Editing Image registration (section)

=== Transformation models ===

Image registration algorithms can also be classified according to the transformation models they use to relate the target image space to the reference image space. The first broad category of transformation models includes [[linear transformation]]s, which include rotation, scaling, translation, and other affine transforms.<ref>http://www.comp.nus.edu.sg/~cs4243/lecture/register.pdf {{Bare URL PDF|date=March 2022}}</ref> [[Linear transformation]]s are global in nature, thus, they cannot model local geometric differences between images.<ref name="AG"/>

The second category of transformations allow 'elastic' or 'nonrigid' transformations. These transformations are capable of locally warping the target image to align with the reference image.  Nonrigid transformations include [[radial basis functions]] ([[Thin plate spline|thin-plate]] or surface splines, [[Radial basis functions#Types|multiquadrics]], and [[support (mathematics)#Compact support|compactly-supported transformations]]<ref name="AG"/>), physical continuum models (viscous fluids), and large deformation models ([[diffeomorphism]]s).

Transformations are commonly described by a parametrization, where the model dictates the number of parameters. For instance, the translation of a full image can be described by a single parameter, a translation vector. These models are called parametric models. Non-parametric models on the other hand, do not follow any parameterization, allowing each image element to be displaced arbitrarily.<ref>{{cite journal|last1=Sotiras|first1=A.|last2=Davatzikos|first2=C.|last3=Paragios|first3=N.|title=Deformable Medical Image Registration: A Survey|journal=IEEE Transactions on Medical Imaging|date=July 2013|volume=32|issue=7|pages=1153–1190|doi=10.1109/TMI.2013.2265603|pmid=23739795|pmc=3745275|url=https://hal.inria.fr/hal-00858737/document}}</ref>

There are a number of programs that implement both estimation and application of a warp-field. It is a part of the [[Statistical parametric mapping|SPM]] and [[AIR (program)|AIR]] programs.