1072 
Figure 3 ' Figure 4 : Triangulation of leaves and stems. 
a) Leaf contour extracted manually; 
b) Contour interpolated according 
to given grid. 
2.4. Three dimensional reconstruction 
The 3-D reconstruction consists in the estimation of the (X, Y, Z) coordinates of the leaf edges. Using the 
matrix M and the expression (1), the intersection of the homologous rays was retrieved from each pair of 
homologous points. Then the 3-D leaf contours required smoothing in order to eliminate the zigzagging due to 
measurement errors. That was carried out by fitting polynomial curve of fifth degree to the original contour of 
each leaf edge. Leaf surfaces were obtained from triangulation in order to estimate their areas. The 
triangulation was based on the smoothed edge points which served as summits of the triangles (figure 4). Stems 
were considered as cylinders of 2 cm diameter and were triangulated using 12 triangles the summits of which 
were positioned on the bottom and the top of the stem. 
3 - RESULTS 
3.1. Accuracy of the estimation of heights and angles 
In order to validate the method. 40 points belonging to known targets were reconstructed by the model and 
compared with their real positions. No bias were observed on X,Y,Z coordinates and the standard deviations 
were: 
- a(X) =a(F) = 1 cm for X and Y (0.4 p.c. of target length on the X or Y axis); 
- a(Z) = 6 cm for Z (3.0 p.c. of target height on the Z axis). 
The equations of regression constrained to the origin are : 
^estimated = LOO ^measured ~ LOO, n — 108) (same for Y) 
^estimated = ^ ^ ^measured ( r — 0.99, n - 108) 
The study of the accuracy of estimated angles should require to build a special target with facets 
inclined according to different angles. This was not realized and control measurements of angles were directly 
made on the leaves. Orientation angles of the normal to the leaf plane were studied : the zenith inclination 
angle 9 and the azimuth angle 9. 
Orientation angles ©estimated’ ^estimated °f laminas planes of leaves at marks locations were 
estimated from stereovision and compared to in situ measurements (clinometer) or photo measurements 
(protractor). The standard deviation a(9) at 25 leaves' marks was 7 °. Equation of regression constrained to the 
origin was: 
^estimated = 0-^8 ^measured ^ ~ 0-79, n ~ ^5)