Topology-adaptive modeling of objects by using variable-size ball marching

The paper proposes a novel method of modeling multiobject scenes or objects of arbitrary topology by a marching method based on mathematical morphology operations with a variable-size structuring element. We assume that 3D data on the whole object surface has been acquired. A narrow-band stopping region is built by merging the neighborhood of every data point. A single close-surface surrounding the data point set is given as an initial shape. The surface shrinks and splits smoothly by repeated erosions with a ball structuring element, whose size increases continuously as the curvature of the surface increases. Every surface point stops moving if it lies in the stopping region. After this surface fitting to the stopping region, the region is narrowed, and the fitting-and-narrowing cycle is repeated until the model is consistent with the object surface on the basis of a topological check. After the above rough estimation, for model refinement, we extract a quadrangular mesh from the resultant surface, and then perform precise fitting to the 3D data by using an energy minimisation.