Leaf Reconstruction Based on Gaussian Mixture Model from Point Clouds of Leaf Boundaries and Veins

Three-dimensional (3D) models of leaves are expected to contribute to a wide range of applications, including the study of plant morphology and leaf design. Leaf boundaries and veins are key factors in determining leaf shape in both botany and design. This motivated us to design a leaf-shape generator that uses leaf boundaries and veins. We propose an algorithm to reconstruct leaf geometry as a surface mesh generated from point clouds of leaf boundaries and veins. First, it determines the interior region of the leaf using the multi-level partition of unity implicits approach. Then, based on the Gaussian mixture model, it expresses the 3D shape of the leaf, where the values vary depending on the distances from the leaf boundary to veins. The use of differentiable functions for leaf shapes realizes smooth underlying surfaces and enables various shape analyses using differential operations.