see https://github.com/C4IR/FAIR.m for details and license issues.

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FAIR stands for Flexible Algorithms for Image Registration and is a MATLAB (https://de.mathworks.com/) written package for solving the so-called image registration problem (alas co-registration, correspondence, fusion, matching, optical flow, warping, ...).

A solid documentation is

Jan Modersitzki: FAIR - Flexible Algorithms for Image Registration, SIAM 2009

@BOOK{2009-FAIR,
  title = {{FAIR}: Flexible Algorithms for Image Registration},
  publisher = {SIAM},
  address = {Philadelphia},
  year = {2009},
  author = {J. Modersitzki},
}

see also http://www.siam.org/books/fa06/ for a free PDF.

The objective is to automatically establish point-to-point correspondences between objects in two different scenes. Given are two (or more) images T and R. Wanted is a geometrical transformation y (correction, deformation, displacement, distortion, ...) such that the transformed image T(y) is similar to R. Given a similarity/distance measure D and a regularization for y the problem is phrased in a variational setting:

Minimize the joint energy J with respect to y
J(y) = D(T(y),R) + S(y)

The toolbox provides a variety of

- example data for T,R         kernel/data
- image models                 kernel/imgModels
- distance measures D          kernel/diatnces
- regularizer S                kernel/regularizers
- transfomation models y       kernel/transformations
- image viewers                kernel/viewers

Additionally, the toolbox provides

- numerical tools/optimization    kernel/numeric
- matrix-free operators           kernel/matrixFree
- landmark registrations          kernel/landmarks
- genral tools (i/o etc)          kernel/tools

FAIR is primarily designed as an academic and teaching tool. It can be used to explore existing techniques or to invent new features (please let us know and contribute to the community). Though the focus is on exploring methods, FAIR can be - and already has been - used as a prototyping tool for practically relevant registration problems.

The main differences to older versions of the codes are

• now available via github which allows for direct interaction with the community
• replaced the interpolation toolbox by an appropriate image model
• includes a nonlinear hyperelastic regularization energy
• the package is supplemented by parallelized C versions of otherwise computationally costly mfiles

• Provide even better tools (enhance the pieces)
• Provide add-ons for specific application

• Jan Modersitzki Institute of Mathematics and Image Computing, University of Lübeck, Germany
• Lars Ruthotto, Dept. of Mathematics and Computer Science, Emory University, Atlanta, USA
• Fabian Gigengack, European Institute for Molecular Imaging (EIMI), University of Münster, Germany

The following list presents all intermediate results and the m-file for a non-parametric multi-level image registration with an affine linear pre-registration for 2D PET-CT data using the normalized gradient field as a distance measure and elastic regularization; a Gauss-Newton scheme is used as optimizer in a matrix free setting (using multigrid for the linear solve). The time was about 10sec for 128x128 data on a standard PC including all graphics and data pre-processing.

Under construction [mfile] [data] [multi-level representation] [PIR results level 4] [NPIR results level 4] [NPIR results level 5] [NPIR results level 6] [NPIR results level 7] [final results] [output]

FAIR not only provides opportunities to develop specific building blocks but also to redesign fundamental structures. As modifications can be severe, we decided to split the toolbox into a kernel and add-ons. The stand alone kernel provides all the basic functionality. The add-ons can be tuned to even overlay standard behaviour. In the following, we present some examples. We hope to extend this list with the help of your contributions.

Please see the folder add-ons for currently available extensions.