Discrete tomography

Discrete tomography[1][2] focuses on the problem of reconstruction of binary images (or finite subsets of the integer lattice) from a small number of their projections.

In general, tomography deals with the problem of determining shape and dimensional information of an object from a set of projections.

A special case of discrete tomography deals with the problem of the reconstruction of a binary image from a small number of projections.

In the same year, David Gale found the same consistency conditions, but in connection with the network flow problem.

[22][23] Various algorithms have been applied in image processing,[18] medicine, three-dimensional statistical data security problems, computer tomograph assisted engineering and design, electron microscopy[24][25] and materials science, including the 3DXRD microscope.

A discrete tomography reconstruction problem for two vertical and horizontal directions (left), together with its (non-unique) solution (right). The task is to color some of the white points black so that the number of black points in the rows and columns match the blue numbers.