Projective Reconstruction from N Views Having One View in Common ⋆ M. Urban, T. Pajdla, and V. Hlav´ aˇ c Center for Machine Perception Czech Technical University, Prague Karlovo n´am. 13, 121 35 Prague, Czech Republic, urbanm@cmp.felk.cvut.cz http://cmp.felk.cvut.cz Abstract. Projective reconstruction recovers projective coordinates of 3D scene points from their several projections in 2D images. We intro- duce a method for the projective reconstruction based on concatenation of trifocal constraints around a reference view. This configuration sim- plifies computations significantly. The method uses only linear estimates which stay “close” to image data. The method requires correspondences only across triplets of views. However, it is not symmetrical with respect to views. The reference view plays a special role. The method can be viewed as a generalization of Hartley’s algorithm [11], or as a particular application of Triggs’ [21] closure relations. 1 Introduction Finding a projective reconstruction of the scene from its images is a problem whichwasaddressedinmanyworks[7,22,12,13,9].Itisadifficultproblemmainly because of two reasons. Firstly, if more images of a scene are available, it is difficult to see all scene points in all images as some of the points become often occluded by the scene itself. Secondly, image data are affected by noise so that there is usually no 3D reconstruction that is consistent with raw image data. In order to find an approximate solution which would be optimal with respect to errors in image data, a nonlinear bundle adjustment has to be performed or an approximate methods have to be used. In past, the research addressed both problems. Methods for finding a projec- tive reconstruction of the scene from many images assuming that all correspon- dences are available were proposed [20,21,18]. On the other hand, if only two, three, or four images were used, methods for obtaining a projective reconstruc- tion by a linear Least Squares method were presented [11,9]. Weconcentrateonthesituationwhentherearemorethanfourviewsandnot all correspondences are available. We show that a linear Least Squares method ⋆ This research is supported by the Grant Agency of the Czech Republic under the grants 102/97/0480, 102/97/0855, and 201/97/0437, and by the Czech Ministry of Education under the grant VS 96049. B. Triggs, A. Zisserman, R. Szeliski (Eds.): Vision Algorithms’99, LNCS 1883, pp. 116–131, 2000. c  Springer-Verlag Berlin Heidelberg 2000