# 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 Automatic alignment method to use TransformationClass Automatic geometrical 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

open allclose all

## Basic Examples(2)

Determine the spatial transformation between two sets of positions:

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Find the similarity transformation between two sets of two points:

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