ADvanced IMage Algebra (ADIMA): a novel method for depicting multiple sclerosis lesion heterogeneity, as demonstrated by quantitative MRI

Background: There are modest correlations between multiple sclerosis (MS) disability and white matter lesion (WML) volumes, as measured by T2-weighted (T2w) magnetic resonance imaging (MRI) scans (T2-WML). This may partly reflect pathological heterogeneity in WMLs, which is not apparent on T2w scans. Objective: To determine if ADvanced IMage Algebra (ADIMA), a novel MRI post-processing method, can reveal WML heterogeneity from proton-density weighted (PDw) and T2w images. Methods: We obtained conventional PDw and T2w images from 10 patients with relapsing–remitting MS (RRMS) and ADIMA images were calculated from these. We classified all WML into bright (ADIMA-b) and dark (ADIMA-d) sub-regions, which were segmented. We obtained conventional T2-WML and T1-WML volumes for comparison, as well as the following quantitative magnetic resonance parameters: magnetisation transfer ratio (MTR), T1 and T2. Also, we assessed the reproducibility of the segmentation for ADIMA-b, ADIMA-d and T2-WML. Results: Our study’s ADIMA-derived volumes correlated with conventional lesion volumes ( p < 0.05). ADIMA-b exhibited higher T1 and T2, and lower MTR than the T2-WML ( p < 0.001). Despite the similarity in T1 values between ADIMA-b and T1-WML, these regions were only partly overlapping with each other. ADIMA-d exhibited quantitative characteristics similar to T2-WML; however, they were only partly overlapping. Mean intra- and inter-observer coefficients of variation for ADIMA-b, ADIMA-d and T2-WML volumes were all < 6 % and < 10 %, respectively. Conclusion: ADIMA enabled the simple classification of WML into two groups having different quantitative magnetic resonance properties, which can be reproducibly distinguished.

FUZZY SIMILARITIES TO COMPARE DEFORMED IMAGES

We use the concept of fuzzy similarity to compare the objects of a free image algebra (a set of objects which a group is acting on). In particular, we study those fuzzy similarities that are preserved by the action of the group. Later we consider a deformation mechanism of the image algebra and trackle the problem of comparing deformed images. For that purpose, we characterize those deformation mechanisms that are equivalent to the induced action from a subgroup of the group of deformations. In that case, by using techniques from group representation theory, we extend any fuzzy similarity defined on the image algebra to a fuzzy similarity defined on the whole space of deformed images. Moreover, we prove that the invariance of the similarity with respect to the group action is preserved by this extension.

Aberration correction past and present

Electron lenses are extremely poor: if glass lenses were as bad, we should see as well with the naked eye as with a microscope! The demonstration by Otto Scherzer in 1936 that skilful lens design could never eliminate the spherical and chromatic aberrations of rotationally symmetric electron lenses was therefore most unwelcome and the other great electron optician of those years, Walter Glaser, never ceased striving to find a loophole in Scherzer’s proof. In the wartime and early post-war years, the first proposals for correcting C s were made and in 1947, in a second milestone paper, Scherzer listed these and other ways of correcting lenses; soon after, Dennis Gabor invented holography for the same purpose. These approaches will be briefly summarized and the work that led to the successful implementation of quadupole–octopole and sextupole correctors in the 1990s will be analysed. In conclusion, the elegant role of image algebra in describing image formation and processing and, above all, in developing new methods will be mentioned.