Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Geometric computation for machine vision
Geometric computation for machine vision
Linear subspace methods for recovering translational direction
Proceedings of the 1991 York conference on Spacial vision in humans and robots
Models of statistical visual motion estimation
CVGIP: Image Understanding
Computer Vision and Image Understanding
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Linear Differential Algorithm for Motion Recovery: AGeometric Approach
International Journal of Computer Vision
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
International Journal of Computer Vision
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
Motion and Structure from Image Sequences
Motion and Structure from Image Sequences
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion Recovery from Image Sequences: Discrete Viewpoint vs. Differential Viewpoint
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Optimization Criteria, Sensitivity and Robustness of Motion and Structure Estimation
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Comparison of Approaches to Egomotion Computation
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Understanding the Relationship Between the Optimization Criteria in Two-View Motion Analysis
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Analytical results on error sensitivity of motion estimation from two views
Image and Vision Computing
Optimization Criteria, Sensitivity and Robustness of Motion and Structure Estimation
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Manifold statistics for essential matrices
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
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The prevailing efforts to study the standard formulation of motion and structure recovery have been recently focused on issues of sensitivity and robustness of existing techniques. While many cogent observations have been made and verified experimentally, many statements do not hold in general settings and make a comparison of existing techniques difficult. With an ultimate goal of clarifying these issues we study the main aspects of the problem: the choice of objective functions, optimization techniques and the sensitivity and robustness issues in the presence of noise. We clearly reveal the relationship among different objective functions, such as "(normalized) epipolar constraints", "reprojection error" or "triangulation", which can all be be unified in a new "optimal triangulation" procedure formulated as a constrained optimization problem. Regardless of various choices of the objective function, the optimization problems all inherit the same unknown parameter space, the so called "essential manifold", making the new optimization techniques on Riemanian manifolds directly applicable. Using these analytical results we provide a clear account of sensitivity and robustness of the proposed linear and nonlinear optimization techniques and study the analyticaland practical equivalence of different objective functions. The geometric characterization of critical points of a function defined on essential manifold and the simulation results clarify the difference between the effect of bas relief ambiguity and other types of local minima leading to a consistent interpretations of simulation results over large range of signal-to-noise ratio and variety of configurations.