Imagine that you give me a videotape of your room that you have made by walking around with your hand-held camcorder. Using only that videotape, is it possible to create a three-dimensional model of the room as well as determine the camera trajectory?

The solution to this problem, often called the structure-from-motion problem, has eluded vision researchers for years. We have developed a new method, called Factorization, which can give a robust solution to this problem. The method is based on the theorem that the geometrical constraints due to incidence relations among projection rays can be expressed as the degeneracy of a matrix that gathers all the image measurements. The theorem results in an algorithm that factorizes the measurement matrix into two matrices that represent shape and motion, respectively, based on the robust singular value decomposition (SVD) technique.