FindGeometricTransform

FindGeometricTransform[pts1,pts2]

finds a geometric transformation that aligns positions specified by pts2 with pts1, returning the alignment error together with the transformation function.

FindGeometricTransform[ref,{pts1,pts2,…}]

finds geometric transformations that align each of the ptsi with ref.

FindGeometricTransform[{pts1,pts2,…}]

finds geometric transformations that align each of the ptsi with pts1.

Details and Options

  • FindGeometricTransform returns an expression of the form {err,trfun}, where err is an estimate of the average alignment error, and trfun is a transformation function. The function trfun can be applied to the positions pts2 to align them with the positions pts1.
  • The geometries pts1 and pts2 can be given as lists of position coordinates or Wolfram Language graphics objects.
  • FindGeometricTransform[image1,image2] finds the geometric transformation to align 2D or 3D images.
  • FindGeometricTransform works with points in any dimensions as well as with built-in 2D and 3D graphics primitives.
  • The following options can be specified:
  • Method Automaticalignment method to use
    TransformationClass Automaticgeometrical relation between images
  • By default, the most suitable alignment method and transformation class are used for calculating the transformation.
  • Available fitting methods:
  • "Linear"linear solver based on SVD
    "RANSAC"random sample consensus method
    "FindFit"uses FindFit
    {"ImageAlign",method}ImageAlign transformation using the given method
  • With the setting "RANSAC", some positions may be considered as outliers and may not be used to determine the geometric transformation.
  • Possible settings for the TransformationClass option include:
  • "Translation"translation only
    "Rigid"translation and rotation
    "Similarity"translation, rotation, and scaling
    "Affine"linear transformation and translation
    "Perspective"linear fractional transformation

Examples

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Basic Examples  (2)

Determine the spatial transformation between two sets of positions:

Find the similarity transformation between two sets of two points:

Scope  (6)

Transformation between graphic primitives:

Apply the transformation and display the result:

A three-dimensional geometric transformation:

Transformation between images:

Transformation between 3D images:

Find transformations between reference points and each point set of a list:

Find transformations between each element of a list and the first element:

Options  (8)

Method  (4)

The method "Linear" is typically faster than "RANSAC":

The "RANSAC" method works best if there are outliers or erroneous correspondences:

For images, the "ImageAlign" method returns the transformation found by ImageAlign:

Use the "Keypoints" method using KAZE keypoints:

TransformationClass  (4)

Find a linear fractional transformation:

Find an affine transformation:

Find a rigid transformation:

Find a translation transform:

Applications  (3)

Use an estimated transformation of the corresponding points for aligning two images:

A basic image-stitching method:

Find the geometric transformation that aligns images:

Transform one image and compose on top of the other one:

Find a geometric alignment for a list of images with different exposures:

Properties & Relations  (2)

Find a 3D transformation and apply it using GeometricTransformation:

Find the parameters of an affine transformation:

Wolfram Research (2010), FindGeometricTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGeometricTransform.html (updated 2017).

Text

Wolfram Research (2010), FindGeometricTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/FindGeometricTransform.html (updated 2017).

CMS

Wolfram Language. 2010. "FindGeometricTransform." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/FindGeometricTransform.html.

APA

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

BibTeX

@misc{reference.wolfram_2024_findgeometrictransform, author="Wolfram Research", title="{FindGeometricTransform}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/FindGeometricTransform.html}", note=[Accessed: 13-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_findgeometrictransform, organization={Wolfram Research}, title={FindGeometricTransform}, year={2017}, url={https://reference.wolfram.com/language/ref/FindGeometricTransform.html}, note=[Accessed: 13-December-2024 ]}