The Robotics Institute

Carnegie Mellon Robotics Institute

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Abstract

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 ready to solve. Our final reconstruction algorithm is simple and has intuitive geometric interpretation. In contrast to existing random sampling or local minimization approaches, our algorithm is deterministic and guarantees a predefined accuracy of the minimization result. Moreover, the quasiconvexity provides an intuitive method to handle directional uncertainties and outliers in measurements. We demonstrate the effectiveness of our algorithm by experiments on both synthetic and real data.

Notes

Associated Center(s) / Consortia: Vision and Autonomous Systems Center

Number of pages: 33

Text Reference

Qifa Ke and Takeo Kanade, "Quasiconvex Optimization for Robust Geometric Reconstruction," tech. report CMU-RI-TR-05-57, Robotics Institute, Carnegie Mellon University, November, 2005

BibTeX Reference

@techreport{Ke_2005_5312,
   author = "Qifa Ke and Takeo Kanade",
   title = "Quasiconvex Optimization for Robust Geometric Reconstruction",
   booktitle = "",
   institution = "Robotics Institute",
   month = "November",
   year = "2005",
   number= "CMU-RI-TR-05-57",
   address= "Pittsburgh, PA",
}

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