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

TL;DR

This paper introduces a novel implicit surface reconstruction method for thin, noisy leaf surfaces using polyharmonic splines and partition of unity, enabling efficient and smooth reconstructions suitable for biological simulations.

Contribution

It presents a new approach that reconstructs thin, noisy leaf surfaces from point clouds without requiring a closed surface assumption, using scalable interpolation techniques.

Findings

Reconstruction of leaf surfaces from noisy point clouds is feasible.

The method operates in linear time relative to data size.

Generated surfaces are smooth enough for droplet spreading simulations.

Abstract

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.