Non-rigid registration of breast surfaces using the laplace and diffusion equations

A semi-automated, non-rigid breast surface registration method is presented that involves solving the Laplace or diffusion equations over undeformed and deformed breast surfaces. The resulting potential energy fields and isocontours are used to establish surface correspondence. This novel surface-based method, which does not require intensity images, anatomical landmarks, or fiducials, is compared to a gold standard of thin-plate spline (TPS) interpolation. Realistic finite element simulations of breast compression and further testing against a tissue-mimicking phantom demonstrate that this method is capable of registering surfaces experiencing 6 - 36 mm compression to within a mean error of 0.5 - 5.7 mm

Using Laplace’s equation for non-rigid registration of breast surfaces

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