Application of surface fitting techniques for the representation of leaf surfaces

Leaves play a vital role in the development of a plant, as they are major resource collectors. Adequate representations of leaves are therefore required for the modelling of plants. Such representations may be important to generate a realistic visualisation, or they may be used to study biological processes such as photosynthesis and canopy light environment. Accurate leaf surface representations are rarely found in the plant modelling community. This paper aims to show how detailed, accurate representations of leaf surfaces can be created from data; representations that may then be used as parts of virtual plants for applications in fields as diverse as the arts, agriculture or computer games. The techniques used here are mathematical methods of surface fitting applied to data that has been sampled from real leaves with a laser scanner (Polhemus FastSCAN 3D). These methods are interpolating finite element techniques, one using linear triangular elements, the other piecewise cubic triangles. The size of a laser scanned data set can be enormous and it may be important to represent the surface with significantly fewer points. An incremental algorithm is therefore used to identify significant points that result in a surface fit that approximates the entire data set to a pre-specified accuracy. The algorithms are applied to two examples, a Frangipani leaf and a Flame Tree leaf. Figure 1 visualises results for the Flame Tree leaf. The images represent (a) a photo of this particular leaf, (b) the complete set of more than 5000 digitised data points, (c) positions of data points after application of the incremental algorithm for the piecewise cubic approach with an accuracy of 1%, (d) the same rotated to show the shape of the surface represented by these points, (e) the resulting triangulation and (f) the surface fit. From these point locations, guidelines are deduced describing where data points should be positioned, for example for measurement by lower resolution devices such as a sonic digitiser. The reduced point sets contain about one tenth of the number of points in the original data set. The research presented in this paper is the first to model detailed and accurate leaf surfaces based on three-dimensional data points captured from real leaf surfaces. It provided a basis on which further research can be built. For example, detailed and accurate surface representations may be used in the simulation of pesticide deposition on leaf surfaces to determine the effectiveness of a treatment and help develop improved pesticide application techniques.