Rim points reconstruction

We have seen in the previous section that more than two images are needed to estimate the local properties of the surface ${\cal S}$. We show here that by using three images, a local approximation up to order 2 of ${\cal S}$ can be computed. Moreover, if points between occluding contours of ${\cal S}$are matched according to the epipolar correspondence, this approximation leads to a linear estimation of the position and the curvatures of ${\cal S}$ at a point P. Unlike previous methods [Cip 90,Vai 92,Sze 93,Jos 95] which use an a priori plane in order to estimate the epipolar curve, no assumption is made on the camera motion or the local surface shape. Instead, a local parametrisation of the surface ${\cal S}$ is used which in turn leads to a local surface approximation. We first present the local parametrisation (x,y) that is used and the induced local approximation of the surface. We show then that such a parametrisation allows linear equations to be derived for both depth and normal curvature in the viewing direction.