Sobolev's original definition of his spaces revisited and a comparison with nowadays definition

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Stable registration of pathological 3D-OCT scans using retinal vessels

We propose a multiple scanner vendor registration method for pathological retinal 3D spectral domain optical coherence tomography volumes based on Myronenko’s Coherent Point Drift and our automated vessel shadow segmentation. Coherent point drift is applied to the segmented retinal vessel point sets used as landmarks to generate the registration parameters required. In contrast to other registration methods, our solution incorporates a landmark detection and extraction method that specifically limits the extraction of false positives and a registration method capable of handling any such noise in the landmark point sets. Our experiments show modified Hausdorff distance is reduced by a minimum of 91% between target and registered vessel point sets with at least 94% of bifurcations correctly overlapping based on ground truth, a significant improvement over current methods

Evaluation of optical coherence tomography findings in age-related macular degeneration: a reproducibility study of two independent reading centres

International audienceBackground/aims : To determine the reproducibility among readers of two independent certified centers, the Vienna Reading Center (VRC) and the University of Wisconsin-Madison Reading Center (UW-FPRC) for OCT images in age-related macular degeneration (AMD). Methods : Fast macular thickness scans and 6 mm cross hair scans were obtained from 100 eyes with all subtypes of AMD using Stratus OCT. Consensus readings were performed by two certified OCT readers of each Reading Center using their grading protocol. Common variables of both grading protocols, such as presence of cystoid spaces, subretinal fluid, vitreomacular traction and retinal pigment epithelial detachment were compared using kappa statistics. In addition, the intraclass correlation coefficient (ICC) was calculated for center point thickness (CPT) of values remeasured manually in the presence of alignment errors. Results : The reproducibility was dependent on the variable measured with a kappa value of 0.81 for the presence of cystoid spaces, 0.78 for the presence of subretinal fluid and 0.795 for the presence of vitreomacular traction. The lowest reproducibility was found for the presence of retinal pigment epithelial detachment with a kappa value of 0.51. The CPT was remeasured in 29 out of 100 scans at both sites with an ICC of the remeasured thicknesses of 0.92. Conclusion : OCT scan data are crucial in monitoring treatment efficacy in AMD clinical trials. For comparison of results obtained by different Reading Centers, the inter-Reading Center reproducibility is essential. Although the reproducibility is generally high, the reliability depends on the selected morphological parameters

Prevalence of Age-Related Macular Degeneration in Europe: The Past and the Future

Purpose Age-related macular degeneration (AMD) is a frequent, complex disorder in elderly of European ancestry. Risk profiles and treatment options have changed considerably over the years, which may have affected disease prevalence and outcome. We determined the prevalence of early and late AMD in Europe from 1990 to 2013 using the European Eye Epidemiology (E3) consortium, and made projections for the future. Design Meta-analysis of prevalence data. Participants A total of 42 080 individuals 40 years of age and older participating in 14 population-based cohorts from 10 countries in Europe. Methods AMD was diagnosed based on fundus photographs using the Rotterdam Classification. Prevalence of early and late AMD was calculated using random-effects meta-analysis stratified for age, birth cohort, gender, geographic region, and time period of the study. Best-corrected visual acuity (BCVA) was compared between late AMD subtypes; geographic atrophy (GA) and choroidal neovascularization (CNV). Main Outcome Measures Prevalence of early and late AMD, BCVA, and number of AMD cases. Results Prevalence of early AMD increased from 3.5% (95% confidence interval [CI] 2.1%–5.0%) in those aged 55–59 years to 17.6% (95%

Measure and Integration on Lipschitz-Manifolds

The first part of this paper is concerned with various definitions of a $k$-dimensional Lipschitz manifold ${\cal M}^k$ and a discussion of the equivalence of these definitions. The second part is then devoted to the geometrically intrinsic construction of a $\sigma$-algebra ${\cal L}({\cal M}^k)$ of subsetsof ${\cal M}^k$ and a measure $\mu_k$ on ${\cal L}({\cal M}^k)$