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 disjoint, hv-convex polyominoes, each of which has a separate colour. The main results presented here are two algorithms for unordered C-colour reconstruction that have time complexities of O(C^2n^{2C +1}m^{2C +1}) and O(C^2 min(n^{2C}, m^{2C})nm), an ordered C-colour reconstruction algorithm that is O(Cmin(n^{2C}, m^{2C})nm), and an NP-completeness proof when the number of colours is unbounded.

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 disjoint, hv-convex polyominoes, each of which has a separate colour. The main results presented here are two algorithms for unordered C-colour reconstruction that have time complexities of O(C^2n^{2C +1}m^{2C +1}) and O(C^2 min(n^{2C}, m^{2C})nm), an ordered C-colour reconstruction algorithm that is O(Cmin(n^{2C}, m^{2C})nm), and an NP-completeness proof when the number of colours is unbounded.