22 March 2007 Using Laplace's equation for non-rigid registration of breast surfaces
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Recent advances in breast cancer imaging have generated new ways to characterize the disease. Many analysis techniques require a method for determining correspondence between a pendant breast surface before and after a deformation. In this paper, an automated point correspondence method that uses the surface Laplacian or the diffusion equation coupled to an isocontour matching and interpolation scheme are presented. This method is compared to a TPS interpolation of surface displacements tracked by fiducial markers. The correspondence methods are tested on two realistic finite element simulations of a breast deformation and on a breast phantom. The Laplace correspondence method resulted in a mean TRE ranging from 1.0 to 7.7 mm for deformations ranging from 13 to 33 mm, outperforming the diffusion method. The TPS method, in part because it utilizes fiducial information, performed better than the Laplace method, with mean TRE ranging from 0.3 to 1.9 mm for the same range of deformations. The Laplace and TPS methods have the potential to be used by analyses requiring point correspondence between deforming surfaces.
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Rowena E. Ong, Rowena E. Ong, Jao J. Ou, Jao J. Ou, Michael I. Miga, Michael I. Miga, "Using Laplace's equation for non-rigid registration of breast surfaces", Proc. SPIE 6509, Medical Imaging 2007: Visualization and Image-Guided Procedures, 650936 (22 March 2007); doi: 10.1117/12.712288; https://doi.org/10.1117/12.712288

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