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Iterative extensions of the Sturm/Triggs algorithm: convergence and nonconvergence.
John Oliensis1, Richard Hartley
1Computer Science Department, Stevens Institute of Technology, Hoboken, NJ 07030, USA. oliensis@cs.stevens.edu
IEEE Transactions on Pattern Analysis and Machine Intelligence
|October 16, 2007
Summary
The new CIESTA algorithm reliably initializes other algorithms by iteratively decreasing error, unlike previous methods like SIESTA that yield incorrect results. CIESTA offers stable convergence for improved computational accuracy.
Area of Science:
- Computer Vision
- Numerical Analysis
Background:
- Iterative algorithms are crucial for solving complex problems in computer vision and related fields.
- Existing extensions of the Sturm/Triggs algorithm, such as SIESTA, have demonstrated convergence issues, leading to unreliable results.
Purpose of the Study:
- To provide a theoretical convergence analysis of iterative extensions of the Sturm/Triggs algorithm.
- To introduce and validate a novel algorithm, CIESTA, that overcomes the limitations of existing methods.
Main Methods:
- Theoretical convergence analysis of iterative algorithms.
- Introduction of the CIESTA algorithm, a modification of SIESTA with an additional computation.
- Proof of CIESTA's error decrease and convergence properties under weak assumptions.
- Experimental validation comparing CIESTA with other iterative methods.
Main Results:
- SIESTA and other proposed extensions exhibit convergence to incorrect results or instability.
- CIESTA is proven to iteratively decrease error and converge to fixed points under specified assumptions.
- CIESTA demonstrates unique convergence properties.
- Experimental results show CIESTA outperforms existing iterative algorithms.
Conclusions:
- CIESTA provides a reliable method for initializing algorithms like bundle adjustment.
- The algorithm combines stable convergence with the benefits of minimizing in projective depths.
- CIESTA represents a significant advancement in iterative algorithms for computer vision and related applications.
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