Vertex-Level Three-Dimensional Shape Deformability Measurement Based on Line Segment Advection

The measurement to the intrinsic deformability of arbitrary small-scale subdivision of a shape is an interesting meanwhile valuable research topic. Such measurement can be directly utilized as a reliable criteria to partition object shape into small components and then assist in accurate shape modeling and description. Compared with single global shape modeling, through constructing subdivision-based complex shape description, the accuracy and flexibility of shape representation can be significantly improved. In this paper, we propose a line segment advection based vertex-level three-dimensional shape deformability measuring method. This measuring strategy can highlight the deformability characteristics of each shape part in any scale and size, at the same time, quantitatively describe them. The measurement is realized mainly based on the advection of line segments connecting neighboring shape mesh vertices. For 3D shapes, since the line segment of triangular mesh facet directly reflects the minimal neighborhood relationships and mesh microstructure, its advection can capture the finest details of shape deformability. Then, after transferring those information into neighboring vertices, a vertex-level shape deformability measurement can be acquired. Besides the measuring method, in order to demonstrate its value to shape partitioning and piecewise shape modeling, a straightforward shape partitioning method based on the proposed measurement is introduced as well, which is implemented through unsupervised clustering. Extensive experiments on three publicly available databases are conducted to verify the effectiveness of