8,827 research outputs found
Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in EIT
In this paper, we develop a shape optimization-based algorithm for the
electrical impedance tomography (EIT) problem of determining a piecewise
constant conductivity on a polygonal partition from boundary measurements. The
key tool is to use a distributed shape derivative of a suitable cost functional
with respect to movements of the partition. Numerical simulations showing the
robustness and accuracy of the method are presented for simulated test cases in
two dimensions
BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning
The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples
eulerForce: Force-directed Layout for Euler Diagrams
Euler diagrams use closed curves to represent sets and their relationships. They facilitate set analysis, as humans tend to perceive distinct regions when closed curves are drawn on a plane. However, current automatic methods often produce diagrams with irregular, non-smooth curves that are not easily distinguishable. Other methods restrict the shape of the curve to for instance a circle, but such methods cannot draw an Euler diagram with exactly the required curve intersections for any set relations. In this paper, we present eulerForce, as the first method to adopt a force-directed approach to improve the layout and the curves of Euler diagrams generated by current methods. The layouts are improved in quick time. Our evaluation of eulerForce indicates the benefits of a force-directed approach to generate comprehensible Euler diagrams for any set relations in relatively fast time
Design and Optimizing of On-Chip Kinesin Substrates for Molecular Communication
Lab-on-chip devices and point-of-care diagnostic chip devices are composed of
many different components such as nanosensors that must be able to communicate
with other components within the device. Molecular communication is a promising
solution for on-chip communication. In particular, kinesin driven microtubule
(MT) motility is an effective means of transferring information particles from
one component to another. However, finding an optimal shape for these channels
can be challenging. In this paper we derive a mathematical optimization model
that can be used to find the optimal channel shape and dimensions for any
transmission period. We derive three specific models for the rectangular
channels, regular polygonal channels, and regular polygonal ring channels. We
show that the optimal channel shapes are the square-shaped channel for the
rectangular channel, and circular-shaped channel for the other classes of
shapes. Finally, we show that among all 2 dimensional shapes the optimal design
choice that maximizes information rate is the circular-shaped channel.Comment: accepted for publication in IEEE Transactions on Nanotechnolog
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
Molecular dynamics simulations of complex shaped particles using Minkowski operators
The Minkowski operators (addition and substraction of sets in vectorial
spaces) has been extensively used for Computer Graphics and Image Processing to
represent complex shapes. Here we propose to apply those mathematical concepts
to extend the Molecular Dynamics (MD) Methods for simulations with
complex-shaped particles. A new concept of Voronoi-Minkowski diagrams is
introduced to generate random packings of complex-shaped particles with tunable
particle roundness. By extending the classical concept of Verlet list we
achieve numerical efficiencies that do not grow quadratically with the body
number of sides. Simulations of dissipative granular materials under shear
demonstrate that the method complies with the first law of thermodynamics for
energy balance.Comment: Submitted to Phys. Rev.
Polygonal Building Segmentation by Frame Field Learning
While state of the art image segmentation models typically output
segmentations in raster format, applications in geographic information systems
often require vector polygons. To help bridge the gap between deep network
output and the format used in downstream tasks, we add a frame field output to
a deep segmentation model for extracting buildings from remote sensing images.
We train a deep neural network that aligns a predicted frame field to ground
truth contours. This additional objective improves segmentation quality by
leveraging multi-task learning and provides structural information that later
facilitates polygonization; we also introduce a polygonization algorithm that
utilizes the frame field along with the raster segmentation. Our code is
available at https://github.com/Lydorn/Polygonization-by-Frame-Field-Learning.Comment: CVPR 2021 - IEEE Conference on Computer Vision and Pattern
Recognition, Jun 2021, Pittsburg / Virtual, United State
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