PMC

Hausdorff distance and continuous chirality measure in a chiral cubic compound based on space group 198 with a single 4a Wyckoff position occupied. Shown are the dependencies of and on the position parameter u of the Wyckoff position . The character (R and L) of structures in space group 198 is adopted from the handedness of the closest chiral space group 213 or 212.

Registration metrics: tSE (left) measures the Hausdorff distance between the ground truth shape (green) and the shape estimated by our algorithm in shape space (blue), not taking the final transformation computed by the algorithm into consideration. tRE (right) measures the Hausdorff distance between the ground truth shape (green) and the estimated shape (blue) transformed to sample point space, therefore also adding the transformation computed by our algorithms into the error metric.

Typical tumor registration examples for (A) glioblastoma and (B) lower-grade glioma. Axial slices with delineated pre- and post-operative tumor are shown in patient space (left), ICBM2009a space (middle) and after non-linear transformation by the DARTEL registration package (right). (A) A 66-year-old female with a 46.4 mL preoperative tumor and 3.8 mL postoperative tumor. Dice scores are 0.67 for preoperative tumor and 0.43 for postoperative tumor, and modified Hausdorff distances are 4.1 and 2.5 mm, respectively. (B) A 34-year old male with a 25 mL preoperative tumor and 12 mL postoperative tumor. Dice scores are 0.62 for pre-operative tumor and 0.55 for postoperative tumor, and modified Hausdorff distances are 4.5 and 4.2 mm, respectively.

Left: A pair of curves which are close in Hausdorff distance. Right: The continuous polar angle functions of the curves are quite different, resulting in images under F_a,b which are far apart in Hausdorff distance.