A method for reconstructing 3D scene geometry from a set of projected shadows is presented. It is composed of two stages. First, the scene geometry is retrieved up to three scalar unknowns using only the information contained in the observed shadow edges on the image plane. Then, the three remaining unknowns are computed making use of the known depths at three points. This technique improves upon previous results in that it does not require the presence of a reference plane in the background. A mathematical analysis is presented using dual-space geometry, a formalism that provides adequate tools to carry out all the derivations in a compact and intuitive manner. A linear algorithm based on singular value decomposition (SVD) is presented leading to a closed form solution for reconstruction.