Discrete analytical curve reconstruction without patches

Invertible Euclidean reconstruction methods without patches for 2D and 3D discrete curves are proposed. From a discrete 4-connected curve in 2D, or 6-connected curve in 3D, the proposed algorithms compute a polygonal line which digitization with the standard model is equal to all the pixels or voxels of the curve. The framework of this method is the discrete analytical geometry and parameter spaces are used in order to simplify the algorithms. Moreover, the reconstructed polyline is more compact than classical methods such as the Marching Cubes.