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Analytic Regularization of Uniform Cubic B-Spline Deformation Fields

Institution:
1Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA, USA.
2Medizinische Fakult ̈t Mannheim der Universit ̈t Heidelberg, Mannheim, Germany.
3Institute of Biophysics and Biomedical Engineering, Faculty of Sciences of the University of Lisbon, Lisbon, Portugal.
4Electrical and Computer Engineering Department, Drexel University, Philadelphia, PA, USA.
Publisher:
Int Conf Med Image Comput Comput Assist Interv. MICCAI 2012
Publication Date:
Oct-2012
Journal:
Med Image Comput Comput Assist Interv
Volume Number:
15
Issue Number:
Pt 2
Pages:
122-9
Citation:
Int Conf Med Image Comput Comput Assist Interv. 2012 Oct;15(Pt 2):122-9.
PubMed ID:
23286040
Keywords:
deformable registration, B-spline, analytic regularization, thin-plate, Bending Energy
Appears in Collections:
NA-MIC
Sponsors:
U54 EB005149/EB/NIBIB NIH HHS/United States
C06 CA059267/CA/NCI NIH HHS/United States
Generated Citation:
Shackleford J.A., Yang Q., Lourenço A.M., Shusharina N., Kandasamy N., Sharp G.C. Analytic Regularization of Uniform Cubic B-Spline Deformation Fields. Int Conf Med Image Comput Comput Assist Interv. 2012 Oct;15(Pt 2):122-9. PMID: 23286040.
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Image registration is inherently ill-posed, and lacks a unique solution. In the context of medical applications, it is desirable to avoid solutions that describe physically unsound deformations within the patient anatomy. Among the accepted methods of regularizing non-rigid image registration to provide solutions applicable to medical practice is the penalty of thin-plate bending energy. In this paper, we develop an exact, analytic method for computing the bending energy of a three-dimensional B-spline deformation field as a quadratic matrix operation on the spline coefficient values. Results presented on ten thoracic case studies indicate the analytic solution is between 61-1371x faster than a numerical central differencing solution.

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