Abstract
Automatic multi-modal image registration is central to numerous tasks in medical imaging today and has a vast range of applications e.g., image guidance, atlas construction, etc. In this paper, we present a novel multi-modal 3D non-rigid registration algorithm where in 3D images to be registered are represented by their corresponding local frequency maps efficiently computed using the Riesz transform as opposed to the popularly used Gabor filters. The non-rigid registration between these local frequency maps is formulated in a statistically robust framework involving the minimization of the integral squared error a.k.a. L 2 E (L 2 error). This error is expressed as the squared difference between the true density of the residual (which is the squared difference between the non-rigidly transformed reference and the target local frequency representations) and a Gaussian or mixture of Gaussians density approximation of the same. The non-rigid transformation is expressed in a B-spline basis to achieve the desired smoothness in the transformation as well as computational efficiency.
The key contributions of this work are (i) the use of Riesz transform to achieve better efficiency in computing the local frequency representation in comparison to Gabor filter-based approaches, (ii) new mathematical model for local-frequency based non-rigid registration, (iii) analytic computation of the gradient of the robust non-rigid registration cost function to achieve efficient and accurate registration. The proposed non-rigid L 2 E-based registration is a significant extension of research reported in literature to date. We present experimental results for registering several real data sets with synthetic and real non-rigid misalignments.
This research was in part supported by RO1-NS 42075.
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References
Chui, H., Win, L., Schultz, R., Duncan, J., Rangarajan, A.: A unified non-rigid feature registration method for brain mapping. Medical Image Analysis 7, 112–130 (2003)
Maintz, J.B.A., Viergever, M.A.: A survey of medical image registration. Medical Image Analysis 2, 1–36 (1998)
Irani, M., Anandan, P.: Robust Multi-sensor Image Alignment. In: International Conference on Computer Vision, Bombay, India, pp. 959–965 (1998)
Liu, J., Vemuri, B.C., Marroquin, J.L.: Local frequency representations for robust multimodal image registration. IEEE Transactions on Medical Imaging 21, 462–469 (2002)
Mellor, M., Brady, J.M.: Non-rigid multimodal image registration using local phase. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 789–796. Springer, Heidelberg (2004)
Roche, A., Pennec, X., Malandain, G., Ayache, N.: Rigid registration of 3-d ultrasound with mr images: A new approach combining intensity and gradient information. IEEE Transactions on Medical Imaging 20, 1038–1049 (2001)
Szeliski, R., Coughlan, J.: Spline-based image registration. Int. J. Comput. Vision 22, 199–218 (1997)
Lai, S.H., Fang, M.: Robust and efficient image alignment with spatially-varying illumination models. In: IEEE Conference on Computer Vision and Pattern Recognition, vol. II, pp. 167–172 (1999)
Guimond, A., Roche, A., Ayache, N., Menuier, J.: Three-Dimensional Multimodal Brain Warping Using the Demons Algorithm and Adaptive Intensity Corrections. IEEE Trans. on Medical Imaging 20, 58–69 (2001)
Thirion, J.P.: Image matching as a diffusion process: an analogy with maxwell’s demons. Medical Image Analysis 2, 243–260 (1998)
Viola, P.A., Wells, W.M.: Alignment by maximization of mutual information. In: Fifth Intl. Conference on Computer Vision, MIT, Cambridge (1995)
Collignon, A., Maes, F., Delaere, D., Vandermeulen, D., Suetens, P., Marchal, G.: Automated multimodality image registration based on information theory. In: Bizais, Y., Barillot, C., Di Paola, R. (eds.) Information Processing in Medical Imaging (1995)
Studholme, C., Hill, D., Hawkes, D.J.: Automated 3D registration of MR and CT images in the head. Medical Image Analysis 1, 163–175 (1996)
Studholme, C., Hill, D.L.G., Hawkes, D.J.: An overlap invariant entropy measure of 3D medical image alignment. Pattern Recognition 32, 71–86 (1999)
Rueckert, D., Frangi, A.F., Schnabel, J.A.: Automatic construction of 3d statistical deformation models of the brain using non-rigid registration. IEEE Trans. Med. Imaging 22, 1014–1025 (2003)
Hermosillo, G., Chefd’hotel, C., Faugeras, O.: Variational methods for multimodal image matching. Int. J. Comput. Vision 50, 329–343 (2002)
Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., Hawkes, D.J.: Nonrigid registration using free-form deformations: Application to breast mr images. IEEE Trans. on Medical Imaging 18, 712–721 (1999)
Leventon, M.E., Grimson, W.E.L.: Multi-modal volume registration using joint intensity distributions. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 1057–1066. Springer, Heidelberg (1998)
Gaens, T., Maes, F., Vandermeulen, D., Suetens, P.: Non-rigid multimodal image registration using mutual information. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 1099–1106. Springer, Heidelberg (1998)
Servin, M., Quiroga, J.A., Marroquin, J.L.: General n-dimensional quadrature transform and its application to interferogram demodulation. Journal of the Optical Society of America A 20, 925–934 (2003)
Kwan, C.C., Evans, K., Brainweb, R.: online interface to a 3-d mri simulated brain database (1997)
Stewart, G., Sun, J.: Matrix Perturbation Theory. Academic Press, London (1990)
Scott, D.: Parametric statistical modeling by minimum integrated square Error. Technometrics 43, 274–285 (2001)
Mattes, D., Haynor, D.R., Vesselle, H., Lewellen, T.K., Eubank, W.: Non-rigid multimodality image registration. In: Proc. SPIE, Medical Imaging 2001: Image Processing, Bellingham, WA, vol. 4322, pp. 1609–1620 (2001)
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Jian, B., Vemuri, B.C., Marroquin, J.L. (2005). Robust Nonrigid Multimodal Image Registration Using Local Frequency Maps. In: Christensen, G.E., Sonka, M. (eds) Information Processing in Medical Imaging. IPMI 2005. Lecture Notes in Computer Science, vol 3565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505730_42
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DOI: https://doi.org/10.1007/11505730_42
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