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
International Journal of Computer Vision
Analytical results on error sensitivity of motion estimation from two views
Image and Vision Computing - Special issue on the first ECCV 1990
Geometric optimization methods for adaptive filtering
Geometric optimization methods for adaptive filtering
Geometric computation for machine vision
Geometric computation for machine vision
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
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
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
Structure and Motion from Line Segments in Multiple Images
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)
Optimal Structure from Motion: Local Ambiguities and Global Estimates
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Understanding the Relationship Between the Optimization Criteria in Two-View Motion Analysis
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Understanding the Behavior of SFM Algorithms: A Geometric Approach
International Journal of Computer Vision
Optimization Criteria, Sensitivity and Robustness of Motion and Structure Estimation
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
A Differential Geometric Approach to Multiple View Geometry in Spaces of Constant Curvature
International Journal of Computer Vision - Special Issue on Computer Vision Research at the Beckman Institute of Advanced Science and Technology
Optimal Linear Representations of Images for Object Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The least-squares error for structure from infinitesimal motion
International Journal of Computer Vision
A hierarchy of cameras for 3D photography
Computer Vision and Image Understanding - Model-based and image-based 3D scene representation for interactive visalization
An Efficient and Accurate Method for 3D-Point Reconstruction from Multiple Views
International Journal of Computer Vision
Two-View Multibody Structure from Motion
International Journal of Computer Vision
Estimation of Nonlinear Errors-in-Variables Models for Computer Vision Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold
International Journal of Computer Vision
A Novel Pose Estimation Algorithm Based on Points to Regions Correspondence
Journal of Mathematical Imaging and Vision
International Journal of Systems Science - The Seventh Portuguese Conference on Automatic Control (Controlo'2006)
Nonlinear Mean Shift over Riemannian Manifolds
International Journal of Computer Vision
When Discrete Meets Differential
International Journal of Computer Vision
Effective pose estimation from point pairs
Image and Vision Computing
Distributed consensus on camera pose
IEEE Transactions on Image Processing
Behaviour of SFM algorithms with erroneous calibration
Computer Vision and Image Understanding
Building detection and 3D reconstruction from two-view of monocular camera
ICCCI'11 Proceedings of the Third international conference on Computational collective intelligence: technologies and applications - Volume Part I
Building face reconstruction from sparse view of monocular camera
ICIC'11 Proceedings of the 7th international conference on Advanced Intelligent Computing Theories and Applications: with aspects of artificial intelligence
Conjugate gradient on Grassmann manifolds for robust subspace estimation
Image and Vision Computing
Advances in matrix manifolds for computer vision
Image and Vision Computing
Gauss---Newton method for convex composite optimizations on Riemannian manifolds
Journal of Global Optimization
Manifold statistics for essential matrices
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Consensus algorithms in a multi-agent framework to solve PTZ camera reconfiguration in UAVs
ICIRA'12 Proceedings of the 5th international conference on Intelligent Robotics and Applications - Volume Part I
Calibrating a wide-area camera network with non-overlapping views using mobile devices
ACM Transactions on Sensor Networks (TOSN)
Hi-index | 0.00 |
Prevailing efforts to study the standard formulation of motion and structure recovery have recently been 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 motion and structure recovery: the choice of objective function, optimization techniques and 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,” all of which can be unified in a new “optimal triangulation” procedure. Regardless of various choices of the objective function, the optimization problems all inherit the same unknown parameter space, the so-called “essential manifold.” Based on recent developments of optimization techniques on Riemannian manifolds, in particular on Stiefel or Grassmann manifolds, we propose a Riemannian Newton algorithm to solve the motion and structure recovery problem, making use of the natural differential geometric structure of the essential manifold.We provide a clear account of sensitivity and robustness of the proposed linear and nonlinear optimization techniques and study the analytical and practical equivalence of different objective functions. The geometric characterization of critical points and the simulation results clarify the difference between the effect of bas-relief ambiguity, rotation and translation confounding and other types of local minima. This leads to consistent interpretations of simulation results over a large range of signal-to-noise ratio and variety of configurations.