Local shape similarity and mean-shift curvature for deformable surface mapping of anatomical structures

This paper reports a novel method for deformable registration of digital anatomical surfaces. The method capitalizes upon the iterative local affine iterative closest point (ICP) approach that applies an affine transformation per surface vertex along with a regularization constraint to force neighboring surface vertices to undergo similar transformations. More robust vertex correspondence with respect to simple closest point was obtained by exploiting local shape similarity metrics, which includes vertex distance, surface normal, and local curvature. The local curvature was mean shifted at run-time, during the iterative optimization, to make the point correspondence process less dependent upon the surface noise and resolution. The experimental validation was performed on three surface datasets (femur, hemi-pelvic bone, and liver). The registration results showed that the proposed method outperforms, across all the three surface datasets (rmse: 0.19 mm, 0.30 mm, 0.61 mm), global affine ICP (rmse: 2.89 mm, 3.95 mm, and 8.30 mm), local affine ICP (rmse: 0.31 mm, 1.61 mm, and 1.63 mm) and coherent point drift (rmse: 1.99 mm, 2.39 mm, and 4.78 mm) methods. As a whole, the mean-shifted curvature increased the registration accuracy by about 20%.