We propose a new deformable slice-to-volume registration method to register a 2D Transvaginal Ultrasound (TVUS) to a 3D Magnetic Resonance (MR) volume. Our main goal is to find a cross-section of the MR volume such that the endometrial implants and their depth of infiltration can be mapped from TVUS to MR. The proposed TVUS-MR registration method uses contour to surface correspondences through a novel variational one-step deformable Iterative Closest Point (ICP) method. Specifically, we find a smooth deformation field while establishing point correspondences automatically. We demonstrate the accuracy of the proposed method by quantitative and qualitative tests on both semi-synthetic and clinical data. To generate semi-synthetic data sets, 3D surfaces are deformed with 4–40% degrees of deformation and then various intersection curves are obtained at 0–20° cutting angles. Results show an average mean square error of 5.7934±0.4615mm, average Hausdorff distance of 2.493±0.14mm, and average Dice similarity coefficient of 0.9750±0.0030. 
Mapping and characterizing endometrial implants by registering 2D transvaginal ultrasound to 3D pelvic magnetic resonance images