Registration errors on the face data with noise.

<p>(a) Registration errors on face data with Gaussian noise, (b) registration errors on face data with uniform noise. Our algorithm is robust against uniform noise and Gaussian noise, and outperformed CPD and TPS-RPM.</p

Impacts of <i>ω</i> on registration of CPD.

<p>The registration results of CPD are sensitive to the parameter <i>ω</i>.</p

Registration of CSF boundary point sets with outliers.

<p>(a) CSF boundary point sets with outliers, 184 red outliers clustered into 11 outlier sets, and 54 black points clustered into 4 outlier sets. (b) Our algorithm, (c) CPD, (d) Jian and Verimu's algorithm <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091381#pone.0091381-Chui2" target="_blank">[7]</a> (TPS-L2), (e) TPS-RPM. One outlier set was aligned to the CSF boundary points by CPD, and two outlier sets are aligned to the boundary points by TPS-L2 and TPS-RPM.</p

Registration results on 3D face data containing 40% artificially added Gaussian noise with <i>ó</i> = 5.

<p>(a) 3D face data sets with Gaussian noise (<i>σ</i> = 5), (b) our SMM-based algorithm(<i>e_r</i> = 3.36%), (c) CPD(<i>e_r</i> = 10.7%), (d) TPS-L2(<i>e_r</i> = 15.4%), (e) TPS-RPM(<i>e_r</i> = 21.1%).</p

Iterations of the four non-rigid registration algorithms.

<p>The convergence of our algorithm takes 40 iterations, while the CPD algorithm takes about 50 iterations and the TPS-L2 algorithm and the TPS-RPM algorithm takes more than 50 iterations.</p

Deformation vectors of central points.

<p>(a) Our algorithm, (b) CPD, (c) TPS-L2, (d) TPS-RPM. The deformation vectors produced by our algorithm are more regularized than the ones produced by CPD, and the registration result of our algorithm is more accurate than TPS-L2 and TPS-RPM. Some deformation vectors produced by CPD were crossed, which broke the topological structure of the point sets. The aligned point set was too smooth to fit the CSF boundary points by using TPS-RPM.</p

Registration of 2D CSF boundary points without outliers or noise.

<p>The 2D CSF points are segmented on the images from <a href="http://www.insight-journal.org/rire/download.php" target="_blank">http://www.insight-journal.org/rire/download.php</a>. (a) Ideal CSF boundary points, the black point set contains 488 points and the red one contains 398 points. (b) The registration of our SMM-based algorithm (<i>β</i> = 2.2, <i>λ</i> = 2), (c) CPD, (d) the Jian and Verimu's algorithm <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091381#pone.0091381-Bing1" target="_blank">[10]</a> (TPS-L2), (e) TPS-RPM. The green vectors denote the deformation vectors produced by non-rigid registration algorithms.</p

3D lung point set registration on a subject.

<p>(a) 3D lung point sets before registration, (b) SMM-based algorithm, (c) CPD, (d) TPS-L2, (e) TPS-RPM. Our algorithm performs the best.</p

Performance of the four non-rigid registration algorithms on 5 subjects.

<p>Our algorithm is the most accurate one of the all.</p

Registration results on 3D face data without the display of artificially added noise.

<p>(a) Our SMM-based algorithm (b) CPD, (c) TPS-L2, (d) TPS-RPM. The correspondences are aligned accurately by our algorithm, which demonstrates that our SMM-based algorithm is robust against the significant amount of noise. The CPD algorithm and the TPS-L2 algorithm failed to align some correspondences in the margin, and the TPS-RPM algorithm absolutely failed to align the marginal face points.</p