An efficient recursive factorization method for determining structure from motion

A recursive method is presented for recovering 3D object shape and camera motion under orthography from an extended sequence of video images. This may be viewed as a natural extension of both the original and the sequential factorization methods. A critical aspect of these factorization approaches is the estimation of the so-called shape space, and they may in part be characterized by the manner in which this subspace is computed. If P points are tracked through F frames, the recursive least-squares method proposed in this paper updates the shape space with complexity O(P) per frame. In contrast, the sequential factorization method updates the shape space with complexity O(P² ) per frame. The original factorization method is intended to be used in batch mode using points tracked across all available frames. It effectively computes the shape space with complexity O(FP²) after F frames. Unlike other methods, the recursive approach does not require the estimation or updating of a large measurement or covariance matrix. Experiments with real and synthetic image sequences confirm the recursive method´s low computational complexity and good performance, and indicate that it is well suited to real-time applications