Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Inherent Ambiguities in Recovering 3-D Motion and Structure from a Noisy Flow Field
IEEE Transactions on Pattern Analysis and Machine Intelligence
Analytical results on error sensitivity of motion estimation from two views
Image and Vision Computing - Special issue on the first ECCV 1990
Optimal Visual Motion Estimation: A Note
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Analysis of Inherent Ambiguities in Recovering 3-D Motion from a Noisy Flow Field
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric computation for machine vision
Geometric computation for machine vision
The first order expansion of motion equations in the uncalibrated case
Computer Vision and Image Understanding
Shape Ambiguities in Structure From Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recursive 3-D Visual Motion Estimation Using Subspace Constraints
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision - Special issue on image-based servoing
Optimal Structure from Motion: Local Ambiguities and Global Estimates
International Journal of Computer Vision
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Fast and Accurate Algorithms for Projective Multi-Image Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
International Journal of Computer Vision
Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
Understanding the Behavior of SFM Algorithms: A Geometric Approach
International Journal of Computer Vision
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A New Structure-from-Motion Ambiguity
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comparison of Approaches to Egomotion Computation
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Computing the Camera Heading from Multiple Frames
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Optimal Structure from Motion: Local Ambiguities and Global Estimates
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Optimal instantaneous rigid motion estimation insensitive to local minima
Computer Vision and Image Understanding
Joint estimation of segmentation and structure from motion
Computer Vision and Image Understanding
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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-relief ambiguity, and analyze the error's local minima. For nonplanar scenes, we derive simplified error approximations for reasonable assumptions on the image and scene. For example, we show that the error tends to have a simpler form when many points are tracked. We show experimentally that our analysis for zero image noise gives a good model of the error for large noise. We show theoretically and experimentally that the error for projective structure from motion is simpler but flatter than the error for calibrated images.