Vampire - Variational Algorithm for Mass-Preserving Image REgistration

Fabian Gigengack^1,2, Lars Ruthotto^3,4,5, Martin Burger⁴,
Carsten H. Wolters⁵, Xiaoyi Jiang², and Klaus Schäfers¹

¹ European Institute for Molecular Imaging (EIMI), University of Münster, Germany
² Department of Mathematics and Computer Science, University of Münster, Germany
³ Institute of Mathematics and Image Computing (MIC), University of Lübeck, Germany
⁴ Institute for Computational and Applied Mathematics, University of Münster, Germany
⁵ Institute for Biomagnetism and Biosignalanalysis, University of Münster, Germany

Abstract

Vampire is a mass-preserving image registration approach. Our main area of application is motion correction in gated positron emission tomography (PET) of the human heart. Intensity modulations caused by the highly non-rigid cardiac motion are considered by means of a mass-preserving transformation model. Vampire is highly robust against noise due to hyperelastic regularization and leads to accurate and realistic motion estimates.

Methods

Given a template image T and a reference image R, find the optimal transformation y which aligns the two images by minimizing the following functional:

S denotes the hyperelastic regularization functional [11] and alpha a scalar weighting factor. More details are given in [1] and [2]-[9].

Example

Petnomc2 — (b) PET reconstruction without motion correction.

Petmc3 — (c) PET reconstruction after Vampire-based motion correction.

Due to inherent respiratory and cardiac motion, illustrated in (a), reconstructed images of cardiac PET scans show motion artifacts in terms of blurring. A reconstruction without motion correction is shown in (b). After the application of Vampire-based motion correction the motion blur is visibly reduced, which is shown in (c).

(Images: Courtesy of University Hospital of Münster, Department of Nuclear Medicine, Prof. Dr. Michael Schäfers)

Get the code

To get the code, please fill out the >copyright form<. Scan it and send it back to >Fabian Gigengack< or >Lars Ruthotto<.
Please note that Vampire is implemented as an application of the MATLAB based >FAIR registration toolbox< [10]. Hence, FAIR needs to be downloaded as well. You can get it >here<.

References

[1]	F. Gigengack, L. Ruthotto, M. Burger, C.H. Wolters, X. Jiang, and K.P. Schäfers: Motion Correction in Dual Gated Cardiac PET using Mass-Preserving Image Registration. In IEEE Transactions on Medical Imaging (TMI), IEEE, 2012.
[2]	F. Gigengack, L. Ruthotto, T. Kösters, X. Jiang, J. Modersitzki, M. Burger, C.H. Wolters, and K.P. Schäfers: Pipeline for Motion Correction in Dual Gated PET with an L¹-like Data Term. Annual Meeting of the Society of Nuclear Medicine & Molecular Imaging (SNMMI), 2013.
[3]	X. Jiang, M. Dawood, F. Gigengack, B. Risse, S. Schmid, D. Tenbrinck, and K.P. Schäfers: Biomedical Imaging: A Computer Vision Perspective. In Proc. of CAIP, 2013.
[4]	H. Yan, F. Gigengack, X. Jiang, and K.P. Schäfers: Super-Resolution in Cardiac PET using Mass-Preserving Image Registration. In Proc. of ICIP, IEEE, 2013.
[5]	F. Gigengack, L. Ruthotto, T. Kösters, X. Jiang, J. Modersitzki, M. Burger, C.H. Wolters, and K.P. Schäfers: Pipeline for Motion Correction in Dual Gated PET. In Proc. of NSS/MIC, IEEE, 2012.
[6]	L. Ruthotto, F. Gigengack, M. Burger, C.H. Wolters, X. Jiang, K.P. Schäfers, and J. Modersitzki: A Simplified Pipeline for Motion Correction in Dual Gated Cardiac PET. In Proc. of Bildverarbeitung für die Medizin, Springer, 2012.
[7]	F. Gigengack, L. Ruthotto, M. Burger, C.H. Wolters, X. Jiang, and K.P. Schäfers: Mass-Preserving Motion Correction of Dual Gated Cardiac PET. In Proc. of NSS/MIC, IEEE, 2011.
[8]	F. Gigengack, L. Ruthotto, M. Burger, C.H. Wolters, X. Jiang, and K.P. Schäfers: Mass-Preserving Motion Correction of PET: Displacement Field vs. Spline Transformation. In Proc. of NSS/MIC, IEEE, 2011.
[9]	F. Gigengack, L. Ruthotto, M. Burger, C.H. Wolters, X. Jiang, and K.P. Schäfers: Motion correction of cardiac PET using mass-preserving registration. In Proc. of NSS/MIC, IEEE, 2010.
[10]	J. Modersitzki: FAIR: Flexible Algorithms for Image Registration. SIAM, Philadelphia, 2009.
[11]	M. Burger, J. Modersitzki, and L. Ruthotto: A hyperelastic regularization energy for image registration. SIAM Journal on Scientific Computing, 2013.