4D polygonal approximation of the skeleton for 3D object decomposition

We improve a method to decompose a 3D object into parts (called kernels, simple-regions and bumps) starting from the partition of the distance labeled skeleton into components (called complex-sets, simple-curves and single-points). In particular, each simple-curve of the partition is here interpreted as a curve in a 4D space, where the coordinates of each point are related to the three spatial coordinates of the corresponding voxel of the 3D simple-curve and to its associated distance label. Then, a split type polygonal approximation method is employed to subdivide, in the limits of the adopted tolerance, each curve in the 4D space into straight-line segments. Vertices found in the 4D curve are used to identify corresponding vertices in the 3D simple-curve. The skeleton partition is then used to recover the parts into which the object is decomposed. Finally, region merging is taken into account to obtain a decomposition of the object more in accordance with human intuition.