A Comparison of Techniques for the Reconstruction of Leaf Surfaces from Scanned Data

Abstract

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modeling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D 2 -splines [R. Arcangéli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, New York, 2004], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, SIAM J. Numer. Anal., 1 (2003), pp. 208-234], and the radial basis function Clough-Tocher method [M. N. Oqielat, I. W. Turner, and J. A. Belward, Appl. Math. Model., 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D 2 -splines produce reconstructed leaf surfaces which better represent the original physical leaf. 1. Introduction. The application of pesticides, herbicides, and fertilizers is important in agriculture. They provide improved growing conditions for the plants to which they are applied. Recently, studies have been undertaken to model the adhesion and movement of these solutions on the plants [3, 6, 16, 20]. Realistic virtual plant models are developed to model the behavior of these solutions accurately. This fundamental research of leaf surface construction from scattered data is of importance in the context of the larger framework in which the current work resides, where droplet impaction, retention, and deposited droplet behavior are investigated [4].Many known species of plants are able to be distinguished from their leaves alone [18, p. 108]. For this reason, the plant model for a particular species should have a foliage structure appropriate to that species. Furthermore, if the plant model is to be used in future studies for modeling droplet motion on the surface or some other biological process, then a realistic representation of the plant under consideration will provide more reliable results. This can occur only if an accurate and realistic model of the foliage for the particular species is used, as the foliage of the plant performs many vital functions, such as photosynthesis and transpiration [18]. Accurate representations of a leaf surface have been previously considered by Loch and coworkers [11,12], and then this work was developed further by Oqielat and coworkers [14,15,16], using

Mathematical Model for Simulating the Movement of Water Droplet on Artificial Leaf Surface

“…The water droplets animation has been studied by a few researchers [21][22][23][24] since the 1980s. Nevertheless, in the 1990s, a few methods addressed the phenomenon of droplets flowing on surfaces.…”

“…Nevertheless, in the 1990s, a few methods addressed the phenomenon of droplets flowing on surfaces. For example [25], modeled droplet shapes using meta-balls on a flat surface [26,27], used meta-balls to model water flows by suggesting a volume-preserving technique [21], proposed a physical model to model droplets morphing [28], studied droplet animation on a glass plate, but the model failed to capture the droplet movements on a curved surface [29,30], proposed a model for the water droplet animation on curved surface where the wetting and merging phenomenon are addressed in the model [31]. Suggested a physical model based on a bump map surface to capture the trend of the droplet flows where a solid sphere is considered to model the droplet.…”

“…A few researchers have considered the fluid dynamics to produce a realistic motion of fluids. For example, Chen [21,22,[33][34][35] applied the Navier-Stokes equations to simulate the flow of water droplets.…”

“…The proposed techniques are based on 3D data points collected from the surface of a real Anthurium leaf using a scanner. Moreover, the authors [19] proposed a comparison between some methods based on surface fitting and concluded that the best is the hybrid multiquadric RBF-CT. Kempthorne [20,21] suggested smoothing D 2 -splines to create the cotton and wheat leaf surface. In this paper, we adapted our proposed CT-MRBFC method [1] to reconstruct the surface of the Anthurium leaf from 3D real scattered points.…”

Simulating spray droplet impaction outcomes: comparison with experimental data

“…Such a system has been described in previous publications for retention of virtual sprays by virtual plants. The virtual plant models were derived from scanning real plants, transforming the point clouds into triangulated virtual surfaces, and incorporating them into the overall ‘plant retention spray model’ (PRSm). The mathematical retention models used within this system include a particle trajectory model and evolutions of drop impaction models for bounce (or adhesion) and shatter, expanded to include oblique impact angles .…”