Quasiconvex Optimization for Robust Geometric Reconstruction

Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex fo...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2007-10, Vol.29 (10), p.1834-1847
Main Authors: Qifa Ke, Kanade, T.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Artificial Intelligence
Cameras
Computer errors
Computer science
control theory
systems
Computer vision
convex programming
Cost function
directional uncertainty
Errors
Exact sciences and technology
geometric reconstruction
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image reconstruction
Imaging, Three-Dimensional - methods
Information Storage and Retrieval - methods
Intelligence
Large-scale systems
Minimization
Minimization methods
multi-view geometry
Optimization
Pattern Recognition, Automated - methods
Pattern recognition. Digital image processing. Computational geometry
Reconstruction
Reconstruction algorithms
Reproducibility of Results
robust
Robustness
Sensitivity and Specificity
Studies
Upper bound
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Summary:Geometric reconstruction problems in computer vision are often solved by minimizing a cost function that combines the reprojection errors in the 2D images. In this paper, we show that, for various geometric reconstruction problems, their reprojection error functions share a common and quasiconvex formulation. Based on the quasiconvexity, we present a novel quasiconvex optimization framework in which the geometric reconstruction problems are formulated as a small number of small-scale convex programs that are readily solvable. Our final reconstruction algorithm is simple and has intuitive geometric interpretation. In contrast to existing local minimization approaches, our algorithm is deterministic and guarantees a predefined accuracy of the minimization result. The quasiconvexity also provides an intuitive method to handle directional uncertainties and outliers in measurements. For a large-scale problem or in a situation where computational resources are constrained, we provide an efficient approximation that gives a good upper bound (but not global minimum) on the reconstruction error. We demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data.
ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2007.1083