Reconstruction of Euclidean planes from voxels

We aim to formulate the recognition of a planes from a discrete point set as a nonlinear optimization problem, and we prove a uniqueness theorem for the solution of this problem. We deal with the supercover model in a space for the expression of discrete planes. The algorithm achieves invertible data compression of digital objects, since the algorithm transforms a collection voxels to a collection of plane parameters, which classify the voxels.