A Leaf Modeling and Multi-Scale Remeshing Method for Visual Computation via Hierarchical Parametric Vein and Margin Representation

This paper introduces a novel hierarchical structured representation for leaf modeling and proposes a corresponding multi-resolution remeshing method for large-scale visual computation. Leaf modeling is a very difficult and challenging problem due to the wide variations in the shape and structures among different species of plants. Firstly, we introduce a Hierarchical Parametric Veins and Margin (HPVM) representation approach, which describes the leaf biological structures and exact geometry via interpolation of parametric curves from the extracted vein features from non-manifold data. Secondly, a parametric surface model is constructed using HPVM with geometric and structured constraints. Finally, for a given size, we adapt a multi-step discrete point resampling strategy and a CDT-based (Constrained Delaunay Triangulation) meshing method to generate a mesh model. Our representation consists of three coupled data structures, a core hierarchical parametric data structure of veins and margin for the leaf skeleton, the corresponding parametric surface model, and a set of unstructured triangular meshes with user-specified density for the leaf membrane. Numerical experiments show that our method can obtain high quality meshes from the scanned non-manifold mesh data with well-preserved biological structures and geometry. This novel approach is suitable for effective leaf simulation, rendering, texture mapping, and simulation of light distribution in crop canopies.