We propose in this article a reconstruction technique which consists in defining a parametric surface lying on a closed curve by setting the extremal behavior of the surface along the curve on which it lies. Therefore, we must build a set of curves in space from a stereo reconstruction of matched and closed contours in an image pair. Then, we use photo-metric information extracted near the image contours to define the local behavior of the surfaces lying on the closed curves. In order to build such a surface we use the duality existing between a stereo-based reconstruction which is able to determine the position of points in the scene space and photo-clinometry which brings information about the shape of the objects in the scene. Our geometric model is composed of a radial set of tri-parametric Gregory patches for each surface to reconstruct. The topological concepts brought by those kind of surfaces and the use of photo-metric models gave to this study a framework leading both image analysis processing and reconstruction geometrical processing.