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Probabilistic Reconstruction of hv-convex Polyominoes from Noisy Projection Data

Goupy A., Pagani S. M. C.

Fundamenta Informaticae

2014

Vol. 135, nr 1/2

117--134

In this paper the well-known problem of reconstructing hv-convex polyominoes is considered from a set of noisy data. Differently from the usual approach of Binary Tomography, this leads to a probabilistic evaluation in the reconstruction algorithm, where different pixels assume different probabilities to be part of the reconstructed image. An iterative algorithm is then applied, which, starting from a random choice, leads to an explicit reconstruction matching the noisy data.

The Reconstruction of Polyominoes from Horizontal and Vertical Projections and Morphological Skeleton is NP-complete

Hantos N., Balázs P.

Fundamenta Informaticae

2013

Vol. 125, nr 3/4

343--359

Reconstruction of binary images from their projections is one of the main tasks in many image processing areas, therefore determining the computational complexity of those problems is essential. The reconstruction complexity is highly dependent on the requirements of the image. In this paper, we will show that the reconstruction is NP-complete if the horizontal and vertical projections and the morphological skeleton of the image are given, and it is supposed that the image is 4-connected.