Generally in SPM, images are assumed to be 3D. However, the number of dimensions in the data is irrelevant to computing joint intensity histograms. People have been using joint intensity histograms for aligning 3D images since about 1995:
Collignon A, Maes F, Delaere D, Vandermeulen D, Suetens P, Marchal G. Automated multi-modality image registration based on information theory. In Information processing in medical imaging 1995 Jun (Vol. 3, No. 6, pp. 263-274).
Viola P, Wells III WM. Alignment by maximization of mutual information,(1995). Medical Image Analysis. 1995;1(1):17-34.
Histograms are one way of encoding joint intensity distributions, but there are other ways too. My own favourite is to encode this sort of information via a Gaussian mixture model (which many people think of as a way to cluster data, but
I prefer to think of it as a way of encoding probability densities).
The basic idea is to have one image fixed and the other image is resliced to match it. Then the first voxel is taken for the two images, and the corresponding bin of the 2D histogram is incremented by one. The appropriate bin is determined by the intensities
at that voxel in the image pair. Then the second voxel position, with its pair of voxel intensities, and so on. The number of dimensions in the histogram corresponds to the number of images.
If images are not well aligned at all, the intensity distribution for one image would be independent from the intensity distribution of the other. When the images are aligned, there is structure in the histogram that allows intensity distributions for voxels
in one image to be predicted from the intensities in the other image (and vice versa). You can get an idea of this from the graphics shown when you use Coreg. If the initial alignment is poor, then there is less structure in the "before" histogram, whereas
the "after" histogram should show more structure.
Best regards,
-John
Hello everyone,
I have some questions concerning joint histograms. The Joint Histograms in Coregister (Estimate) is between a reference 2D mean functional image and the 3D anatomical image or are both of the images in 3D? I was reading a paper on Joint Histograms and there
was no mention of two 3D images registered together. Is this special to SPM12?
Also, The voxel intensities between the mean functional and structural images don't compare. How would the Joint Histogram look? Would the bright clusters be around the line of correspondence as other Joint Histograms would normally look? Does the Joint Histogram
compare voxel intensity similarities or something else to get a line of correspondence?
Thank you for your help!
Ali Hendricks