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Journal of Mathematical Imaging and Vision

, Volume 49, Issue 2, pp 352–376 | Cite as

Estimation of Intrinsic Volumes from Digital Grey-Scale Images

  • Anne Marie Svane
Article

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.

Keywords

Digital grey-scale images Local algorithms Design based set-up Surface area Integrated mean curvature 

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsAarhus UniversityAarhus CDenmark

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