# Reconstructing hv-Convex Polyominoes from Orthogonal Projections

@article{Chrobak1999ReconstructingHP, title={Reconstructing hv-Convex Polyominoes from Orthogonal Projections}, author={M. Chrobak and C. D{\"u}rr}, journal={ArXiv}, year={1999}, volume={cs.DS/9906021} }

Abstract We address the problem of reconstructing a discrete 2D object, represented by a set of grid cells, from its orthogonal projections. We focus on objects called hv-convex polyominoes, which are connected objects with the property that the cells in each row and column are consecutive. The main result of this paper is a simple, O(mn min(m2,n2))-time algorithm for reconstructing hv-convex polyominoes.

#### 137 Citations

Reconstructing hv-convex polyominoes with multiple colours

- Mathematics
- 2009

This thesis examines the problem of reconstructing multiple discrete 2D objects, represented by a set of cells arranged in an m×n grid, from their projections. The objects being constructed are… Expand

Reconstructing hv-convex multi-coloured polyominoes

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2010

This paper focuses on the case where there are multiple disjoint polyominoes that are hv-convex, i.e., any intersection with a horizontal or vertical line is contiguous, and shows that reconstruction of such polyaminoes is polynomial if the number of colours is constant, but NP-hard for an unbounded number of colors. Expand

Reconstruction of Canonical hv-Convex Discrete Sets from Horizontal and Vertical Projections

- Mathematics, Computer Science
- IWCIA
- 2009

An intermediate class is defined --- the class of hv -convex canonical discrete sets --- and a constructive proof is given that the above problem remains computationally tractable for this class, too. Expand

A uniqueness result for reconstructing hv-convex polyominoes from horizontal and vertical projections and morphological skeleton

- Computer Science, Mathematics
- 2013 8th International Symposium on Image and Signal Processing and Analysis (ISPA)
- 2013

This article shows that the uniqueness of the reconstruction in a special class of 4-connected hv-convex images, using two projections and the so-called morphological skeleton depends only on the values of those parameters. Expand

Approximating hv-Convex Binary Matrices and Images from Discrete Projections

- Mathematics, Computer Science
- DGCI
- 2008

Since the problem of reconstructing hv-convex binary matrices from few projections is NP-complete, an iterative approximation based on a longest path and a min-cost/max-flow model is provided. Expand

Probabilistic Reconstruction of hv-convex Polyominoes from Noisy Projection Data

- Mathematics, Computer Science
- Fundam. Informaticae
- 2014

The well-known problem of reconstructing hv-convex polyominoes is considered from a set of noisy data, and a probabilistic evaluation in the reconstruction algorithm, where different pixels assume different probabilities to be part of the reconstructed image. Expand

Reconstruction of convex polyominoes with a blocking component

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2016

The two problems concerning convex polyominoes in discrete tomography and an approach to reconstruct objects even in the case that some of the projections are unavailable, due to a particularly dense part of the scanned object, are merged. Expand

Reconstruction in Different Classes of 2D Discrete Sets (Invited Paper)

- Computer Science
- DGCI
- 1999

It is shown that the reconstruction algorithms used in the class of hv-convex 4-connected sets (polyominoes) can be used, with small modifications, for reconstructing hV- Convex 8- connected sets and the directed h-Convex sets are uniquely reconstructible with respect to the row and column sum vectors. Expand

The Reconstruction of Some 3D Convex Polyominoes from Orthogonal Projections

- Computer Science
- SOFSEM
- 2002

A polynomial algorithm for reconstruction of some class of convex three-dimensional polyominoes that has time complexity O(n7 log n) is given. Expand

A Fast Algorithm for Reconstructing hv-Convex Binary Images from Their Horizontal Projection

- Computer Science
- ISVC
- 2014

This paper provides a fast polynomial-time algorithm for reconstructing canonical hv-convex images with given number of 4-connected components and with minimal number of columns satisfying a prescribed horizontal projection and shows that the method gives a solution that is always 8-connected. Expand

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