Segmentation of 3D Articulated Components by Slice-Based Vertex-Weighted Reeb Graph

A fast and efficient algorithm for segmentation of the articulated components of 3D objects is proposed. The algorithm is marked by several novel features, such as DCEL-based fast

orthogonal slicing

,

weighted Reeb graph

with slice areas as vertex weights, and graph cut by

exponential averaging

. Each of the three sets of orthogonal slices obtained from the object is represented by a vertex-weighted Reeb graph of low complexity, as the slicing is done with an appropriate grid resolution. Each linear subgraph in a Reeb graph is traversed from its leaf node up to an articulation node or up to a node whose weight exceeds a dynamically-set threshold, based on exponential averaging of the predecessor weights in the concerned subgraph. The nodes visited in each linear subgraph are marked by a unique component number, thereby helping the inverse mapping for marking the articulated regions during final segmentation. Theoretical analysis shows that the algorithm runs faster for objects with smaller surface area and for larger grid resolutions. The algorithm is stable, invariant to rotation, and leads to natural segmentation, as evidenced by experimentation with a varied dataset.