In this study we present a non-rigid point set registration for 3D curves (composed by 3D set of points). The method was evaluated in the task of registration of 3D superficial vessels of the brain where it was used to match vessel centerline points. It consists of a combination of the Coherent Point Drift (CPD) and the Thin-Plate Spline (TPS) semilandmarks. The CPD is used to perform the initial matching of centerline 3D points, while the semilandmark method iteratively relaxes/slides the points.
For the evaluation, a Magnetic Resonance Angiography (MRA) dataset was used. Deformations were applied to the extracted vessels centerlines to simulate brain bulging and sinking, using a TPS deformation where a few control points were manipulated to obtain the desired transformation (T1). Once the correspondences are known, the corresponding points are used to define a new TPS deformation(T2). The errors are measured in the deformed space, by transforming the original points using T1 and T2 and measuring the distance between them. To simulate cases where the deformed vessel data is incomplete, parts of the reference vessels were cut and then deformed. Furthermore, anisotropic normally distributed noise was added.
The results show that the error estimates (root mean square error and mean error) are below 1 mm, even in the presence of noise and incomplete data.
We aim at reconstructing superficial vessels of the brain. Ultimately, they will serve to guide the deformation methods to compensate for the brain shift. A pipeline for three-dimensional (3-D) vessel reconstruction using three mono-complementary metal-oxide semiconductor cameras has been developed. Vessel centerlines are manually selected in the images. Using the properties of the Hessian matrix, the centerline points are assigned direction information. For correspondence matching, a combination of methods was used. The process starts with epipolar and spatial coherence constraints (geometrical constraints), followed by relaxation labeling and an iterative filtering where the 3-D points are compared to surfaces obtained using the thin-plate spline with decreasing relaxation parameter. Finally, the points are shifted to their local centroid position. Evaluation in virtual, phantom, and experimental images, including intraoperative data from patient experiments, shows that, with appropriate camera positions, the error estimates (root-mean square error and mean error) are ∼1 mm.