Polynomial Solvers for Saturated Ideals

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In this paper we present a new method for creating polynomial
solvers for problems where a (possibly infinite) subset
of the solutions are undesirable or uninteresting. These
solutions typically arise from simplifications made during
modeling, but can also come from degeneracies which are
inherent to the geometry of the original problem.
The proposed approach extends the standard action matrix
method to saturated ideals. This allows us to add constraints
that some polynomials should be non-zero on the
solutions. This does not only offer the possibility of improved
performance by removing superfluous solutions, but
makes a larger class of problems tractable. Previously,
problems with infinitely many solutions could not be solved
directly using the action matrix method as it requires a
zero-dimensional ideal. In contrast we only require that
after removing the unwanted solutions only finitely many
remain. We evaluate our method on three applications, optimal
triangulation, time-of-arrival self-calibration and optimal
vanishing point estimation.
Titel på värdpublikation 2017 IEEE International Conference on Computer Vision (ICCV)
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Antal sidor10
ISBN (elektroniskt)978-1-5386-1032-9
StatusPublished - 2017 okt.
Evenemanginternational conference on computer vision, 2017 - Palazzon del Cinema - Venice Convention Centre , Venice, Italien
Varaktighet: 2017 okt. 222017 okt. 29


Konferensinternational conference on computer vision, 2017
Förkortad titelICCV

Ämnesklassifikation (UKÄ)

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