Monge e il problema del vertice di piramide: una applicazione alla restituzione di quote e volumi da una fotografia del 1892 Monge and the three point space resection problem: an application to the reconstruction of heights and volumes from a photograph of 1892

The purpose of photogrammetric restitution is the reconstruction of the volumes, now lost, located along the road that crosses the village, on the left side of the photo. The reconstruction of points in space from twodimensional images is possible if these photos are projective figure and we have at least two projective oriented stars. The first image is a vintage photograph, the second is a figure reconstructed from an aerial photo of AM in 1938 and from the survey of the masonry still present at the site. For the survey, one of the two projective stars is assimilated to a class of vertical straight lines. With regard to photography, the problem is decomposed into two typical phases of photogrammetric processes: the internal orientation and the absolute orientation. For the absolute orientation we used the method of the pyramid vertex which, in use since the Eighteenth Century, consists in determining the projection center from three given points of which are known the positions in space.