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
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
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Subspace algorithms for the stochastic identification problem
Automatica (Journal of IFAC)
Geometric computation for machine vision
Geometric computation for machine vision
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Performance of optical flow techniques
International Journal of Computer Vision
A paraperspective factorization method for shape and motion recovery
ECCV '94 Proceedings of the third European conference on Computer Vision (Vol. II)
Recursive 3-D Visual Motion Estimation Using Subspace Constraints
International Journal of Computer Vision
Linear Differential Algorithm for Motion Recovery: AGeometric Approach
International Journal of Computer Vision
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Ambiguities in Structure from Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Representation of Scenes from Collections of Images
VSR '95 Proceedings of the IEEE Workshop on Representation of Visual Scenes
Linear Differential Algorithm for Motion Recovery: AGeometric Approach
International Journal of Computer Vision
Understanding the Behavior of SFM Algorithms: A Geometric Approach
International Journal of Computer Vision
Structure from Motion Causally Integrated Over Time
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exact Two-Image Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Building Roadmaps of Local Minima of Visual Models
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Building Roadmaps of Minima and Transitions in Visual Models
International Journal of Computer Vision
The least-squares error for structure from infinitesimal motion
International Journal of Computer Vision
Pose and Motion Recovery from Feature Correspondences and a Digital Terrain Map
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal instantaneous rigid motion estimation insensitive to local minima
Computer Vision and Image Understanding
An Efficient Linear Method for the Estimation of Ego-Motion from Optical Flow
Proceedings of the 31st DAGM Symposium on Pattern Recognition
When Discrete Meets Differential
International Journal of Computer Vision
Machine Vision and Applications
Behaviour of SFM algorithms with erroneous calibration
Computer Vision and Image Understanding
Error characteristics of SFM with erroneous focal length
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part I
A review and evaluation of methods estimating ego-motion
Computer Vision and Image Understanding
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“Structure From Motion” (SFM) refers to the problem of estimating spatial properties of a three-dimensional scene from the motion of its projection onto a two-dimensional surface, such as the retina. We present an analysis of SFM which results in algorithms that are provably convergent and provably optimal with respect to a chosen norm.In particular, we cast SFM as the minimization of a high-dimensional quadratic cost function, and show how it is possible to reduce it to the minimization of a two-dimensional function whose stationary points are in one-to-one correspondence with those of the original cost function. As a consequence, we can plot the reduced cost function and characterize the configurations of structure and motion that result in local minima. As an example, we discuss two local minima that are associated with well-known visual illusions. Knowledge of the topology of the residual in the presence of such local minima allows us to formulate minimization algorithms that, in addition to provably converge to stationary points of the original cost function, can switch between different local extrema in order to converge to the global minimum, under suitable conditions. We also offer an experimental study of the distribution of the estimation error in the presence of noise in the measurements, and characterize the sensitivity of the algorithm using the structure of Fisher's Information matrix.