451 research outputs found
A Hybridized Weak Galerkin Finite Element Scheme for the Stokes Equations
In this paper a hybridized weak Galerkin (HWG) finite element method for
solving the Stokes equations in the primary velocity-pressure formulation is
introduced. The WG method uses weak functions and their weak derivatives which
are defined as distributions. Weak functions and weak derivatives can be
approximated by piecewise polynomials with various degrees. Different
combination of polynomial spaces leads to different WG finite element methods,
which makes WG methods highly flexible and efficient in practical computation.
A Lagrange multiplier is introduced to provide a numerical approximation for
certain derivatives of the exact solution. With this new feature, HWG method
can be used to deal with jumps of the functions and their flux easily. Optimal
order error estimate are established for the corresponding HWG finite element
approximations for both {\color{black}primal variables} and the Lagrange
multiplier. A Schur complement formulation of the HWG method is derived for
implementation purpose. The validity of the theoretical results is demonstrated
in numerical tests.Comment: 19 pages, 4 tables,it has been accepted for publication in SCIENCE
CHINA Mathematics. arXiv admin note: substantial text overlap with
arXiv:1402.1157, arXiv:1302.2707 by other author
Towards Effective Codebookless Model for Image Classification
The bag-of-features (BoF) model for image classification has been thoroughly
studied over the last decade. Different from the widely used BoF methods which
modeled images with a pre-trained codebook, the alternative codebook free image
modeling method, which we call Codebookless Model (CLM), attracted little
attention. In this paper, we present an effective CLM that represents an image
with a single Gaussian for classification. By embedding Gaussian manifold into
a vector space, we show that the simple incorporation of our CLM into a linear
classifier achieves very competitive accuracy compared with state-of-the-art
BoF methods (e.g., Fisher Vector). Since our CLM lies in a high dimensional
Riemannian manifold, we further propose a joint learning method of low-rank
transformation with support vector machine (SVM) classifier on the Gaussian
manifold, in order to reduce computational and storage cost. To study and
alleviate the side effect of background clutter on our CLM, we also present a
simple yet effective partial background removal method based on saliency
detection. Experiments are extensively conducted on eight widely used databases
to demonstrate the effectiveness and efficiency of our CLM method
Extrinsic Calibration of a Camera and Laser Range Finder
We describes theoretical and experimental results for the extrinsic calibration of sensor platform consisting of a camera and a laser range finder. The proposed technique requires the system to observe a planar pattern in several poses, and the constraints are based upon data captured simultaneously from the camera and the laser range finder. The planar pattern surface and the laser scanline on the planar pattern are related, so these data constrain the relative position and orientation of the camera and laser range finder. The calibration procedure starts with a closed-from solution, which provides initial conditions for a subsequent nonlinear refinement. We present the results from both computer simulated data and an implementation on a B21rT M Mobile Robot from iRobot Corporation, using a Sony firewire digital camera and SICK PLS laser scanner
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