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

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 D²-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 D²-splines produce reconstructed leaf surfaces which better represent the original physical leaf.