8 research outputs found
The decision problem for a three-sorted fragment of set theory with restricted quantification and finite enumerations
We solve the satisfiability problem for a three-sorted fragment of set theory
(denoted ), which admits a restricted form of quantification over
individual and set variables and the finite enumeration operator over individual variables, by showing that it
enjoys a small model property, i.e., any satisfiable formula of
has a finite model whose size depends solely on the length of
itself. Several set-theoretic constructs are expressible by
-formulae, such as some variants of the power set operator and the
unordered Cartesian product. In particular, concerning the unordered Cartesian
product, we show that when finite enumerations are used to represent the
construct, the resulting formula is exponentially shorter than the one that can
be constructed without resorting to such terms
A sparse resultant based method for efficient minimal solvers
Many computer vision applications require robust and efficient estimation of
camera geometry. The robust estimation is usually based on solving camera
geometry problems from a minimal number of input data measurements, i.e.
solving minimal problems in a RANSAC framework. Minimal problems often result
in complex systems of polynomial equations. Many state-of-the-art efficient
polynomial solvers to these problems are based on Gr\"obner bases and the
action-matrix method that has been automatized and highly optimized in recent
years. In this paper we study an alternative algebraic method for solving
systems of polynomial equations, i.e., the sparse resultant-based method and
propose a novel approach to convert the resultant constraint to an eigenvalue
problem. This technique can significantly improve the efficiency and stability
of existing resultant-based solvers. We applied our new resultant-based method
to a large variety of computer vision problems and show that for most of the
considered problems, the new method leads to solvers that are the same size as
the the best available Gr\"obner basis solvers and of similar accuracy. For
some problems the new sparse-resultant based method leads to even smaller and
more stable solvers than the state-of-the-art Gr\"obner basis solvers. Our new
method can be fully automatized and incorporated into existing tools for
automatic generation of efficient polynomial solvers and as such it represents
a competitive alternative to popular Gr\"obner basis methods for minimal
problems in computer vision
Sparse resultant based minimal solvers in computer vision and their connection with the action matrix
Many computer vision applications require robust and efficient estimation of
camera geometry from a minimal number of input data measurements, i.e., solving
minimal problems in a RANSAC framework. Minimal problems are usually formulated
as complex systems of sparse polynomials. The systems usually are
overdetermined and consist of polynomials with algebraically constrained
coefficients. Most state-of-the-art efficient polynomial solvers are based on
the action matrix method that has been automated and highly optimized in recent
years. On the other hand, the alternative theory of sparse resultants and
Newton polytopes has been less successful for generating efficient solvers,
primarily because the polytopes do not respect the constraints on the
coefficients. Therefore, in this paper, we propose a simple iterative scheme to
test various subsets of the Newton polytopes and search for the most efficient
solver. Moreover, we propose to use an extra polynomial with a special form to
further improve the solver efficiency via a Schur complement computation. We
show that for some camera geometry problems our extra polynomial-based method
leads to smaller and more stable solvers than the state-of-the-art Grobner
basis-based solvers. The proposed method can be fully automated and
incorporated into existing tools for automatic generation of efficient
polynomial solvers. It provides a competitive alternative to popular Grobner
basis-based methods for minimal problems in computer vision. We also study the
conditions under which the minimal solvers generated by the state-of-the-art
action matrix-based methods and the proposed extra polynomial resultant-based
method, are equivalent. Specifically we consider a step-by-step comparison
between the approaches based on the action matrix and the sparse resultant,
followed by a set of substitutions, which would lead to equivalent minimal
solvers.Comment: arXiv admin note: text overlap with arXiv:1912.1026
Aeronautical engineering: A continuing bibliography with indexes (supplement 291)
This bibliography lists 757 reports, articles, and other documents introduced into the NASA scientific and technical information system in May. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics
Aeronautical engineering: A continuing bibliography with indexes (supplement 284)
This bibliography lists 974 reports, articles, and other documents introduced into the NASA scientific and technical information system in Oct. 1992. The coverage includes documents on design, construction, evaluation, testing, operation, and performance of aircraft (including aircraft engines) and associated components, equipment, and systems. It also includes research and development in aerodynamics, aeronautics, and ground support equipment for aeronautical vehicles
Aeronautical Engineering: a Continuing Bibliography with Indexes (Supplement 244)
This bibliography lists 465 reports, articles, and other documents introduced into the NASA scientific and technical information system in September 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics