A sequential factorization method for recovering shape and motion from image streams

We present a sequential factorization method for recovering the three-dimensional shape of an object and the motion of the camera from a sequence of images, using tracked features. The factorization method originally proposed by Tomasi and Kanade produces robust and accurate results incorporating the singular value decomposition. However, it is still difficult to apply the method to real-time applications, since it is based on a batch-type operation and the cost of the singular value decomposition is large. We develop the factorization method into a sequential method by regarding the feature positions as a vector time series. The new method produces estimates of shape and motion at each frame. The singular value decomposition is replaced with an updating computation of only three dominant eigenvectors, which can be performed in O(P-2) time, while the complete singular value decomposition requires O(FP2) operations for an F x P matrix. Also, the method is able to handle infinite sequences, since it does not store any increasingly large matrices. Experiments using synthetic and real images illustrate that the method has nearly the same accuracy and robustness as the original method.