6,370 research outputs found
A clever elimination strategy for efficient minimal solvers
We present a new insight into the systematic generation of minimal solvers in
computer vision, which leads to smaller and faster solvers. Many minimal
problem formulations are coupled sets of linear and polynomial equations where
image measurements enter the linear equations only. We show that it is useful
to solve such systems by first eliminating all the unknowns that do not appear
in the linear equations and then extending solutions to the rest of unknowns.
This can be generalized to fully non-linear systems by linearization via
lifting. We demonstrate that this approach leads to more efficient solvers in
three problems of partially calibrated relative camera pose computation with
unknown focal length and/or radial distortion. Our approach also generates new
interesting constraints on the fundamental matrices of partially calibrated
cameras, which were not known before.Comment: 13 pages, 7 figure
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
MLPnP - A Real-Time Maximum Likelihood Solution to the Perspective-n-Point Problem
In this paper, a statistically optimal solution to the Perspective-n-Point
(PnP) problem is presented. Many solutions to the PnP problem are geometrically
optimal, but do not consider the uncertainties of the observations. In
addition, it would be desirable to have an internal estimation of the accuracy
of the estimated rotation and translation parameters of the camera pose. Thus,
we propose a novel maximum likelihood solution to the PnP problem, that
incorporates image observation uncertainties and remains real-time capable at
the same time. Further, the presented method is general, as is works with 3D
direction vectors instead of 2D image points and is thus able to cope with
arbitrary central camera models. This is achieved by projecting (and thus
reducing) the covariance matrices of the observations to the corresponding
vector tangent space.Comment: Submitted to the ISPRS congress (2016) in Prague. Oral Presentation.
Published in ISPRS Ann. Photogramm. Remote Sens. Spatial Inf. Sci., III-3,
131-13
Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers
Many computer vision applications require robust estimation of the underlying
geometry, in terms of camera motion and 3D structure of the scene. These robust
methods often rely on running minimal solvers in a RANSAC framework. In this
paper we show how we can make polynomial solvers based on the action matrix
method faster, by careful selection of the monomial bases. These monomial bases
have traditionally been based on a Gr\"obner basis for the polynomial ideal.
Here we describe how we can enumerate all such bases in an efficient way. We
also show that going beyond Gr\"obner bases leads to more efficient solvers in
many cases. We present a novel basis sampling scheme that we evaluate on a
number of problems
- …