What is it about?

When I have developed this algorithm, I had applications in operations Research in mind. These applications where mostly motivated by multiobjective programming. Meanwhile it has turned out that the algorithm is used to solve efficiently problems that appear in image registration in reconstruction problems involving millions of input images.

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Why is it important?

The Minimax Problem structure vomes from the approach to seek the three dimensional coordinates that minimise the maximum reprojection error across all views. The quotient structure comes from the definition of the reprojections error. In "Fast algorithms for L∞ problems in multiview geometry" the authors (Sameer Agarwal ; Noah Snavely and Steven M. Seitz from the University of Washington) state that the algorithm proposed by Gugat ... stands out as a clear winner - this is very pleasing!

Perspectives

In " the paper "Coresets for Triangulation" the 3d reconstruction of Notre Dame is considered in the numerical examples - this motivates the picture of Notre Dame. It is published by Qianggong Zhang andTat-Jun Chin from the University of Adelaide in IEEE Transactions on Pattern Analysis and Machine Intelligence 40.

Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg

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This page is a summary of: A Fast Algorithm for a Class of Generalized Fractional Programs, Management Science, October 1996, INFORMS, DOI: 10.1287/mnsc.42.10.1493.
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