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Multiple-view geometry under the Linfinity-norm.

Fredrik Kahl1, Richard Hartley

  • 1Centre for Mathematical Sciences, Lund University, Lund, Sweden. fredrik@maths.lth.se

IEEE Transactions on Pattern Analysis and Machine Intelligence
|July 12, 2008
PubMed
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This study introduces a novel framework using the L-infinity norm for geometric structure and motion problems, enabling efficient global estimations unlike traditional L2-norm methods. This approach recasts problems into solvable quasi-convex optimization using Second-Order Cone Programming (SOCP).

Area of Science:

  • Computer Vision
  • Optimization
  • Robotics

Background:

  • Traditional methods for geometric structure and motion problems often rely on L2-norm (sum-of-squares) cost functions.
  • L2-norm minimization can lead to local minima and computationally intensive solutions.
  • Existing frameworks may struggle with efficient global estimation for complex geometric tasks.

Purpose of the Study:

  • To present a new framework for solving geometric structure and motion problems using the L-infinity norm.
  • To demonstrate that this L-infinity norm framework allows for efficient computation of global estimates.
  • To show the applicability of this framework to various computer vision tasks like triangulation and camera resectioning.

Main Methods:

  • Utilizing the L-infinity norm to measure model-fitting errors, deviating from the conventional L2-norm.

Related Experiment Videos

  • Reformulating structure and motion problems as quasi-convex optimization problems.
  • Employing Second-Order Cone Programming (SOCP), a standard convex optimization technique, for efficient problem solving.

    • Main Results:

    • The L-infinity norm framework successfully recasts triangulation, camera resectioning, and homography estimation as quasi-convex problems.
    • Problems formulated within this framework are efficiently solvable using SOCP.
    • The implemented Matlab toolbox, based on these methods, is publicly available and shows excellent performance on real-world data.

    Conclusions:

    • The proposed L-infinity norm framework offers an efficient and robust alternative for solving geometric structure and motion problems.
    • SOCP provides an effective computational tool for this framework, enabling global estimations.
    • The publicly available toolbox facilitates the application and validation of these advanced optimization techniques in computer vision.