Computer Vision and Image Understanding
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Solving the Sum-of-Ratios Problem by an Interior-Point Method
Journal of Global Optimization
Analysis of Bounds for Multilinear Functions
Journal of Global Optimization
Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques
Journal of Global Optimization
Using concave envelopes to globally solve the nonlinear sum of ratios problem
Journal of Global Optimization
Uncertain Projective Geometry: Statistical Reasoning For Polyhedral Object Reconstruction (Lecture Notes in Computer Science)
How Hard is 3-View Triangulation Really?
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
Multiple-View Geometry Under the {$L_\infty$}-Norm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
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The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions--they are either plagued by local minima or rely on a non-optimal cost-function. A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals and monomials. The performance of the method is evaluated on real image data.