Fig 1.
Schematic drawing illustrating the grouping procedure.
The figure shows an example of the grouping procedure to down-sample a 2D image with a voxel size 1×1 mm2 into another one with 2x2mm2 resolution. We have four possible groupings, shown here in different colors (red, green, orange and pink). Each grouping relates to a different offset out of the possible four. Notably, at each grouping window a different value is obtained when voxels are averaged, showing how this procedure modifies the information content of the image, particularly when the image to be down-sampled has a large number of edges.
Table 1.
Mathematical formulation of similarity measures.
We used these measures to evaluate the performances of SWIM. In the first column containing the index names, S stands for similarity measure while D stands for dissimilarity measure.
Fig 2.
Co-registration of the phantom dataset.
Images of the phantom dataset acquired at VLF (left panel) and at HF, after co-registration (right panel) at 6 different depths (4–9 mm).
Fig 3.
Co-registration of brain data recorded at 46 μT and 1.5 T.
Panel a) Co-registration results on an in-vivo brain dataset recorded at 46 μT. a) Four sample slides. The left column represents the target ULF images, the middle column contains the HF co-registered images and the right column shows the overlap between the two image sets, where HF images are in grey tones and ULF images in green tones. b) and c) The joint histogram before and after co-registration, respectively. The red ellipses demarcate background voxels. These are badly aligned in the starting histogram, as suggested by the spread peak along the column corresponding to the background in the ULF image (0 gray value) and to background and head voxels in the HF image. In the final histogram the peak is concentrated close to the origin of the joint histogram, suggesting that background voxels are aligned in the final histogram. The violet ellipses represent some brain and skull structures that are misaligned in the starting configuration (the peak is wide); while in the final histogram a sharper peak is shown around ULF gray-level of 50. The yellow ellipses represent some structures with highest gray value like eyes and white matter that are less sharp in the starting joint histogram, while have a more clear structure in final configuration, demonstrating the good alignment of the images.
Fig 4.
NMI as a function of different positions of the grouping window.
The figure shows the interpolated NMI obtained by SWIM sliding the grouping window over the three direction of the xyz space. a) NMI for different offsets in x and z direction at yoff = 1; b) NMI for offsets in y and z directions at xoff = 5; panel c) shows the NMI for different offsets in x and y direction at xoff = 1. The cross-hair shows the highest value of NMI obtained at xoff = 5, yoff = 1, zoff = 0.
Fig 5.
Comparison between SWIM and fMRI software packages.
The results obtained with SWIM on the brain images recorded at 46 μT are compared with the outcomes of two different co-registration software packages routinely used for fMRI analysis. The corresponding NMI coefficients obtained after optimization are reported in the last row. The best result is obtained with SWIM. The co-registration procedure of fMRI processing software is very fast and efficient for fMRI analysis, but it is not adequate for co-registering ULF and HF images.
Fig 6.
Overlap between the co-registered images.
Segmented images are converted into binary format and the percentage of voxel overlap is reported on the last column for the three different co-registration procedures. Overlapping voxels are shown in white, light gray voxels are the HF voxels not matched in ULF image, dark gray indicates the ULF voxels not present in the brain shown in the HF scans and black indicates matching of the background. The matching of anatomical features is maximal for SWIM.
Table 2.
Similarity/dissimilarity indices for co-registration of HF and ULF MRI at 46 μT.
Different values obtained for the indices in Table 1 applied to images co-registered using SWIM, FSL and SPM are reported in the table. The best values are highlighted in bold.
Fig 7.
Co-registration of HF and ULF images at 50 μT.
a) Co-registration of the dataset acquired at Aalto University. On the left the ULF image of the brain and on the right the down-sampled co-registered image at HF. b) NMI as function of the sliding window offset on the three (x, y, z) directions for xoff = 1, yoff = 1, zoff = 0.
Fig 8.
Distribution of dRMS for SWIM and FSL.
The violin plot of the distribution of dRMS after running the consistency test over one hundred of different starting images for both SWIM and FSL, suggests that SWIM error is significantly lower than FSL coregistration error.