj4
Out[2]=2

Non-invertible transformations will give a degenerate result:

In[1]:=1
✖
https://wolfram.com/xid/0bzqwlfvllpiv6kdy-bnrrpz
Out[1]=1
Wolfram Research (2010), ImagePerspectiveTransformation, Wolfram Language function, https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html (updated 2021).
✖
Wolfram Research (2010), ImagePerspectiveTransformation, Wolfram Language function, https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html (updated 2021).

Text

Wolfram Research (2010), ImagePerspectiveTransformation, Wolfram Language function, https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html (updated 2021).

✖
Wolfram Research (2010), ImagePerspectiveTransformation, Wolfram Language function, https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html (updated 2021).

CMS

Wolfram Language. 2010. "ImagePerspectiveTransformation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html.

✖
Wolfram Language. 2010. "ImagePerspectiveTransformation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2021. https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html.

APA

Wolfram Language. (2010). ImagePerspectiveTransformation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html

✖
Wolfram Language. (2010). ImagePerspectiveTransformation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html

BibTeX

@misc{reference.wolfram_2025_imageperspectivetransformation, author="Wolfram Research", title="{ImagePerspectiveTransformation}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html}", note=[Accessed: 19-April-2025 ]}

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@misc{reference.wolfram_2025_imageperspectivetransformation, author="Wolfram Research", title="{ImagePerspectiveTransformation}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html}", note=[Accessed: 19-April-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_imageperspectivetransformation, organization={Wolfram Research}, title={ImagePerspectiveTransformation}, year={2021}, url={https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html}, note=[Accessed: 19-April-2025 ]}

✖
@online{reference.wolfram_2025_imageperspectivetransformation, organization={Wolfram Research}, title={ImagePerspectiveTransformation}, year={2021}, url={https://reference.wolfram.com/language/ref/ImagePerspectiveTransformation.html}, note=[Accessed: 19-April-2025 ]}