Itk::Transforms supporting spatial derivatives

Please use this identifier to cite or link to this publication:
This document describes the use and implementation of first and second order spatial derivatives of coordinate transformations in the Insight Toolkit url{}). Spatial derivatives are useful for many types of regularising or penalty terms frequently used in image registration. These derivatives are dubbed 'SpatialJacobian' and 'SpatialHessian' to distinguish with the derivative to the transformation parameters themselves, which is called `Jacobian' in the ITK.

In addition to the spatial derivatives, we derived and implemented the derivatives to the registration/transform parameters of these spatial derivatives, required for gradient descent type optimisation routines. These derivatives are implemented in a sparse manner, reducing the computation time for transformations which have local support. All of these derivatives are implemented for the most common ITK coordinate transformation, such as the rigid, affine and B-spline transformation. In addition we derive formulae and code for arbitrary compositions of transformations. The spatial derivatives were subsequently exploited by implementing the bending energy penalty term.

This paper is accompanied with the source code, input data, parameters and output data that the authors used for validating the algorithm described in this paper. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.
minus Automatic Testing Results by Insight-Journal Dashboard on Tue Sep 14 12:08:46 2010 for revision #1
starstarstarstarstar expertise: 5 sensitivity: 5
yellow This project passed all of its tests.
Click here for more details.

Go here to access the main testing dashboard.

There is no review at this time. Be the first to review this publication!

Quick Comments

Download All
Download Paper , View Paper
Download Source code

Statistics more
Global rating: starstarstarstarstar
Review rating: starstarstarstarstar [review]
Code rating: starstarstarstarstar
Paper Quality: plus minus

Information more
Categories: Derivatives and Integrals, Linear Algebra, Registration
Keywords: image registration, spatial derivatives, penalty terms, regulizers
Toolkits: ITK, CMake
Export citation:


Linked Publications more
Importing Contours from DICOM-RT Structure Sets Importing Contours from DICOM-RT Structure Sets
by Dowling J., Malaterre M., Greer P.B., Salvado O.
Diffeomorphic Demons Using ITK's Finite Difference Solver Hierarchy Diffeomorphic Demons Using ITK's Finite Difference Solver Hierarchy
by Vercauteren T., Pennec X., Perchant A., Ayache N.

View license
Loading license...

Send a message to the author
ISSN 2327-770X
Powered by Midas