255,077 research outputs found
A near-stationary subspace for ridge approximation
Response surfaces are common surrogates for expensive computer simulations in
engineering analysis. However, the cost of fitting an accurate response surface
increases exponentially as the number of model inputs increases, which leaves
response surface construction intractable for high-dimensional, nonlinear
models. We describe ridge approximation for fitting response surfaces in
several variables. A ridge function is constant along several directions in its
domain, so fitting occurs on the coordinates of a low-dimensional subspace of
the input space. We review essential theory for ridge approximation---e.g., the
best mean-squared approximation and an optimal low-dimensional subspace---and
we prove that the gradient-based active subspace is near-stationary for the
least-squares problem that defines an optimal subspace. Motivated by the
theory, we propose a computational heuristic that uses an estimated active
subspace as an initial guess for a ridge approximation fitting problem. We show
a simple example where the heuristic fails, which reveals a type of function
for which the proposed approach is inappropriate. We then propose a simple
alternating heuristic for fitting a ridge function, and we demonstrate the
effectiveness of the active subspace initial guess applied to an airfoil model
of drag as a function of its 18 shape parameters
Gaussian Process Morphable Models
Statistical shape models (SSMs) represent a class of shapes as a normal
distribution of point variations, whose parameters are estimated from example
shapes. Principal component analysis (PCA) is applied to obtain a
low-dimensional representation of the shape variation in terms of the leading
principal components. In this paper, we propose a generalization of SSMs,
called Gaussian Process Morphable Models (GPMMs). We model the shape variations
with a Gaussian process, which we represent using the leading components of its
Karhunen-Loeve expansion. To compute the expansion, we make use of an
approximation scheme based on the Nystrom method. The resulting model can be
seen as a continuous analogon of an SSM. However, while for SSMs the shape
variation is restricted to the span of the example data, with GPMMs we can
define the shape variation using any Gaussian process. For example, we can
build shape models that correspond to classical spline models, and thus do not
require any example data. Furthermore, Gaussian processes make it possible to
combine different models. For example, an SSM can be extended with a spline
model, to obtain a model that incorporates learned shape characteristics, but
is flexible enough to explain shapes that cannot be represented by the SSM. We
introduce a simple algorithm for fitting a GPMM to a surface or image. This
results in a non-rigid registration approach, whose regularization properties
are defined by a GPMM. We show how we can obtain different registration
schemes,including methods for multi-scale, spatially-varying or hybrid
registration, by constructing an appropriate GPMM. As our approach strictly
separates modelling from the fitting process, this is all achieved without
changes to the fitting algorithm. We show the applicability and versatility of
GPMMs on a clinical use case, where the goal is the model-based segmentation of
3D forearm images
Accuracy of one-dimensional collision integral in the rigid spheres approximation
The accuracy of calculation of spectral line shapes in one-dimensional
approximation is studied analytically in several limiting cases for arbitrary
collision kernel and numerically in the rigid spheres model. It is shown that
the deviation of the line profile is maximal in the center of the line in case
of large perturber mass and intermediate values of collision frequency. For
moderate masses of buffer molecules the error of one-dimensional approximation
is found not to exceed 5%.Comment: LaTeX, 24 pages, 8 figure
Extended Object Tracking: Introduction, Overview and Applications
This article provides an elaborate overview of current research in extended
object tracking. We provide a clear definition of the extended object tracking
problem and discuss its delimitation to other types of object tracking. Next,
different aspects of extended object modelling are extensively discussed.
Subsequently, we give a tutorial introduction to two basic and well used
extended object tracking approaches - the random matrix approach and the Kalman
filter-based approach for star-convex shapes. The next part treats the tracking
of multiple extended objects and elaborates how the large number of feasible
association hypotheses can be tackled using both Random Finite Set (RFS) and
Non-RFS multi-object trackers. The article concludes with a summary of current
applications, where four example applications involving camera, X-band radar,
light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are
highlighted.Comment: 30 pages, 19 figure
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Prototyping Large-Sized Objects Using Freeform Thick Layers of Plastic Foam
Current Rapid Prototyping systems are primarily aimed at small-sized objects containing many
shape details. In this paper a Rapid Prototyping technology is presented that is aimed at largesized objects having a complex, freeform outer shape. This new technology builds the model out
ofthick layers, each having freeform outside faces. The paper will present: an overview of current
methods to produce large prototypes, the basics of the new method, the technology used to
produce the layers, the toolpath planning and finally the overall system design.Mechanical Engineerin
Image Segmentation Using Weak Shape Priors
The problem of image segmentation is known to become particularly challenging
in the case of partial occlusion of the object(s) of interest, background
clutter, and the presence of strong noise. To overcome this problem, the
present paper introduces a novel approach segmentation through the use of
"weak" shape priors. Specifically, in the proposed method, an segmenting active
contour is constrained to converge to a configuration at which its geometric
parameters attain their empirical probability densities closely matching the
corresponding model densities that are learned based on training samples. It is
shown through numerical experiments that the proposed shape modeling can be
regarded as "weak" in the sense that it minimally influences the segmentation,
which is allowed to be dominated by data-related forces. On the other hand, the
priors provide sufficient constraints to regularize the convergence of
segmentation, while requiring substantially smaller training sets to yield less
biased results as compared to the case of PCA-based regularization methods. The
main advantages of the proposed technique over some existing alternatives is
demonstrated in a series of experiments.Comment: 27 pages, 8 figure
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