The Least-Squares Error for Structure from Infinitesimal Motion

We analyze the least?squares error for structure from motion with a single infinitesimal motion ("structure from optical flow"). We present asymptotic approximations to the noiseless error over two, complementary regions of motion estimates: roughly forward and non?forward translations. Our approximations are powerful tools for understanding the error. Experiments show that they capture its detailed behavior over the entire range of motions. We illustrate the use of our approximations by deriving new properties of the least?squares error. We generalize the earlier results of Jepson/Heeger/Maybank on the bas?relief ambiguity and of Oliensis on the reflected minimum. We explain the error's complexity and its multiple local minima for roughly forward translation estimates (epipoles within the field of view) and identify the factors that make this complexity likely. For planar scenes, we clarify the effects of the two?fold ambiguity, show the existence of a new, double bas?...

• Type: Conference
• Year: 2004
• Where: ECCV
• Authors: John Oliensis
• Keywords: Asymptotic Approximations, Computer Vision, ECCV 2004, Error Approximations, Least Squares Error, Noiseless Error, Single Infinitesimal Motion