Inherent Ambiguities in Recovering 3-D Motion and Structure from a Noisy Flow Field
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
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multi-Frame Structure-from-Motion Algorithm under Perspective Projection
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Characterizing Depth Distortion under Different Generic Motions
International Journal of Computer Vision
Order Parameters for Detecting Target Curves in Images: When Does High Level Knowledge Help?
International Journal of Computer Vision - Special issue on statistical and computational theories of vision: Part II
Understanding the Behavior of SFM Algorithms: A Geometric Approach
International Journal of Computer Vision
A New Structure-from-Motion Ambiguity
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uncertainty Modeling for Optimal Structure from Motion
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Optimal Structure from Motion: Local Ambiguities and Global Estimates
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
The least-squares error for structure from infinitesimal motion
International Journal of Computer Vision
Affine Reconstruction from Translational Motion under Various Autocalibration Constraints
Journal of Mathematical Imaging and Vision
Towards direct recovery of shape and motion parameters from image sequences
Computer Vision and Image Understanding
Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
Multi-View AAM Fitting and Construction
International Journal of Computer Vision
Multi-View AAM Fitting and Construction
International Journal of Computer Vision
Geometrical recovery of missing data for shape from motion
International Journal of Computer Mathematics
Global Optimization through Rotation Space Search
International Journal of Computer Vision
Geometrical fitting of missing data for shape from motion under noise distribution
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Uncertainty analysis using geometrical property between 2d-to-3d under affine projection
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
A novel recovery algorithm of incomplete observation matrix for converting 2-d video to 3-d content
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
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This paper examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. By examining the eigenvectors associated with null or small eigenvalues of the Hessian matrix, we can quantify the exact nature of these ambiguities and predict how they affect the accuracy of the reconstructed shape. Our results for orthographic cameras show that the bas-relief ambiguity is significant even with many images, unless a large amount of rotation is present. Similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction.