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The stereo SFM combining stereo and motion is a useful vision cue to estimate both the motion of the cameras and the structure of a scene with an absolute scale factor. Most of the works related to the stereo SFM have used both motion correspondence and stereo correspondence. Because it is information redundancy to use these two correspondence simultaneously, they can give accurate results. However, the methods to solve the stereo correspondence problem are not yet reliable enough to have been used in practical applications, while the motion correspondence problem is easy to solve. Therefore, if an absolute scale factor can be acquired by only using motion correspondence without stereo correspondence, it is not necessary to use stereo correspondence for accuracy at the cost of reliability. This paper shows that the scale factor can be determined by using only motion correspondence. Moreover, it is shown that the degenerate cases reported in this paper are all the cases and can be easily avoided. This fact is verified from the two theorems and the simulation results. This paper also describes an implementation of the proposed algorithm. This implementation uses multiple images acquired continuously when a stereo camera moves in a scene and is formulated to be a recursive form for real-time applications. Some peculiar implementation techniques contribute to fast convergence rate and good stability in spite of large initial uncertainty. The simulation and experimental results demonstrate the effectiveness of the algorithm.