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

Kenichi KANATANI  Yasuyuki SUGAYA  Hirotaka NIITSUMA  

IEICE TRANSACTIONS on Information and Systems   Vol.E93-D   No.10   pp.2836-2845
Publication Date: 2010/10/01
Online ISSN: 1745-1361
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Recognition, Computer Vision
consistency constraint satisfaction,  orthogonal projection,  line fitting,  multiview triangulation,  trifocal tensor,  

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We present an alternative approach to what we call the "standard optimization", which minimizes a cost function by searching a parameter space. Instead, our approach "projects" in the joint observation 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 the optimality of our approach.