Error bounds on the reconstruction of binary images from low resolution scans

Authors:
Wagner Fortes;K. Joost Batenburg
Affiliations:
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands and Mathematical Institute, Leiden University, The Netherlands;Centrum Wiskunde & Informatica, Amsterdam, The Netherlands and IBBT-Vision Lab, University of Antwerp, Belgium
Venue:
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Year:
2011

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Abstract

In this paper, we consider the problem of reconstructing a highresolution binary image from several low-resolution scans. Each of the pixels in a low-resolution scan yields the value of the sum of the pixels in a rectangular region of the high-resolution image. For any given set of such pixel sums, we derive an upper bound on the difference between a certain binary image which can be computed effciently, and any binary image that corresponds with the given measurements. We also derive a bound on the difference between any two binary images having these pixel sums. Both bounds are evaluated experimentally for different geometrical settings, based on simulated scan data for a range of images.