Memoirs of the Faculty of Engineering, Okayama University
Published by Faculty of Enginerring, Okayama University

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Memoirs of the School of Engineering, Okayama University

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Optimization without Search: Constraint Satisfaction by Orthogonal Projection with Applications to Multiview Triangulation

金谷 健一 Department of Computer Science Okayama University
Niitsuma Hirotaka Department of Computer Science Okayama University
Sugaya Yasuyuki Department of Information and Computer Sciences Toyohashi University of Technology
We present an alternative approach to what we call the “standard optimization”, which minimizes a cost function by searching a parameter space. Instead, the input is “orthogonally projected” in the joint input space onto the manifold defined by the “consistency constraint”, which demands that any minimal subset of observations produce the same result. This approach avoids many difficulties encountered in the standard optimization. As typical examples, we apply it to line fitting and multiview triangulation. The latter produces a new algorithm far more efficient than existing methods. We also discuss optimality of our approach.