Correlation between the area of increased autofluorescence surrounding geographic atrophy and disease progression in patients with AMD

PURPOSE: To test the hypothesis that the extension of areas with increased fundus autofluorescence (FAF) outside atrophic patches correlates with the rate of spread of geographic atrophy (GA) over time in eyes with age-related macular degeneration (AMD). METHODS: The database of the multicenter longitudinal natural history Fundus Autofluorescence in AMD (FAM) Study was reviewed for patients with GA recruited through the end of August 2003, with follow-up examinations within at least 1 year. Only eyes with sufficient image quality and with diffuse patterns of increased FAF surrounding atrophy were chosen. In standardized digital FAF images (excitation, 488 nm; emission, >500 nm), total size and spread of GA was measured. The convex hull (CH) of increased FAF as the minimum polygon encompassing the entire area of increased FAF surrounding the central atrophic patches was quantified at baseline. Statistical analysis was performed with the Spearman's rank correlation coefficient (rho). RESULTS: Thirty-nine eyes of 32 patients were included (median age, 75.0 years; interquartile range [IQR], 67.8-78.9); median follow-up, 1.87 years; IQR, 1.43-3.37). At baseline, the median total size of atrophy was 7.04 mm2 (IQR, 4.20-9.88). The median size of the CH was 21.47 mm2 (IQR, 15.19-28.26). The median rate of GA progression was 1.72 mm2 per year (IQR, 1.10-2.83). The area of increased FAF around the atrophy (difference between the CH and the total GA size at baseline) showed a positive correlation with GA enlargement over time (rho=0.60; P=0.0002). CONCLUSIONS: FAF characteristics that are not identified by fundus photography or fluorescein angiography may serve as a prognostic determinant in advanced atrophic AMD. As the FAF signal originates from lipofuscin (LF) in postmitotic RPE cells and since increased FAF indicates excessive LF accumulation, these findings would underscore the pathophysiological role of RPE-LF in AMD pathogenesis.

Confidence Bands for Convex Median Curves using Sign-Tests

Suppose that one observes pairs (x1,Y1), (x2,Y2), ..., (xn,Yn), where x1 < x2 < ... < xn are fixed numbers while Y1, Y2, ..., Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex or concave function f. We present a confidence band for this regression function f using suitable multiscale sign tests. While the exact computation of this band seems to require O(n4) steps, good approximations can be obtained in O(n2) steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size n tends to infinity.

Marshall's Lemma for Convex Density Estimation

Marshall's (1970) lemma is an analytical result which implies root-n-consistency of the distribution function corresponding to the Grenander (1956) estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on [0,\infty).

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensionality, we keep numerical complexity at bay by restricting the space of solutions and by exploiting an efficient Primal-Dual formulation. Comparisons with state of the art techniques, on both synthetic and real data, show promising performances.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.