The spatio-temporal multiple view geometry can represent the geometry of multiple images in the case where non-rigid arbitrary motions are viewed from multiple translational cameras. However, it requires many corresponding points and is sensitive to the image noise. In this paper, we investigate mutual projections of cameras in four-dimensional space and show that it enables us to reduce the number of corresponding points required for computing the spatio-temporal multiple view geometry. Surprisingly, take three views for instance, we no longer need any corresponding point to calculate the spatio-temporal multiple view geometry, if all the cameras are projected to the other cameras mutually for two time intervals. We also show that the stability of the computation of spatio-temporal multiple view geometry is drastically improved by considering the mutual projections of cameras.