ImagePerspectiveTransformation

ImagePerspectiveTransformation[image,m]

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

ImagePerspectiveTransformation[image,tf]

uses the TransformationFunction given by tf.

ImagePerspectiveTransformation[image,…,size]

gives an image of the specified size.

ImagePerspectiveTransformation[video,…]

transforms frames of a video.

Details and Options

ImagePerspectiveTransformation is typically used to modify camera position, orientation and field of view of a scene.

The transformation matrix m corresponds to the following case:

	image 2D, m 2×2	AffineTransform[m]
	image 2D, m 3×3	LinearFractionalTransform[m]
	image 3D, m 3×3	AffineTransform[m]
	image 3D, m 4×4	LinearFractionalTransform[m]

Possible settings for size are:

	Automatic	automatic image size
	All	same as input image size
	width	explicit width, automatic height
	{width,height}	explicit width and height
	{width,depth,height}	explicit width, depth and height in 3D

ImagePerspectiveTransformation 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

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:

	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

When PlotRange is not Automatic, size is chosen based on the size of the original 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.

Examples

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Basic Examples (2)

Transform an image using a perspective transformation:

Perspective transformation of a 3D image:

Scope (13)

Data (4)

Transform a grayscale image by scaling with a factor of :

Transform a color image:

Transform frames of a video:

Transform a 3D image:

Transformations (8)

2D Images (4)

A pure rescaling:

A clockwise rotation of an image:

A shearing transformation:

A pure translation:

A general affine transformation:

A perspective transformation:

Use a geometric transformation function to rotate an image:

Rotate about the opposite image corner:

Rotate about the image center:

Shear an image using ShearingTransform:

Transform an image using a general TransformationFunction object:

3D Images (4)

A pure rescaling of a 3D image:

Rotate a 3D image around the axis:

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

Rotate a 3D image using RotationTransform:

An affine transformation of a 3D image:

A linear fractional transformation of a 3D image:

Size (1)

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

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

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

Specify the width of the resulting image:

Specify the width and height of the resulting image:

Use a scaled value:

Use a predefined named size value:

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 DataRangeFull when defining translation in pixel coordinates:

Specify a custom DataRange:

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

Masking (1)

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

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

Use an arbitrary mask:

Padding (1)

By default, the Padding0 is used:

Use a named color:

Use reflected padding:

PlotRange (1)

By default, PlotRangeAutomatic is used:

Use the PlotRangeAll option to show all the transformed pixels from the original image:

Use a custom PlotRange setting:

Use pixel coordinates with PlotRangeFull option:

Resampling (1)

A cubic interpolant is used by default:

Use a different resampling method:

Applications (4)

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

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

Apply the transformation function to the image:

Remove the perspective distortion of the road:

Enhance the perspective effect:

Segment out the building in an image:

Shear the image to straighten up the building:

Properties & Relations (2)

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

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

Possible Issues (2)

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

Non-invertible transformations will give a degenerate result:

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	All	input image only
	Full	input image and padding
	mask	any mask image