Variances of surface area estimators based on pixel configuration counts. (English) Zbl 1522.68694
Summary: The surface area of a set which is only observed as a binary pixel image is often estimated by a weighted sum of pixel configurations counts. In this paper we examine these estimators in a design based setting – we assume that the observed set is shifted uniformly randomly. Bounds for the difference between the essential supremum and the essential infimum of such an estimator are derived, which imply that the variance is in \(O(t^2)\) as the lattice distance \(t\) tends to zero. In particular, it is asymptotically neglectable compared to the bias. A simulation study shows that the theoretically derived convergence order is optimal in general, but further improvements are possible in special cases.
MSC:
| 68U10 | Computing methodologies for image processing |
| 52C07 | Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) |
| 62G20 | Asymptotic properties of nonparametric inference |
| 65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
Software:
MAVIReferences:
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