Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Reconstructing hv-convex polyominoes from orthogonal projections
Information Processing Letters
An introduction to periodical discrete sets from a tomographical perspective
Theoretical Computer Science
Scanning integer matrices by means of two rectangular windows
Theoretical Computer Science
Generic iterative subset algorithms for discrete tomography
Discrete Applied Mathematics
Planar configurations induced by exact polyominoes
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Error bounds on the reconstruction of binary images from low resolution scans
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
A decomposition theorem for homogeneous sets with respect to diamond probes
Computer Vision and Image Understanding
How to decompose a binary matrix into three hv-convex polyominoes
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
| Hi-index | 5.23 |
A binary matrix can be scanned by moving a fixed rectangular window (sub-matrix) across it, rather like examining it closely under a microscope. With each viewing, a convenient measurement is the number of 1s visible in the window, which might be thought of as the luminosity of the window. The rectangular scan of the binary matrix is then the collection of these luminosities presented in matrix form. We show that, at least in the technical case of a smoothmxn binary matrix, it can be reconstructed from its rectangular scan in polynomial time in the parameters m and n, where the degree of the polynomial depends on the size of the window of inspection. For an arbitrary binary matrix, we then extend this result by determining the entries in its rectangular scan that preclude the smoothness of the matrix.