Estimation of intrinsic volumes from digital grey-scale images
arXiv:1309.3842 · doi:10.1007/s10851-013-0469-9
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.
33 pages
Cited by in corpus (5)
- Voronoi-based estimation of Minkowski tensors from finite point samples
- Intrinsic Volumes of Random Cubical Complexes
- Detecting structured sources in noisy images via Minkowski maps
- Local digital algorithms for estimating the integrated mean curvature of r-regular sets
- Asymptotic variance of grey-scale surface area estimators