It has been known since the work of Carlsson and Weinshall that there is a du- alization principle that allows one to interchange the role of points being viewed by several cameras and the camera centres themselves. In principle this implies the possibility ofdualizing projective reconstruction algorithms to obtain new algorithms. In this paper, this theme is developed at a theoretical and algorith- mic level. The nature of the duality mapping is explored and its application to reconstruction ambiguity is discussed. An explicit method for dualizing any projective reconstruction algorithm is given. At the practical implementation level, however, it is shown that there are diculties which have so far defeated successful application of this dualization method to produce working algorithms.