3D shape and motion by SVD under higher-order approximation of perspective projection

The factorization method, first developed by Tomasi and Kanade (1992), recovers both shape and motion from a sequence of images, by tracking a large number of feature points and using singular value decomposition (SVD). However, in this approach, the nonlinear perspective projection is linearized by approximating it using orthographic projection, weak perspective projection, and para-perspective projection, which limits the range of motions that the approach can be accommodated. In this paper, we present a new approach based on a higher-order approximation of perspective projection to recover 3D shape and motion from image sequences. The accuracy of this approximation is higher than orthographic projection, weak perspective projection and para-perspective projection, so it can be used in wider circumstances in the real world. Experimental results with synthesized and real data show that this approach is promising.