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New techniques for 3-D reconstruction of plants using stereovision have been proposed (Chapron et al,
1992, Jia and Krutz, 1992). The present paper describes a new manual approach of plant identification, images
matching and final 3-D reconstruction based on stereovision allowing to perform a realistic crop model.
2 - MATERIAL AND METHOD
2.1. Stereovision Principle
The stereovision method is based upon geometrical rules in the 3-D space and assess reconstruction of objects
thanks to the difference between two images taken from different viewpoints (see Faugeras 1988 for an
overview). Let us consider two cameras watching a given 3-D scene (figure 1). These cameras, called "left" and
"right" according to their respective positions, are represented by their optical centres Op O2 and their image
planes, the 3-D position of which are supposed to be known. Let us consider the point P, the coordinates
(Xp, Yp, Zp) of which have to be estimated. and P2 are the projections of P in the images and their location
(Uj, Vj) and (U2, V2) can be easily read. Thus, the intersection of the homologous rays PjOj and P2O2
provides the coordinates (Xp, Yp, Zp) of P in the 3-D space. According to Umesh and Aggarval (1989) there
are three main steps in the stereovision computation :
- calibration, giving the geometrical model of the cameras;
- stereo matching, where pairs of points such as Pj and P2, called "homologous", are formed;
- 3-D reconstruction, providing the intersection of the homologous rays in the space.
2.2. Camera Calibration and Experimental Set Up
The calibration method was developed by Toscani (1988) and programmed by Liu (1991). It considers each
camera as a "pin hole" model providing perfect perspective transform of the observed objets through the lens.
The method consists in the estimation of a matrix M, called "perspective transform matrix", which describes
the relationships between the 3-D coordinates (Xp, Yp, Zp) of P and its 2-D coordinates (U, V) in the
corresponding image (equation 1).
M represents a 3 lines x 4 columns matrix, the elements of which are calculated by using a set of points, such
as P, called "calibration or reference points". The 3-D space coordinates and the 2-D image location of these
points are supposed to be known. The matrix M is calculated by using the Greville's inversion method
(Greville 1960) from a system of equations (1) written for each calibration point. The M elements are related
to 10 calibration parameters specific of the camera. Four of these parameters are called "intrinsic" and represent
the camera focal length and the centre of the corresponding image. The six others are "extrinsic" and relative to
Figure 1 : Principle of the stereovision method. The
3-D scene is observed by two cameras represented by
their optical centres and image planes. The point P is
located in the 3-D space by using the intersection of
two homologous rays PjO^ and P2O2 in the space.
y
V =M
( 1 )
