THE EXPLICIT SOLUTION OF THE SINGLE PICTURE RESECTION PROBLEM, WITH A LEAST SQUARES ADJUSTMENT TO REDUNDANT CONTROL

It does not seem to be widely recognised that the solution of the space resection problem from measurements made on a single photograph of three ground control points is not unique. There are, in general, four solutions, so that either the camera orientation must be approximately known (as is the case for near vertical photography) or extra control must be used to discriminate between these solutions. The iterative solution commonly used will only yield one solution, which will be correct if the photography is nearly vertical, but which is liable to be wrong in the general case. An explicit solution is therefore preferred since all solutions may be examined in the light of such extra control as is available. This paper gives a method for such a solution and shows how the discrimination should be used. The paper goes on to derive a method of adjusting the result to redundant control by least squares. Resume Il ne semble pas que ľon reconnaisse generalement le fait que le probleme du relevement dans ľespace ďun seul clicheďapres trois points de controle admet plusieures solution, quatre en general. Une idee approximative des parametres de la photo nous permet ďarriver a la solution voulue, ou on peut se servir des points de controle surabondants afin de distinguer entre les quatre solutions. Selon le point de depart un calcul iteratif ne donnera qu'une seule solution; et il est done preferable ďemployer une methode directe qui donnera toutes les solutions qui peuvent etre comparees ľune aľautre avec les points terrestres surabondants. Ľauteur donne une methode directe qui comprend le moyen de distinguer entre les quatre solutions et de calculer les parametres par la methode des moindres carres utilisant tous les points de controle disponibles.