1,008 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
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
SAT-based Explicit LTL Reasoning
We present here a new explicit reasoning framework for linear temporal logic
(LTL), which is built on top of propositional satisfiability (SAT) solving. As
a proof-of-concept of this framework, we describe a new LTL satisfiability
tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the
effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly
outperforms all existing LTL satisfiability solvers. Furthermore, we show that
the framework can be extended from propositional LTL to assertional LTL (where
we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and
demonstrating that this can yield an exponential improvement in performance
On the Two-View Geometry of Unsynchronized Cameras
We present new methods for simultaneously estimating camera geometry and time
shift from video sequences from multiple unsynchronized cameras. Algorithms for
simultaneous computation of a fundamental matrix or a homography with unknown
time shift between images are developed. Our methods use minimal correspondence
sets (eight for fundamental matrix and four and a half for homography) and
therefore are suitable for robust estimation using RANSAC. Furthermore, we
present an iterative algorithm that extends the applicability on sequences
which are significantly unsynchronized, finding the correct time shift up to
several seconds. We evaluated the methods on synthetic and wide range of real
world datasets and the results show a broad applicability to the problem of
camera synchronization.Comment: 12 pages, 9 figures, Computer Vision and Pattern Recognition (CVPR)
201
Calibrated and Partially Calibrated Semi-Generalized Homographies
In this paper, we propose the first minimal solutions for estimating the
semi-generalized homography given a perspective and a generalized camera. The
proposed solvers use five 2D-2D image point correspondences induced by a scene
plane. One of them assumes the perspective camera to be fully calibrated, while
the other solver estimates the unknown focal length together with the absolute
pose parameters. This setup is particularly important in structure-from-motion
and image-based localization pipelines, where a new camera is localized in each
step with respect to a set of known cameras and 2D-3D correspondences might not
be available. As a consequence of a clever parametrization and the elimination
ideal method, our approach only needs to solve a univariate polynomial of
degree five or three. The proposed solvers are stable and efficient as
demonstrated by a number of synthetic and real-world experiments
Partially calibrated semi-generalized pose from hybrid point correspondences
In this paper we study the problem of estimating the semi-generalized pose of
a partially calibrated camera, i.e., the pose of a perspective camera with
unknown focal length w.r.t. a generalized camera, from a hybrid set of 2D-2D
and 2D-3D point correspondences. We study all possible camera configurations
within the generalized camera system. To derive practical solvers to previously
unsolved challenging configurations, we test different parameterizations as
well as different solving strategies based on the state-of-the-art methods for
generating efficient polynomial solvers. We evaluate the three most promising
solvers, i.e., the H51f solver with five 2D-2D correspondences and one 2D-3D
correspondence viewed by the same camera inside generalized camera, the H32f
solver with three 2D-2D and two 2D-3D correspondences, and the H13f solver with
one 2D-2D and three 2D-3D correspondences, on synthetic and real data. We show
that in the presence of noise in the 3D points these solvers provide better
estimates than the corresponding absolute pose solvers
Trust Your IMU: Consequences of Ignoring the IMU Drift
In this paper, we argue that modern pre-integration methods for inertial
measurement units (IMUs) are accurate enough to ignore the drift for short time
intervals. This allows us to consider a simplified camera model, which in turn
admits further intrinsic calibration. We develop the first-ever solver to
jointly solve the relative pose problem with unknown and equal focal length and
radial distortion profile while utilizing the IMU data. Furthermore, we show
significant speed-up compared to state-of-the-art algorithms, with small or
negligible loss in accuracy for partially calibrated setups. The proposed
algorithms are tested on both synthetic and real data, where the latter is
focused on navigation using unmanned aerial vehicles (UAVs). We evaluate the
proposed solvers on different commercially available low-cost UAVs, and
demonstrate that the novel assumption on IMU drift is feasible in real-life
applications. The extended intrinsic auto-calibration enables us to use
distorted input images, making tedious calibration processes obsolete, compared
to current state-of-the-art methods
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