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.
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Shackleford, J.A., Yang, Q., Lourenço, A.M., Shusharina, N., Kandasamy, N., Sharp, G.C. (2012). Analytic Regularization of Uniform Cubic B-spline Deformation Fields. In: Ayache, N., Delingette, H., Golland, P., Mori, K. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2012. MICCAI 2012. Lecture Notes in Computer Science, vol 7511. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33418-4_16
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DOI: https://doi.org/10.1007/978-3-642-33418-4_16
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