This project is in collaboration with the company SODIMEL which goal is to produce wine-producing equipment. A device has been developped to compute the volume of a grape without needing to pick it up. The grape is assumed to be a set of prolate ellipsoids of revolution. We reconstruct the visible part of the grape.

This work has lead to one poster in a summer school and two publications :

**Summer school in Figeac (Nouveaux outils mathématiques pour l'analyse d'images et la vision par ordinateur):** Multiple view reconstruction of a quadric of revolution from its occluding contours *(Pierre Gurdjos, Jérôme Guénard, Vincent Charvillat and Géraldine Morin)* pdf

**ACCV 2009:** Multiple view reconstruction of a quadric of revolution from its occluding contours *(Pierre Gurdjos, Jérôme Guénard, Vincent Charvillat and Géraldine Morin)* pdf , presentation

**abstract:** The problem of reconstructing a quadric from its occluding
contours is one of the earliest problems in computer vision e.g., see [1-3].
It is known that three contours from three views are required for this
problem to be well-posed while Cross et al. have proved in [4] that, with
only two contours, what can be obtained is a 1D linear family of solutions
in the dual projective space.
In this work, we describe a multiple view algorithm that unambiguously
reconstructs so-called Prolate Quadrics of Revolution (PQoR's, see text),
given at least two finite projective cameras (see terminology in [5, p157]).
In particular, we show how to obtain a closed-form solution.
The key result on which is based this work is a dual parameterization
of a PQoR, using a 7-dof "linear combination" of the quadric dual to the
principal focus-pair and the Dual Absolute Quadric (DAQ).
One of the contributions is to prove that the images of the principal foci
of a PQoR can be recovered set-wise from the images of the PQoR and
the DAQ. The performance of the proposed algorithm is illustrated on
simulations and experiments with real images.

**AFIG 2009:** De la reconstruction de quadriques de révolution à partir d'images à la complémentation d'objets naturels *(Jérôme Guénard, Géraldine Morin, Pierre Gurdjos and Vincent Charvillat)* pdf , presentation

**abstract:** The aim of this paper is to reconstruct a set of quadrics of revolution from two images. In the application described
here, this set models a cluster of grapes.
First we are interested in the problem of reconstructing a prolate quadric of revolution (QRP) from its occluding
contour. Cross [CZ98] has shown that three contours were needed to reconstruct a general quadric [CZ98].
We propose two major contributions : first, a parameterisation of a quadric of revolution in the dual projective
space and second, we prove that it is possible to recover the images of the principal focuses of the QRP from its
occluding contour in a calibrated view. Then, we describe a new linear triangulation scheme with two types of
constraints to find the QRP from two views only.
We shall use the first algorithm to reconstruct all QRPs visible on two views of a cluster and then we want to
complement the cluster coherently. First, we shall reconstruct berries visible on only one view usinginformation
frmo the reconstructed QRPs. Then, we describe a method for adding new QRPs consistently to the hidden parts.
The goal is to get a realistic 3D model of the cluster.