The Least-Squares Error for Structure from Infinitesimal Motion

  • John Oliensis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3024)


We analyze the least–squares error for structure from motion (SFM) with a single infinitesimal motion (“structure from optical flow”). We present approximations to the noiseless error over two, complementary regions of motion estimates: roughly forward and non–forward translations. Experiments show that these capture the error’s detailed behavior over the entire motion range. They can be used to derive new error properties, including generalizations of the bas–relief ambiguity. As examples, we explain the error’s complexity for epipoles near the field of view; for planar scenes, we derive a new, double bas–relief ambiguity and prove the absence of local minima. For nonplanar scenes, our approximations simplify under reasonable assumptions. We show that our analysis applies even for large noise, and that the projective error has less information for estimating motion than the calibrated error. Our results make possible a comprehensive error analysis of SFM.


Image Point True Error Bundle Adjustment True Motion Projective Error 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • John Oliensis
    • 1
  1. 1.Computer Science DepartmentStevens Institute of TechnologyHobokenUSA

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