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Elastic Registration of Biological Images Using Vector-Spline Regularization

C.Ó.S. Sorzano, P. Thévenaz, M. Unser

IEEE Transactions on Biomedical Engineering, vol. 52, no. 4, pp. 652-663, April 2005.


We present an elastic registration algorithm for the alignment of biological images. Our method combines and extends some of the best techniques available in the context of medical imaging. We express the deformation field as a B-spline model, which allows us to deal with a rich variety of deformations. We solve the registration problem by minimizing a pixelwise mean-square distance measure between the target image and the warped source. The problem is further constrained by way of a vector-spline regularization which provides some control over two independent quantities that are intrinsic to the deformation: its divergence, and its curl. Our algorithm is also able to handle soft landmark constraints, which is particularly useful when parts of the images contain very little information or when its repartition is uneven. We provide an optimal analytical solution in the case when only landmarks and smoothness considerations are taken into account. We have applied our approach to perform the elastic registration of images such as electrophoretic gels and fly embryos. The validation of the results by experts has been favorable in all cases.

Erratum

  • p. 657, first column, last equation, one of the indices is incorrect. The corrected equation should read ∂Erough ⁄ ∂c2 = (P22+P22T) c2 + P12T c1 instead of ∂Erough ⁄ ∂c2 = (P22+P22T) c1 + P12T c1.

@ARTICLE(http://bigwww.epfl.ch/publications/sorzano0501.html,
AUTHOR="S{\'{a}}nchez Sorzano, C.{\'{O}}. and Th{\'{e}}venaz, P. and
	Unser, M.",
TITLE="Elastic Registration of Biological Images Using Vector-Spline
	Regularization",
JOURNAL="{IEEE} Transactions on Biomedical Engineering",
YEAR="2005",
volume="52",
number="4",
pages="652--663",
month="April",
note="")

© 2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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