Abstract-In this paper, we present a stable, recursive algorithm for the Gabor filter that achieves-to within a multiplicative constant-the fastest possible implementation. For a signal consisting of samples, our implementation requires ( ) multiply-and-add (MADD) operations, that is, the number of computations per input sample is constant. Further, the complexity is independent of the values of and in the Gabor kernel, and the coefficients of the recursive equation have a simple, closed-form solution given and . Our implementation admits not only a "forward" Gabor filter but an inverse filter that is also ( ) complexity.

Abstract-In this paper, we present a stable, recursive algorithm for the Gabor filter that achieves-to within a multiplicative constant-the fastest possible implementation. For a signal consisting of samples, our implementation requires ( ) multiply-and-add (MADD) operations, that is, the number of computations per input sample is constant. Further, the complexity is independent of the values of and in the Gabor kernel, and the coefficients of the recursive equation have a simple, closed-form solution given and . Our implementation admits not only a "forward" Gabor filter but an inverse filter that is also ( ) complexity.

The effect of chronological age on skin characteristics is readily visible, and its underlying histological changes have been a field of study for several years. However, the effect of biological age (i.e. a person’s rate of ageing compared to their chronological age) on the skin has so far only been studied in facial photographs. Skin biopsies obtained from middle-aged offspring of nonagenarian siblings that are genetically enriched for longevity were compared to their partners who represent the general Dutch population. Though of the same chronological age, the offspring were previously observed to be of a younger biological age than their partners. The biopsies were analysed on several aspects epidermal and elastic fibre morphology. We investigated whether these skin characteristics were dependent on chronological age, familial longevity (the difference between the offspring and partners) and Framingham heart risk scores, adjusted for external stressors. A decreased thickness and flattening of the epidermis as well as an increased amount of elastic fibres in the reticular dermis were observed with chronological age (P < 0.001, P < 0.001 and P = 0.03, respectively), but no effect of familial longevity was found. The Framingham heart risk score was associated with some skin characteristics. A slower rate of skin ageing does not mark offspring from nonagenarian siblings. Epidermal and elastic fibre morphometric characteristics are not a potential marker for familial longevity in middle-aged subjects enriched for familial longevity.Electronic supplementary materialThe online version of this article (doi:10.1007/s11357-011-9314-5) contains supplementary material, which is available to authorized users.

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We present a novel approach to parameterised curve detection. The method is based on the generalised Radon transform, which is traditionally applied to a 2D edge/line map. The novelty of our method is the mapping of the original 2D image to a 3D orientation space, which then forms the input for the Radon transform. The orientation space representation can represent multiple intersecting structures and contains local orientation information. We demonstrate our approach on a problem in geology and show that we can detect curves in a heterogeneous and noisy background.