Vertex‐level three‐dimensional shape deformability measurement based on line segment advection

Abstract

Measuring the intrinsic deformability of arbitrary small-scale subdivision of a shape is an interesting meanwhile valuable research topic. Such measurement can be directly utilised as a reliable criteria to partition shape into small components and then assist in shape modelling and description. Compared to global modelling, through constructing subdivision-based complex shape description, the accuracy and flexibility of shape representation can be significantly improved. In this study, the authors propose a line segment advection (LSA)-based vertex-level three-dimensional shape deformability measuring method. It can highlight the deformability characteristics of each shape part in any scale and size. The measurement is realised mainly based on the advection of line segments connecting neighbouring shape mesh vertices. For 3D shapes, since the line segment of triangular mesh facet directly reflects the minimal neighbourhood relationships and mesh microstructure, its advection can capture the finest details of shape deformability. Then, after transferring that information into neighbouring vertices, a vertex-level shape deformability measurement can be acquired. Besides, to demonstrate the value of the proposed measuring method to shape partitioning and piecewise shape modelling, a straightforward shape partitioning method is introduced as well. Extensive experiments on three publicly available databases are conducted to verify the effectiveness of proposed methods.