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Quasiconvex optimization for robust geometric reconstruction.

Qifa Ke1, Takeo Kanade

  • 1Ricoh Innovations, Inc., California Research Center, Menlo Park, CA 94025-7022, USA. qifa@rii.ricoh.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 19, 2007
PubMed
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This study introduces a new quasiconvex optimization framework for geometric reconstruction. It simplifies complex problems into solvable convex programs, offering deterministic accuracy and robust outlier handling for computer vision tasks.

Area of Science:

  • Computer Vision
  • Optimization Theory
  • Geometric Reconstruction

Background:

  • Geometric reconstruction in computer vision commonly uses cost functions minimizing 2D reprojection errors.
  • Existing methods often rely on local minimization, which can lack determinism and guaranteed accuracy.

Purpose of the Study:

  • To present a novel quasiconvex optimization framework for geometric reconstruction problems.
  • To develop a deterministic algorithm with guaranteed accuracy and robust outlier handling.

Main Methods:

  • Identified a common quasiconvex formulation for reprojection error functions in geometric reconstruction.
  • Developed a framework that decomposes reconstruction problems into small-scale convex programs.
  • Proposed an efficient approximation for large-scale problems with constrained resources.

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Main Results:

  • The proposed algorithm is simple, deterministic, and guarantees predefined minimization accuracy.
  • The framework effectively handles directional uncertainties and outliers in measurements.
  • Experimental results on synthetic and real data demonstrate the algorithm's effectiveness.

Conclusions:

  • The quasiconvex optimization framework offers a robust and accurate approach to geometric reconstruction.
  • The method provides a deterministic alternative to local minimization techniques.
  • The approach is versatile, handling uncertainties and outliers effectively in computer vision applications.