Stabilizing the focal length computation for 3-D reconstruction from two uncalibrated views

In order to reconstruct 3-D shape from two uncalibrated views, one needs to resolve two problems: (i) the computed focal lengths can be imaginary; (ii) the computation fails for fixated images. We present a practical remedy for these by subsampling feature points and fixing the focal length. We first summarize theoretical backgrounds and then do simulations, which reveal a rather surprising fact that when the focal length is actually fixed, not using that knowledge yields better results for non-fixated images. We give an explanation to this seeming paradox and derive a hybrid method switching the computation by judging whether or not the images are fixated. Doing simulations and real image experiments, we demonstrate the effectiveness of our method.