Scattered data approximation using radial basis function with a cubic polynomial reproduction for modelling leaf surface

Figures & data

Table 1. A comparison of the RMS error using the global and the local MRBF with a cubic polynomial.

Function	C	With a cubic polynomial
		Global MRBF	Local MRBF
F1	0.1842	3.1e–003	5.0e–003
F2	0.0634	4.8e–003	4.4e–003
F3	0.5370	2.5e–004	4.0e–004
F4	0.8527	1.6e–005	1.4e–004
F5	0.5593	2.6e–004	2.4e–003
F6	1.0563	5.0e–005	7.4e–005

Figure 1. The 4688 scanned points for the Anthurium leaf (left figure) and the 3388 scanned points for the Frangipani leaf (right figure) in 2D.

Figure 2. The Anthurium leaf data before projection into a new reference plane (left figure) and after projection (right figure).

Figure 3. The 212 points that used to construct a global MRBF for the Anthurium leaf (left figure). The figure on the right represents the 141 points that used to construct a global MRBF for the Frangipani leaf.

Table 2. The relative RMS and relative maximum error for the Anthurium and Frangipani leaf data points computed using the global MRBF with a cubic polynomial.

	Global MRBF With a cubic polynomial
	Anthurium leaf	Frangipani leaf
Maximum error	4.7e00–2	9.9e–002
Relative RMS	7.8e00–3	1.7e–002
Number of points tested	4555	3264
Number of boundary points	79	17
The RBF shape parameter (c)	0.5	0.1

Figure 4. (a) and (b) represent the Anthurium and Frangipani leaf surface model, respectively, constructed from the points (shown in Figure 2) using the proposed CMRBF method. (c) and (d) the corresponding visualization of the Anthurium and Frangipani leaf model.