Implicit reconstructions of thin leaf surfaces from large, noisy point clouds

• Published in: Applied Mathematical Modelling Vol. 98; pp. 416 - 434
• Main Authors: Whebell, Riley M., Moroney, Timothy J., Turner, Ian W., Pethiyagoda, Ravindra, McCue, Scott W.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.10.2021; Elsevier BV
• Subjects: Implicit surface reconstruction; Octrees; Partition of unity; Polyharmonic spline; Radial basis function; Reconstruction; Spline functions; Thin surface; Radial basis function; Partition of unity; Implicit surface reconstruction; Polyharmonic spline; Thin surface
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.05.014

•Implicit reconstruction can be accurate and efficient for thin leaf surfaces.•Whole plant reconstructions are handled naturally, including clustering of leaves.•Reconstructed leaf surfaces have continuous mean curvature. Thin surfaces, such as the leaves of a plant, pose a significant challenge for implicit surface reconstruction techniques, which typically assume a closed, orientable surface. We show that by approximately interpolating a point cloud of the surface (augmented with off-surface points) and restricting the evaluation of the interpolant to a tight domain around the point cloud, we need only require an orientable surface for the reconstruction. We use polyharmonic smoothing splines to fit approximate interpolants to noisy data, and a partition of unity method with an octree-like strategy for choosing subdomains. This method enables us to interpolate an N-point dataset in O(N) operations. We present results for point clouds of capsicum and tomato plants, scanned with a handheld device. An important outcome of the work is that sufficiently smooth leaf surfaces are generated that are amenable for droplet spreading simulations.