Abstract
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.
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Oliensis, J. (2004). The Least-Squares Error for Structure from Infinitesimal Motion. In: Pajdla, T., Matas, J. (eds) Computer Vision - ECCV 2004. ECCV 2004. Lecture Notes in Computer Science, vol 3024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24673-2_43
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DOI: https://doi.org/10.1007/978-3-540-24673-2_43
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