12,989 research outputs found
A segmentation-free isogeometric extended mortar contact method
This paper presents a new isogeometric mortar contact formulation based on an
extended finite element interpolation to capture physical pressure
discontinuities at the contact boundary. The so called two-half-pass algorithm
is employed, which leads to an unbiased formulation and, when applied to the
mortar setting, has the additional advantage that the mortar coupling term is
no longer present in the contact forces. As a result, the computationally
expensive segmentation at overlapping master-slave element boundaries, usually
required in mortar methods (although often simplified with loss of accuracy),
is not needed from the outset. For the numerical integration of general contact
problems, the so-called refined boundary quadrature is employed, which is based
on adaptive partitioning of contact elements along the contact boundary. The
contact patch test shows that the proposed formulation passes the test without
using either segmentation or refined boundary quadrature. Several numerical
examples are presented to demonstrate the robustness and accuracy of the
proposed formulation.Comment: In this version, we have removed the patch test comparison with the
classical mortar method and removed corresponding statements. They will be
studied in further detail in future work, so that the focus is now entirely
on the new IGA mortar formulatio
Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts
Formulations of the Image Decomposition Problem as a Multicut Problem (MP)
w.r.t. a superpixel graph have received considerable attention. In contrast,
instances of the MP w.r.t. a pixel grid graph have received little attention,
firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are
hard to solve in practice, and, secondly, due to the lack of long-range terms
in the objective function of the MP. We propose a generalization of the MP with
long-range terms (LMP). We design and implement two efficient algorithms
(primal feasible heuristics) for the MP and LMP which allow us to study
instances of both problems w.r.t. the pixel grid graphs of the images in the
BSDS-500 benchmark. The decompositions we obtain do not differ significantly
from the state of the art, suggesting that the LMP is a competitive formulation
of the Image Decomposition Problem. To demonstrate the generality of the LMP,
we apply it also to the Mesh Decomposition Problem posed by the Princeton
benchmark, obtaining state-of-the-art decompositions
The whole mesh Deformation Model for 2D and 3D image segmentation
In this paper we present a novel approach for image segmentation using Active Nets and Active Volumes. Those solutions are based on the Deformable Models, with slight difference in the method for describing the shapes of interests - instead of using a contour or a surface they represented the segmented objects with a mesh structure, which allows to describe not only the surface of the objects but also to model their interiors. This is obtained by dividing the nodes of the mesh in two categories, namely internal and external ones, which will be responsible for two different tasks. In our new approach we propose to negate this separation and use only one type of nodes. Using that assumption we manage to significantly shorten the time of segmentation while maintaining its quality
Image Segmentation with Eigenfunctions of an Anisotropic Diffusion Operator
We propose the eigenvalue problem of an anisotropic diffusion operator for
image segmentation. The diffusion matrix is defined based on the input image.
The eigenfunctions and the projection of the input image in some eigenspace
capture key features of the input image. An important property of the model is
that for many input images, the first few eigenfunctions are close to being
piecewise constant, which makes them useful as the basis for a variety of
applications such as image segmentation and edge detection. The eigenvalue
problem is shown to be related to the algebraic eigenvalue problems resulting
from several commonly used discrete spectral clustering models. The relation
provides a better understanding and helps developing more efficient numerical
implementation and rigorous numerical analysis for discrete spectral
segmentation methods. The new continuous model is also different from
energy-minimization methods such as geodesic active contour in that no initial
guess is required for in the current model. The multi-scale feature is a
natural consequence of the anisotropic diffusion operator so there is no need
to solve the eigenvalue problem at multiple levels. A numerical implementation
based on a finite element method with an anisotropic mesh adaptation strategy
is presented. It is shown that the numerical scheme gives much more accurate
results on eigenfunctions than uniform meshes. Several interesting features of
the model are examined in numerical examples and possible applications are
discussed
A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching
We propose a combinatorial solution for the problem of non-rigidly matching a
3D shape to 3D image data. To this end, we model the shape as a triangular mesh
and allow each triangle of this mesh to be rigidly transformed to achieve a
suitable matching to the image. By penalising the distance and the relative
rotation between neighbouring triangles our matching compromises between image
and shape information. In this paper, we resolve two major challenges: Firstly,
we address the resulting large and NP-hard combinatorial problem with a
suitable graph-theoretic approach. Secondly, we propose an efficient
discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge
this is the first combinatorial formulation for non-rigid 3D shape-to-image
matching. In contrast to existing local (gradient descent) optimisation
methods, we obtain solutions that do not require a good initialisation and that
are within a bound of the optimal solution. We evaluate the proposed method on
the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image
registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization
In this paper, we propose a general framework for constructing IGA-suitable
planar B-spline parameterizations from given complex CAD boundaries consisting
of a set of B-spline curves. Instead of forming the computational domain by a
simple boundary, planar domains with high genus and more complex boundary
curves are considered. Firstly, some pre-processing operations including
B\'ezier extraction and subdivision are performed on each boundary curve in
order to generate a high-quality planar parameterization; then a robust planar
domain partition framework is proposed to construct high-quality patch-meshing
results with few singularities from the discrete boundary formed by connecting
the end points of the resulting boundary segments. After the topology
information generation of quadrilateral decomposition, the optimal placement of
interior B\'ezier curves corresponding to the interior edges of the
quadrangulation is constructed by a global optimization method to achieve a
patch-partition with high quality. Finally, after the imposition of
C1=G1-continuity constraints on the interface of neighboring B\'ezier patches
with respect to each quad in the quadrangulation, the high-quality B\'ezier
patch parameterization is obtained by a C1-constrained local optimization
method to achieve uniform and orthogonal iso-parametric structures while
keeping the continuity conditions between patches. The efficiency and
robustness of the proposed method are demonstrated by several examples which
are compared to results obtained by the skeleton-based parameterization
approach
Patient-specific CFD simulation of intraventricular haemodynamics based on 3D ultrasound imaging
Background: The goal of this paper is to present a computational fluid dynamic (CFD) model with moving boundaries to study the intraventricular flows in a patient-specific framework. Starting from the segmentation of real-time transesophageal echocardiographic images, a CFD model including the complete left ventricle and the moving 3D mitral valve was realized. Their motion, known as a function of time from the segmented ultrasound images, was imposed as a boundary condition in an Arbitrary Lagrangian-Eulerian framework.
Results: The model allowed for a realistic description of the displacement of the structures of interest and for an effective analysis of the intraventricular flows throughout the cardiac cycle. The model provides detailed intraventricular flow features, and highlights the importance of the 3D valve apparatus for the vortex dynamics and apical flow.
Conclusions: The proposed method could describe the haemodynamics of the left ventricle during the cardiac cycle. The methodology might therefore be of particular importance in patient treatment planning to assess the impact of mitral valve treatment on intraventricular flow dynamics
- …