Table 5.
Deformation ranges and mean+standard deviation of the deformation errors between the prediction models (LP, LPC, LPP, LPC2, LPC3) and the optimization model (LO) for the image-to-image registration case.
| Dataset: LPBA40 | ||||||||
|---|---|---|---|---|---|---|---|---|
| Voxel% | 0%-10% | 10%-20% | 20%-30% | 30%-40% | 40%-50% | 50%-60% | 60%-70% | 70%-80% |
| # of Test Cases | 1560(100%) | 1560(100%) | 1560(100%) | 1560(100%) | 1560(100%) | 1560(100%) | 1560(100%) | 1560(100%) |
| Imain | 40 | 40 | 40 | 40 | 40 | 40 | 40 | 40 |
| Deform (mm) | 0.001-0.999 | 0.999-1.400 | 1.400-1.751 | 1.751-2.093 | 2.093-2.450 | 2.450-2.840 | 2.840-3.295 | 3.295-3.873 |
| LP | 0.478 ± 0.323 | 0.564 ± 0.361 | 0.623 ± 0.393 | 0.675 ± 0.425 | 0.728 ± 0.461 | 0.786 ± 0.503 | 0.853 ± 0.556 | 0.941 ± 0.630 |
| LPC | 0.415 ± 0.287 | 0.469 ± 0.327 | 0.509 ± 0.359 | 0.546 ± 0.390 | 0.584 ± 0.424 | 0.626 ± 0.464 | 0.676 ± 0.514 | 0.742 ± 0.583 |
| LPP | 0.543 ± 0.554 | 0.605 ± 0.613 | 0.650 ± 0.684 | 0.691 ± 0.823 | 0.733 ± 0.783 | 0.778 ± 0.852 | 0.830 ± 0.922 | 0.898 ± 1.055 |
| LPC2 | 0.510 ± 0.339 | 0.551 ± 0.378 | 0.582 ± 0.409 | 0.611 ± 0.439 | 0.642 ± 0.471 | 0.676 ± 0.508 | 0.716 ± 0.553 | 0.770 ± 0.617 |
| LPC3 | 0.637 ± 0.410 | 0.674 ± 0.451 | 0.703 ± 0.486 | 0.732 ± 0.516 | 0.762 ± 0.550 | 0.795 ± 0.588 | 0.834 ± 0.638 | 0.886 ± 0.713 |
| Voxel% | 80%-90% | 90%-99% | 99%-100% | 99.9%-100% | 99.99%-100% | 99.999%-100% | 99.9999%-100% | 99.99999%-100% |
| # of Test Cases | 1560(100%) | 1560(100%) | 1560(100%) | 1474(94.5%) | 417(26.7%) | 72(4.6%) | 30(1.9%) | 8(0.5%) |
| Imain | 40 | 40 | 40 | 38 | 31 | 8 | 2 | 1 |
| Deform (mm) | 3.873-4.757 | 4.757-7.317 | 7.317-23.393 | 9.866-23.393 | 12.435-23.393 | 14.734-23.393 | 16.835-23.393 | 19.090-23.393 |
| LP | 1.079 ± 0.752 | 1.418 ± 1.056 | 2.579 ± 1.869 | 4.395 ± 2.667 | 6.863 ± 3.657 | 9.220 ± 4.829 | 11.568 ± 6.340 | 14.475 ± 7.145 |
| LPC | 0.847 ± 0.696 | 1.101 ± 0.976 | 1.961 ± 1.761 | 3.431 ± 2.656 | 5.855 ± 3.711 | 8.408 ± 4.780 | 10.484 ± 6.148 | 14.041 ± 6.879 |
| LPP | 1.001 ± 1.396 | 1.229 ± 1.558 | 1.760 ± 2.965 | 2.514 ± 5.845 | 4.127 ± 7.988 | 7.097 ± 3.566 | 10.509 ± 5.093 | 11.436 ± 5.688 |
| LPC2 | 0.856 ± 0.721 | 1.064 ± 0.979 | 1.765 ± 1.726 | 3.012 ± 2.644 | 5.351 ± 3.698 | 8.362 ± 4.765 | 11.310 ± 6.117 | 15.957 ± 6.458 |
| LPC3 | 0.968 ± 0.835 | 1.166 ± 1.176 | 1.829 ± 2.880 | 3.019 ± 4.688 | 5.680 ± 10.450 | 11.434 ± 23.727 | 18.939 ± 33.953 | 24.152 ± 38.466 |
| Dataset: IBSR18 | ||||||||
|---|---|---|---|---|---|---|---|---|
| Voxel% | 0%-10% | 10%-20% | 20%-30% | 30%-40% | 40%-50% | 50%-60% | 60%-70% | 70%-80% |
| # of Test Cases | 306(100%) | 306(100%) | 306(100%) | 306(100%) | 306(100%) | 306(100%) | 306(100%) | 306(100%) |
| Imain | 18 | 18 | 18 | 18 | 18 | 18 | 18 | 18 |
| Deform (mm) | 0.003-1.221 | 1.221-1.691 | 1.691-2.101 | 2.101-2.501 | 2.501-2.915 | 2.915-3.370 | 3.370-3.901 | 3.901-4.580 |
| LP | 0.573 ± 0.401 | 0.670 ± 0.448 | 0.742 ± 0.489 | 0.810 ± 0.532 | 0.879 ± 0.580 | 0.957 ± 0.637 | 1.053 ± 0.711 | 1.182 ± 0.815 |
| LPC | 0.450 ± 0.343 | 0.521 ± 0.393 | 0.577 ± 0.435 | 0.631 ± 0.479 | 0.687 ± 0.526 | 0.751 ± 0.582 | 0.829 ± 0.655 | 0.936 ± 0.756 |
| LPP | 0.624 ± 0.553 | 0.698 ± 0.623 | 0.755 ± 0.678 | 0.809 ± 0.729 | 0.863 ± 0.782 | 0.923 ± 0.843 | 0.996 ± 0.918 | 1.094 ± 1.022 |
| LPC2 | 0.505 ± 0.383 | 0.566 ± 0.437 | 0.614 ± 0.480 | 0.660 ± 0.522 | 0.707 ± 0.568 | 0.761 ± 0.622 | 0.827 ± 0.691 | 0.917 ± 0.788 |
| LPC3 | 0.606 ± 0.446 | 0.666 ± 0.504 | 0.713 ± 0.549 | 0.757 ± 0.594 | 0.803 ± 0.640 | 0.854 ± 0.694 | 0.915 ± 0.763 | 1.001 ± 0.860 |
| Voxel% | 80%-90% | 90%-99% | 99%-100% | 99.9%-100% | 99.99%-100% | 99.999%-100% | 99.9999%-100% | 99.99999%-100% |
| # of Test Cases | 306(100%) | 306(100%) | 306(100%) | 125(40.8%) | 46(15.0%) | 12(3.9%) | 3(1.0%) | 3(1.0%) |
| Imain | 18 | 18 | 18 | 10 | 3 | 2 | 1 | 1 |
| Deform (mm) | 4.580-5.629 | 5.629-9.026 | 9.026-36.263 | 14.306-36.263 | 19.527-36.263 | 23.725-36.263 | 27.533-36.263 | 29.154-36.263 |
| LP | 1.397 ± 0.988 | 2.007 ± 1.451 | 5.343 ± 3.868 | 13.103 ± 4.171 | 20.302 ± 2.287 | 24.666 ± 1.688 | 28.081 ± 1.190 | 30.436 ± 1.807 |
| LPC | 1.114 ± 0.924 | 1.609 ± 1.367 | 4.485 ± 3.862 | 11.928 ± 4.800 | 19.939 ± 2.549 | 24.457 ± 1.877 | 27.983 ± 1.218 | 30.000 ± 1.796 |
| LPP | 1.249 ± 1.184 | 1.621 ± 1.572 | 2.894 ± 2.798 | 5.054 ± 4.387 | 9.631 ± 6.406 | 13.541 ± 7.744 | 17.600 ± 7.317 | 15.553 ± 6.339 |
| LPC2 | 1.068 ± 0.951 | 1.488 ± 1.375 | 3.917 ± 3.730 | 10.437 ± 5.395 | 19.345 ± 3.061 | 24.154 ± 2.173 | 27.834 ± 1.403 | 29.654 ± 1.909 |
| LPC3 | 1.141 ± 1.022 | 1.521 ± 1.432 | 3.596 ± 3.555 | 8.962 ± 5.690 | 18.252 ± 4.077 | 23.673 ± 2.583 | 27.681 ± 1.641 | 29.460 ± 2.227 |
| Dataset: CUMC12 | ||||||||
|---|---|---|---|---|---|---|---|---|
| Voxel% | 0%-10% | 10%-20% | 20%-30% | 30%-40% | 40%-50% | 50%-60% | 60%-70% | 70%-80% |
| # of Test Cases | 132(100%) | 132(100%) | 132(100%) | 132(100%) | 132(100%) | 132(100%) | 132(100%) | 132(100%) |
| Imain | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 |
| Deform (mm) | 0.004-1.169 | 1.169-1.602 | 1.602-1.977 | 1.977-2.341 | 2.341-2.717 | 2.717-3.126 | 3.126-3.597 | 3.597-4.189 |
| LP | 0.617 ± 0.433 | 0.709 ± 0.480 | 0.784 ± 0.524 | 0.856 ± 0.570 | 0.929 ± 0.621 | 1.010 ± 0.680 | 1.109 ± 0.758 | 1.239 ± 0.868 |
| LPC | 0.525 ± 0.391 | 0.587 ± 0.441 | 0.640 ± 0.486 | 0.694 ± 0.534 | 0.750 ± 0.586 | 0.813 ± 0.646 | 0.890 ± 0.724 | 0.995 ± 0.834 |
| LPP | 0.653 ± 0.538 | 0.717 ± 0.607 | 0.772 ± 0.667 | 0.829 ± 0.727 | 0.888 ± 0.789 | 0.953 ± 0.859 | 1.032 ± 0.948 | 1.138 ± 1.068 |
| LPC2 | 0.605 ± 0.444 | 0.653 ± 0.496 | 0.696 ± 0.543 | 0.739 ± 0.591 | 0.787 ± 0.645 | 0.839 ± 0.704 | 0.905 ± 0.782 | 0.996 ± 0.891 |
| LPC3 | 0.730 ± 0.519 | 0.775 ± 0.575 | 0.815 ± 0.625 | 0.857 ± 0.675 | 0.903 ± 0.732 | 0.954 ± 0.793 | 1.019 ± 0.872 | 1.107 ± 0.984 |
| Voxel% | 80%-90% | 90%-99% | 99%-100% | 99.9%-100% | 99.99%-100% | 99.999%-100% | 99.9999%-100% | 99.99999%-100% |
| # of Test Cases | 132(100%) | 132(100%) | 132(100%) | 132(100%) | 75(56.8%) | 18(13.6%) | 1(0.8%) | 1(0.8%) |
| Imain | 12 | 12 | 12 | 12 | 9 | 6 | 1 | 1 |
| Deform (mm) | 4.189-5.070 | 5.070-7.443 | 7.443-18.753 | 9.581-18.753 | 12.115-18.753 | 14.383-18.753 | 16.651-18.753 | 18.297-18.753 |
| LP | 1.448 ± 1.050 | 1.955 ± 1.490 | 3.340 ± 2.412 | 4.882 ± 3.106 | 7.281 ± 3.378 | 9.978 ± 3.211 | 14.113 ± 1.211 | 15.868 ± 0.315 |
| LPC | 1.163 ± 1.017 | 1.571 ± 1.451 | 2.676 ± 2.386 | 3.930 ± 3.125 | 5.976 ± 3.646 | 8.527 ± 3.889 | 13.009 ± 1.584 | 14.908 ± 0.437 |
| LPP | 1.305 ± 1.258 | 1.683 ± 1.686 | 2.484 ± 2.503 | 3.047 ± 3.048 | 3.511 ± 3.287 | 2.999 ± 3.150 | 1.196 ± 0.327 | 1.277 ± 0.178 |
| LPC2 | 1.142 ± 1.072 | 1.494 ± 1.494 | 2.405 ± 2.388 | 3.392 ± 3.055 | 5.003 ± 3.702 | 7.176 ± 4.218 | 11.155 ± 2.470 | 13.456 ± 0.812 |
| LPC3 | 1.248 ± 1.165 | 1.581 ± 1.581 | 2.383 ± 2.434 | 3.165 ± 3.015 | 4.422 ± 3.629 | 6.283 ± 4.370 | 9.607 ± 3.120 | 11.757 ± 1.492 |
| Dataset: MGH10 | ||||||||
|---|---|---|---|---|---|---|---|---|
| Voxel% | 0%-10% | 10%-20% | 20%-30% | 30%-40% | 40%-50% | 50%-60% | 60%-70% | 70%-80% |
| # of Test Cases | 90(100%) | 90(100%) | 90(100%) | 90(100%) | 90(100%) | 90(100%) | 90(100%) | 90(100%) |
| Imain | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
| Deform (mm) | 0.003-1.122 | 1.122-1.553 | 1.553-1.929 | 1.929-2.294 | 2.294-2.674 | 2.674-3.089 | 3.089-3.567 | 3.567-4.163 |
| LP | 0.578 ± 0.422 | 0.680 ± 0.471 | 0.757 ± 0.514 | 0.829 ± 0.559 | 0.904 ± 0.610 | 0.986 ± 0.671 | 1.082 ± 0.748 | 1.207 ± 0.858 |
| LPC | 0.486 ± 0.382 | 0.558 ± 0.436 | 0.615 ± 0.481 | 0.669 ± 0.528 | 0.726 ± 0.580 | 0.790 ± 0.640 | 0.865 ± 0.715 | 0.963 ± 0.820 |
| LPP | 0.624 ± 0.556 | 0.701 ± 0.624 | 0.761 ± 0.680 | 0.819 ± 0.737 | 0.881 ± 0.796 | 0.948 ± 0.865 | 1.026 ± 0.948 | 1.127 ± 1.061 |
| LPC2 | 0.562 ± 0.436 | 0.623 ± 0.493 | 0.670 ± 0.541 | 0.716 ± 0.589 | 0.766 ± 0.643 | 0.821 ± 0.703 | 0.886 ± 0.778 | 0.971 ± 0.881 |
| LPC3 | 0.684 ± 0.512 | 0.745 ± 0.574 | 0.792 ± 0.625 | 0.838 ± 0.677 | 0.887 ± 0.734 | 0.942 ± 0.797 | 1.007 ± 0.874 | 1.091 ± 0.979 |
| Voxel% | 80%-90% | 90%-99% | 99%-100% | 99.9%-100% | 99.99%-100% | 99.999%-100% | 99.9999%-100% | 99.99999%-100% |
| # of Test Cases | 90(100%) | 90(100%) | 90(100%) | 89(98.9%) | 37(41.1%) | 7(7.8%) | 3(3.3%) | 2(2.2%) |
| Imain | 10 | 10 | 10 | 9 | 6 | 3 | 1 | 1 |
| Deform (mm) | 4.163-5.047 | 5.047-7.462 | 7.462-18.727 | 9.833-18.727 | 12.607-18.727 | 15.564-18.727 | 17.684-18.727 | 18.534-18.727 |
| LP | 1.408 ± 1.041 | 1.924 ± 1.499 | 3.348 ± 2.341 | 4.873 ± 2.704 | 7.299 ± 3.256 | 10.503 ± 4.049 | 11.764 ± 3.005 | 13.041 ± 1.691 |
| LPC | 1.120 ± 0.998 | 1.526 ± 1.444 | 2.627 ± 2.275 | 3.674 ± 2.621 | 5.283 ± 3.272 | 8.492 ± 4.088 | 9.336 ± 3.738 | 10.499 ± 2.692 |
| LPP | 1.289 ± 1.250 | 1.676 ± 1.705 | 2.430 ± 2.415 | 2.707 ± 2.403 | 2.998 ± 2.214 | 2.695 ± 1.419 | 2.377 ± 1.063 | 2.226 ± 0.365 |
| LPC2 | 1.109 ± 1.055 | 1.455 ± 1.482 | 2.361 ± 2.270 | 3.138 ± 2.585 | 4.267 ± 3.133 | 6.603 ± 3.760 | 7.444 ± 3.657 | 8.415 ± 3.053 |
| LPC3 | 1.225 1.153 | 17551 17570— | 2.358 ± 2.306 | 3.023 ± 2.588 | 3.755 ± 2.957 | 5.214 ± 3.486 | 6.240 ± 3.357 | 7.569 ± 3.283 |
All measures are evaluated within the brain mask only. All deformation values and deformation errors are evaluated in millimeters (mm). Voxel%: percentile range of voxels that fall in a particular deformation range based on the optimization model (LO). # of Test cases: The number of registration cases that contain voxels within a given percentile range. Imain: Minimum number of distinct images required to cover all registration test cases in a particular deformation range either as the moving or the target image. This measure is meant to quantify the influence of few images on very large deformations. For example, for the four registration cases A-B, B-C, B-D and E-A, Imain = 2 as it is sufficient to select images A and B to cover all four registrations. The results show that a comparatively small subset of images is responsible for most of the very large deformations. Of course, all images of a particular dataset are involved in the small deformation ranges. Deform: range of deformations within a given percentile range. The cells with the lowest mean deformation errors for every deformation range are highlighted. Best-viewed in color.