12,392 research outputs found
Stochastic level-set method for shape optimisation
We present a new method for stochastic shape optimisation of engineering
structures. The method generalises an existing deterministic scheme, in which
the structure is represented and evolved by a level-set method coupled with
mathematical programming. The stochastic element of the algorithm is built on
the methods of statistical mechanics and is designed so that the system
explores a Boltzmann-Gibbs distribution of structures. In non-convex
optimisation problems, the deterministic algorithm can get trapped in local
optima: the stochastic generalisation enables sampling of multiple local
optima, which aids the search for the globally-optimal structure. The method is
demonstrated for several simple geometrical problems, and a proof-of-principle
calculation is shown for a simple engineering structure.Comment: 17 pages, 10 fig
A deep level set method for image segmentation
This paper proposes a novel image segmentation approachthat integrates fully
convolutional networks (FCNs) with a level setmodel. Compared with a FCN, the
integrated method can incorporatesmoothing and prior information to achieve an
accurate segmentation.Furthermore, different than using the level set model as
a post-processingtool, we integrate it into the training phase to fine-tune the
FCN. Thisallows the use of unlabeled data during training in a
semi-supervisedsetting. Using two types of medical imaging data (liver CT and
left ven-tricle MRI data), we show that the integrated method achieves
goodperformance even when little training data is available, outperformingthe
FCN or the level set model alone
The Semi Implicit Gradient Augmented Level Set Method
Here a semi-implicit formulation of the gradient augmented level set method
is presented. By tracking both the level set and it's gradient accurate subgrid
information is provided,leading to highly accurate descriptions of a moving
interface. The result is a hybrid Lagrangian-Eulerian method that may be easily
applied in two or three dimensions. The new approach allows for the
investigation of interfaces evolving by mean curvature and by the intrinsic
Laplacian of the curvature. In this work the algorithm, convergence and
accuracy results are presented. Several numerical experiments in both two and
three dimensions demonstrate the stability of the scheme.Comment: 19 Pages, 14 Figure
A Topology-Preserving Level Set Method for Shape Optimization
The classical level set method, which represents the boundary of the unknown
geometry as the zero-level set of a function, has been shown to be very
effective in solving shape optimization problems. The present work addresses
the issue of using a level set representation when there are simple geometrical
and topological constraints. We propose a logarithmic barrier penalty which
acts to enforce the constraints, leading to an approximate solution to shape
design problems.Comment: 10 pages, 4 figure
The level set method for the two-sided eigenproblem
We consider the max-plus analogue of the eigenproblem for matrix pencils
Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible
values of lambda), which is a finite union of intervals, can be computed in
pseudo-polynomial number of operations, by a (pseudo-polynomial) number of
calls to an oracle that computes the value of a mean payoff game. The proof
relies on the introduction of a spectral function, which we interpret in terms
of the least Chebyshev distance between Ax and lambda Bx. The spectrum is
obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we
explain relation to mean-payoff games and discrete event systems, and show
that the reconstruction of spectrum is pseudopolynomia
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