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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.

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Acknowledgements

The author was supported by Centre for Stochastic Geometry and Advanced Bioimaging, funded by the Villum Foundation. The author is wishes to thank Markus Kiderlen for helping with the set-up of this research project and for useful input along the way.

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  1. Department of Mathematics, Aarhus University, 8000, Aarhus C, Denmark

    Anne Marie Svane

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  1. Anne Marie Svane
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Correspondence to Anne Marie Svane.

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Svane, A.M. Estimation of Intrinsic Volumes from Digital Grey-Scale Images. J Math Imaging Vis 49, 352–376 (2014). https://doi.org/10.1007/s10851-013-0469-9

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  • DOI: https://doi.org/10.1007/s10851-013-0469-9

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