# Par0002

## Contents

### Image data

• 3D PET
• brain
• Voxel size 2.59 x 2.59 x 8.0 mm
• Dimension: 128 x 128 x 15
• Stored as in MHD format
• Data originated from the Retrospective Image Registration Evaluation Project [1,2]

• 3D MR T1
• brain
• Voxel size 1.25 x 1.25 x 4.0 mm
• Dimension: 256 x 256 x 26
• Stored as in MHD format
• Data originated from the Retrospective Image Registration Evaluation Project [1,2]

Screen shots:

### Application

The grid effect is a well-known issue in image registration. It refers to the problem that the cost function contains irregularities at locations representing grid-aligning transformations, which can impede the registration process. It has often been studied in the context of interpolation artefacts [3]. In this section it is demonstrated that the sampling mechanism can solve this issue, by taking samples off the voxel grid, as suggested in [4,5].

Brain images were taken from the "Retrospective Image Registration Evaluation" project [2]. We investigated the registration of a T1-weighted MR image (moving image) to a PET image (both of patient 001).

The cost function (MI) was analysed using an exhaustive search in a single translation direction, with a step size of 0.1 mm. Linear interpolation was used to compute $I_M(T_{\mu}(x))$. Different sampling strategies were employed for computing the cost function: all voxels, random sampling on the voxel grid, and random sampling off the voxel grid.

### Registration settings

elastix version: 4.103

Parameter files:

Command line call:

elastix -f PET.mhd -m MR_T1.mhd -p par0002.<?>.txt -out outputdir


### Published in

These registration are described in the publication:

S. Klein, M. Staring, K. Murphy, M.A. Viergever, J.P.W. Pluim, "elastix: a toolbox for intensity based medical image registration," IEEE Transactions on Medical Imaging, vol. 29, no. 1, pp. 196-205, 2010.

See the elastix manual (link) for hints on how to subsequently apply the transformation to the annotated points using transformix.

### References

[2] J. West, J.M. Fitzpatrick, M.Y. Wang, et al., "Comparison and evaluation of retrospective intermodality brain image registration techniques", Journal of Computer Assisted Tomography, vol. 21, no. 4, pp. 554 - 566, 1997.

[3] J.P.W. Pluim, J.B.A. Maintz and M.A. Viergever, "Interpolation artefacts in mutual information-based image registration", Computer Vision and Image Understanding, vol. 77, no. 2, pp. 211 - 232, 2000.

[4] B. Likar and F. Pernus, "A hierarchical approach to elastic registration based on mutual information", Image and Vision Computing, vol. 19, no. 1-2, pp. 33 - 44, 2001.

[5] P. Thevenaz, M. Bierlaire and M. Unser, "Halton Sampling for Image Registration Based on Mutual Information", Sampling Theory in Signal and Image Processing, vol. 7, no. 2, pp. 141 - 171, 2008.