Aligning Projection Images from Binary Volumes

• Autorzy: Bleichrodt F. , de Beenhouwer J. , Sijbers J. , Batenburg K. J.

Identyfikatory

DOI

10.3233/FI-2014-1110

• Języki publikacji: EN

Abstrakty

EN

In tomography, slight differences between the geometry of the scanner hardware and the geometric model used in the reconstruction lead to alignment artifacts. To exploit high-resolution detectors used in many applications of tomography, alignment of the projection data is essential. Markerless alignment algorithms are the preferred choice over alignment with markers, in case a fully automatic tomography pipeline is required. Moreover, marker based alignment is often not feasible or even possible. At the same time, markerless alignment methods often fail in scenarios where only a small number of projections are available. In this case, the angular separation between projection images is large and therefore the correlation between them is low. This is a property that most markerless algorithms rely on. The intermediate reconstruction problem of alignment by projection matching is highly underdetermined in the limited data case. Therefore, we propose a projection matching method that incorporates prior knowledge of the ground truth. We focus on reconstructing binary volumes. A discrete tomography algorithm is employed to generate intermediate reconstructions. This type of reconstruction algorithm does not rely heavily on correlated projection images. Our numerical results suggest that alignment using discrete tomography projection matching produces much better results in the limited angle case, when compared to a projection matching method that employs an algebraic reconstruction method.

Słowa kluczowe

EN

alignment; automatic; binary tomography; prior knowledge

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2014
• Tom: Vol. 135, nr 1/2
• Strony: 21--42
• Opis fizyczny: Bibliogr. 26 poz., rys., wykr.

Twórcy

autor

Bleichrodt F.

• Centrum Wiskunde & Informatica, 1098 XG Amsterdam, The Netherlands

autor

de Beenhouwer J.

• iMinds - Vision Lab, University of Antwerp, B-2610 Wilrijk, Belgium

autor

Sijbers J.

• iMinds - Vision Lab, University of Antwerp, B-2610 Wilrijk, Belgium

autor

Batenburg K. J.

• Centrum Wiskunde & Informatica, 1098 XG Amsterdam, The Netherlands

Bibliografia

• [1] Batenburg, K. J.: An evolutionary algorithm for discrete tomography, Discrete Applied Mathematics, 151(1), 2005, 36–54.
• [2] Batenburg, K. J., van Aarle, W., Sijbers, J.: A semi-automatic algorithm for grey level estimation in tomography, Pattern Recognition Letters, 32(9), 2011, 1395–1405.
• [3] Batenburg, K. J., Sijbers, J.: DART: A practical reconstruction algorithm for discrete tomography, IEEE Transactions on Image Processing, 20(9), 2011, 2542–2553.
• [4] Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM Journal on Imaging Sciences, 2(1), 2009, 183–202.
• [5] Bleichrodt, F., Batenburg, K. J.: Automatic Optimization of Alignment Parameters for Tomography Datasets, in: Image Analysis, Springer, 2013, 489–500.
• [6] Boas, F. E., Fleischmann, D.: Evaluation of two iterative techniques for reducing metal artifacts in computed tomography, Radiology, 259(3), 2011, 894–902.
• [7] Brandt, S., Heikkonen, J., Engelhardt, P.: Automatic alignment of transmission electron microscope tilt series without fiducial markers, Journal of structural biology, 136(3), 2001, 201–213.
• [8] Candès, E. J., Romberg, J., Tao, T.: Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52(2), 2006, 489–509.
• [9] Fitchard, E., Aldridge, J., Reckwerdt, P., Mackie, T.: Registration of synthetic tomographic projection data sets using cross-correlation, Physics in medicine and biology, 43(6), 1999, 1645.
• [10] Fong, D. C.-L., Saunders, M.: LSMR: An iterative algorithm for sparse least-squares problems, SIAM Journal on Scientific Computing, 33(5), 2011, 2950–2971.
• [11] Frank, J.: Electron tomography: Three-dimensional imaging with the transmission electron microscope, Plenum Pub Corp, 1992.
• [12] Houben, L., Bar Sadan, M.: Refinement procedure for the image alignment in high-resolution electron tomography, Ultramicroscopy, 111, 2011, 1512–1520.
• [13] Joseph, P.: An improved algorithm for reprojecting rays through pixel images, Medical Imaging, IEEE Transactions on, 1(3), 1982, 192–196.
• [14] Madsen, K., Nielsen, H. B., Tingleff, O.: Methods for Non-Linear Least Squares Problems (2nd ed.), 2004.
• [15] Midgley, P. A., Dunin-Borkowski, R. E.: Electron tomography and holography in materials science, Nature materials, 8(4), 2009, 271–280.
• [16] Midgley, P. A.,Weyland, M.: 3D electron microscopy in the physical sciences: the development of Z-contrast and EFTEM tomography, Ultramicroscopy, 96(3), 2003, 413–431.
• [17] Moré, J. J.: The Levenberg-Marquardt algorithm: implementation and theory, in: Numerical analysis, Springer, 1978, 105–116.
• [18] Natterer, F., Wübbeling, F.: Mathematical methods in image reconstruction, SIAM, 2001.
• [19] Nocedal, J., Wright, S.: Numerical optimization, 2nd edition, Springer Verlag, 2006.
• [20] Palenstijn, W. J., Batenburg, K. J., Sijbers, J.: Performance improvements for iterative electron tomography reconstruction using graphics processing units (GPUs), Journal of Structural Biology, 176(2), 2011, 250–253.
• [21] Palenstijn, W. J., Batenburg, K. J., Sijbers, J.: The ASTRA Tomography Toolbox, CMMSE 2013 : Proceedings of the 13th International Conference on Computational and Mathematical Methods - Almería , Spain, 2013.
• [22] Parkinson, D. Y., Knoechel, C., Yang, C., Larabell, C. A., Le Gros, M. A.: Automatic alignment and reconstruction of images for soft X-ray tomography, Journal of Structural Biology, 177(2), 2012, 259–266.
• [23] Schüle, T., Schnörr, C., Weber, S., Hornegger, J.: Discrete tomography by convex–concave regularization and D.C. programming, Discrete Applied Mathematics, 151(1), 2005, 229–243.
• [24] Slaney, M., Kak, A.: Principles of computerized tomographic imaging, SIAM, 1988.
• [25] Williams, J. J., Yazzie, K. E., Phillips, N. C., Chawla, N., Xiao, X., De Carlo, F., Iyyer, N., Kittur, M.: On the Correlation Between Fatigue Striation Spacing and Crack Growth Rate: A Three-Dimensional (3-D) X-ray Synchrotron Tomography Study, Metallurgical and Materials Transactions A, 42(13), 2011, 3845–3848.
• [26] Yang, C., Ng, E., Penczek, P.: Unified 3-D structure and projection orientation refinement using quasi-Newton algorithm, Journal of structural biology, 149(1), 2005, 53–64.