Topology-Preserving Transformation Based on the Correspondence of Control Points Using Radial Basis Functions

Abstract:

For point-based image registration, transformations using radial basis functions on scattered points cause problems with topology-preservation. We propose here a topology-preserving transformation based on expansions of radial basis functions. By analyzing the non-preserving transformation given by the corresponding control points, this method computes the main shifting directions of topology non-preserving regions on deformed surfaces. It then determines the control points leading to the topology non-preservation results. Next, it adaptively relaxes these control points based on the spatial relationships of points, and adjusts the transformation function coefficients using relaxation parameters to construct the topology-preserving transformation. We provide here the method for selecting the control points that cause the topology non-preservation results and estimate the optimal relaxation parameters based on the shifting model of the control points. Experimental results on random point sets, artificial images and medical images show that this method is feasible and practicable.

• Periodical: Applied Mechanics and Materials (Volumes 249-250)
• Pages: 752-758
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.249-250.752
• Online since: December 2012
• Authors: Xuan Yang, Shan Shan Fan
• Keywords: Image Registration, Image Transformation, Radial Basis Function (RBF), Topology Preservation

References

[1] M. Holden, A review of geometric transformations for nonrigid body registration, IEEE Transactions on Medical Imaging. 27(2008) 111–128.

DOI: 10.1109/tmi.2007.904691

[2] Z. Wu, Compactly supported positive definite radial functions, Advances in Computational Mathematics. 4(1995) 283-292.

DOI: 10.1007/bf03177517

[3] O. Muse, F. Heita, J. Armspach, Topology Preserving Deformable Image Matching Using Constrained Hierarchical Parametric Models, IEEE Transactions on Image Processing. 10(2001) 1081-1093.

DOI: 10.1109/83.931102

[4] S. C. Joshi, M. I. Miller, Control point matching via large deformation diffeomorphisms, IEEE Transactions on Image Processing. 9(2000) 1357-1370.

DOI: 10.1109/83.855431

[5] V. Arsigny, X. Pennec, N. Ayache, Polyrigid and Polyaffine Transformations: A New Class of Diffeomorphisms for Locally Rigid or Affine Registration, Med Image Anal. 9(2005) 507-523.

DOI: 10.1007/978-3-540-39903-2_101

[6] R. Narayanan ,  J. A. Fessler ,  H. Park ,  C. R. Meyer, Diffeomorphic nonlinear transformations: A local parametric approach for image registration, LNCS 3565(2005) 174-185.

DOI: 10.1007/11505730_15

[7] S.Y. Chun,   J. A Fessler,   Regularized methods for topology-preserving smooth nonrigid image registration using B-spline basis, 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro (2008) 1099 – 1102.

DOI: 10.1109/isbi.2008.4541192

[8] G.K. Rohde, A. Aldroubi, B.M. Dawant, The adaptive bases algorithm for intensity-based nonrigid image registration, IEEE Trans Med Imaging. 22(2003)1470-1479.

DOI: 10.1109/tmi.2003.819299

[9] V. Noblet,  C. Heinrich,  F. Heitz, J. P. Armspach,  3-D deformable image registration: a topology preservation scheme based on hierarchical deformation models and interval analysis optimization, IEEE Transactions on Image Processing. 14 (2005).

DOI: 10.1109/tip.2005.846026

[10] Z. Zhang, X. Yang, Elastic image warping using a new radial basis function with compact support, Biosignals 1(2008) 216–219.

[11] X. Yang, Performance analysis of compact support radial basis function based on Thin-plate splines, Journal of Computational Information Systems. 11(2011) 3986-3994.

[12] K. Rohr, H.S. Stiehl, R. Sprengel, et al., Point-based elastic registration using approximating thin-plate splines, IEEE Trans Med Imaging. 20(2001) 526-534.

DOI: 10.1109/42.929618