Abstract
The ability to reconstruct multivariate approximating or interpolating functions from sampled data finds many practical applications in medical image analysis. Parameterized reconstruction methods employing B-splines have typically utilized least-squares methodology for data fitting. For large sample sets, solving the resulting linear system is computationally demanding as well as susceptible to ill-conditioning. We present a generalization of a previously proposed fast surface fitting technique for cubic B-splines which avoids the pitfalls of the conventional fitting approach. Our proposed generalization consists of expanding the algorithm to n dimensions, allowing for arbitrary spline degree in the different parametric dimensions, permitting wrapping of the parametric domain, and the assignment of confidence values to the data points for more precise control over the fitting results. In addition, we implement our generalized B-spline approximation algorithm within the Insight Toolkit (ITK) for open source dissemination.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Piegl, L., Tiller, W.: The NURBS Book. Springer, Heidelberg (1997)
Riesenfeld, R.F.: Applications of B-Spline Approximation to Geometric Problems of Computer-Aided Design, Ph.D. thesis, Syracuse University (1975)
Lee, S., Wolberg, G., Shin, S.Y.: Scattered data interpolation with multilevel B-splines. IEEE Transactions on Visualization and Computer Graphics 3(3), 228–244 (1997)
Ibanez, L., Schroeder, W., Ng, L., Cates, J.: The ITK Software Guide. Insight Software Consortium, 2nd edn. (November 2005)
de Boor, C.: B-spline basics. In: Fundamental Developments of Computer-Aided Geometric Modeling, pp. 27–49. American Press (1993)
Cox, M.G.: The numerical evaluation of B-splines. Jour. Inst. Math. Applic. 10, 134–149 (1972)
de Boor, C.: On calculating with B-splines. Jour. Approx. Theory 6, 50–62 (1972)
Ma, W., Kruth, J.P.: Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces. Computer-Aided Design 27, 663–675 (1995)
Schoenberg, I.J.: Spline functions and the problem of graduation. Proc. Nat. Acad. Sci. 52, 947–950 (1964)
Tustison, N.J., Davila-Roman, V.G., Amini, A.A.: Myocardial kinematics from tagged MRI based on a 4-D B-spline model. IEEE Trans. Biomed. Eng. 50(8), 1038–1040 (2003)
Tustison, N.J., Amini, A.A.: Biventricular myocardial strains via nonrigid registration of anatomical NURBS model [corrected]. IEEE Trans. Med. Imaging 25(1), 94–112 (2006)
Hjelle, O.: Approximation of scattered data with multilevel B-splines, Tech. Rep. (2001)
Li, T., Schreibmann, E., Thorndyke, B., Tillman, G., Boyer, A., Koong, A., Goodman, K., Xing, L.: Dose reduction in 4D computed tomography. Medical Physics 32, 3650–3659 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tustison, N.J., Gee, J.C. (2006). Generalized n-D C k B-Spline Scattered Data Approximation with Confidence Values. In: Yang, GZ., Jiang, T., Shen, D., Gu, L., Yang, J. (eds) Medical Imaging and Augmented Reality. MIAR 2006. Lecture Notes in Computer Science, vol 4091. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11812715_10
Download citation
DOI: https://doi.org/10.1007/11812715_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37220-2
Online ISBN: 978-3-540-37221-9
eBook Packages: Computer ScienceComputer Science (R0)