Analytic regularization of uniform cubic b-spline deformation fields

Authors:
James A. Shackleford;Qi Yang;Ana M. Lourenço;Nadya Shusharina;Nagarajan Kandasamy;Gregory C. Sharp
Affiliations:
Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA;Medizinische Fakultät Mannheim der Universität Heidelberg, Mannheim, Germany;Institute of Biophysics and Biomedical Engineering, Faculty of Sciences of the University of Lisbon, Lisbon, Portugal;Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA;Electrical and Computer Engineering Department, Drexel University, Philadelphia, PA;Department of Radiation Oncology, Massachusetts General Hospital, Boston, MA
Venue:
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Year:
2012

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Abstract

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.