5,393 research outputs found
Sensor Networks TDOA Self-Calibration: 2D Complexity Analysis and Solutions
Given a network of receivers and transmitters, the process of determining
their positions from measured pseudo-ranges is known as network
self-calibration. In this paper we consider 2D networks with synchronized
receivers but unsynchronized transmitters and the corresponding calibration
techniques,known as TDOA techniques. Despite previous work, TDOA
self-calibration is computationally challenging. Iterative algorithms are very
sensitive to the initialization, causing convergence issues.In this paper, we
present a novel approach, which gives an algebraic solution to three previously
unsolved scenarios. Our solvers can lead to a position error <1.2% and are
robust to noise
Rectification from Radially-Distorted Scales
This paper introduces the first minimal solvers that jointly estimate lens
distortion and affine rectification from repetitions of rigidly transformed
coplanar local features. The proposed solvers incorporate lens distortion into
the camera model and extend accurate rectification to wide-angle images that
contain nearly any type of coplanar repeated content. We demonstrate a
principled approach to generating stable minimal solvers by the Grobner basis
method, which is accomplished by sampling feasible monomial bases to maximize
numerical stability. Synthetic and real-image experiments confirm that the
solvers give accurate rectifications from noisy measurements when used in a
RANSAC-based estimator. The proposed solvers demonstrate superior robustness to
noise compared to the state-of-the-art. The solvers work on scenes without
straight lines and, in general, relax the strong assumptions on scene content
made by the state-of-the-art. Accurate rectifications on imagery that was taken
with narrow focal length to near fish-eye lenses demonstrate the wide
applicability of the proposed method. The method is fully automated, and the
code is publicly available at https://github.com/prittjam/repeats.Comment: pre-prin
Trifocal Relative Pose from Lines at Points and its Efficient Solution
We present a new minimal problem for relative pose estimation mixing point
features with lines incident at points observed in three views and its
efficient homotopy continuation solver. We demonstrate the generality of the
approach by analyzing and solving an additional problem with mixed point and
line correspondences in three views. The minimal problems include
correspondences of (i) three points and one line and (ii) three points and two
lines through two of the points which is reported and analyzed here for the
first time. These are difficult to solve, as they have 216 and - as shown here
- 312 solutions, but cover important practical situations when line and point
features appear together, e.g., in urban scenes or when observing curves. We
demonstrate that even such difficult problems can be solved robustly using a
suitable homotopy continuation technique and we provide an implementation
optimized for minimal problems that can be integrated into engineering
applications. Our simulated and real experiments demonstrate our solvers in the
camera geometry computation task in structure from motion. We show that new
solvers allow for reconstructing challenging scenes where the standard two-view
initialization of structure from motion fails.Comment: This material is based upon work supported by the National Science
Foundation under Grant No. DMS-1439786 while most authors were in residence
at Brown University's Institute for Computational and Experimental Research
in Mathematics -- ICERM, in Providence, R
A Bramble-Pasciak conjugate gradient method for discrete Stokes equations with random viscosity
We study the iterative solution of linear systems of equations arising from
stochastic Galerkin finite element discretizations of saddle point problems. We
focus on the Stokes model with random data parametrized by uniformly
distributed random variables and discuss well-posedness of the variational
formulations. We introduce a Bramble-Pasciak conjugate gradient method as a
linear solver. It builds on a non-standard inner product associated with a
block triangular preconditioner. The block triangular structure enables more
sophisticated preconditioners than the block diagonal structure usually applied
in MINRES methods. We show how the existence requirements of a conjugate
gradient method can be met in our setting. We analyze the performance of the
solvers depending on relevant physical and numerical parameters by means of
eigenvalue estimates. For this purpose, we derive bounds for the eigenvalues of
the relevant preconditioned sub-matrices. We illustrate our findings using the
flow in a driven cavity as a numerical test case, where the viscosity is given
by a truncated Karhunen-Lo\`eve expansion of a random field. In this example, a
Bramble-Pasciak conjugate gradient method with block triangular preconditioner
outperforms a MINRES method with block diagonal preconditioner in terms of
iteration numbers.Comment: 19 pages, 1 figure, submitted to SIAM JU
- …