Estimation of intrinsic volumes from digital grey-scale images

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Abstract

Local algorithms are common tools for estimating intrinsic volumes from black-and-white digital images. However, these algorithms are typically biased in the design based setting, even when the resolution tends to infinity. Moreover, images recorded in practice are most often blurred grey-scale images rather than black-and-white. In this paper, an extended definition of local algorithms, applying directly to grey-scale images without thresholding, is suggested. We investigate the asymptotics of these new algorithms when the resolution tends to infinity and apply this to construct estimators for surface area and integrated mean curvature that are asymptotically unbiased in certain natural settings.
Original languageEnglish
PublisherCentre for Stochastic Geometry and Advanced Bioimaging, Aarhus University
Number of pages34
Publication statusPublished - 2013
Externally publishedYes
SeriesCSGB Research Reports
Number04

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