3-D interpretation of optical flow by renormalization

This article studies 3-D interpretation of optical flow induced by a general camera motion relative to a surface of general shape. First, we describe, using the image sphere representation, an analytical procedure that yields an exact solution when the data are exact: we solve theepipolar equation written in terms of theessential parameters and thetwisted optical flow. Introducing a simple model of noise, we then show that the solution is statistically biased. In order to remove the statistical bias, we propose an algorithm calledrenormalization, which automatically adjusts to unknown image noise. A brief discussion is also given to thecritical surface that yields ambiguous 3-D interpretations and the use of theimage plane representation.