3,137 research outputs found
An Octree-Based Approach towards Efficient Variational Range Data Fusion
Volume-based reconstruction is usually expensive both in terms of memory
consumption and runtime. Especially for sparse geometric structures, volumetric
representations produce a huge computational overhead. We present an efficient
way to fuse range data via a variational Octree-based minimization approach by
taking the actual range data geometry into account. We transform the data into
Octree-based truncated signed distance fields and show how the optimization can
be conducted on the newly created structures. The main challenge is to uphold
speed and a low memory footprint without sacrificing the solutions' accuracy
during optimization. We explain how to dynamically adjust the optimizer's
geometric structure via joining/splitting of Octree nodes and how to define the
operators. We evaluate on various datasets and outline the suitability in terms
of performance and geometric accuracy.Comment: BMVC 201
InferenceMAP: Mapping of Single-Molecule Dynamics with Bayesian Inference
Single-particle tracking (SPT) grants unprecedented insight into cellular
function at the molecular scale [1]. Throughout the cell, the movement of
single-molecules is generally heterogeneous and complex. Hence, there is an
imperative to understand the multi-scale nature of single-molecule dynamics in
biological systems. We have previously shown that with high-density SPT,
spatial maps of the parameters that dictate molecule motion can be generated to
intricately describe cellular environments [2,3,4]. To date, however, there
exist no publically available tools that reconcile trajectory data to generate
the aforementioned maps. We address this void in the SPT community with
InferenceMAP: an interactive software package that uses a powerful Bayesian
method to map the dynamic cellular space experienced by individual
biomolecules.Comment: 56 page
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
A fast and robust patient specific Finite Element mesh registration technique: application to 60 clinical cases
Finite Element mesh generation remains an important issue for patient
specific biomechanical modeling. While some techniques make automatic mesh
generation possible, in most cases, manual mesh generation is preferred for
better control over the sub-domain representation, element type, layout and
refinement that it provides. Yet, this option is time consuming and not suited
for intraoperative situations where model generation and computation time is
critical. To overcome this problem we propose a fast and automatic mesh
generation technique based on the elastic registration of a generic mesh to the
specific target organ in conjunction with element regularity and quality
correction. This Mesh-Match-and-Repair (MMRep) approach combines control over
the mesh structure along with fast and robust meshing capabilities, even in
situations where only partial organ geometry is available. The technique was
successfully tested on a database of 5 pre-operatively acquired complete femora
CT scans, 5 femoral heads partially digitized at intraoperative stage, and 50
CT volumes of patients' heads. The MMRep algorithm succeeded in all 60 cases,
yielding for each patient a hex-dominant, Atlas based, Finite Element mesh with
submillimetric surface representation accuracy, directly exploitable within a
commercial FE software
An anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems
Heterogeneous anisotropic diffusion problems arise in the various areas of
science and engineering including plasma physics, petroleum engineering, and
image processing. Standard numerical methods can produce spurious oscillations
when they are used to solve those problems. A common approach to avoid this
difficulty is to design a proper numerical scheme and/or a proper mesh so that
the numerical solution validates the discrete counterpart (DMP) of the maximum
principle satisfied by the continuous solution. A well known mesh condition for
the DMP satisfaction by the linear finite element solution of isotropic
diffusion problems is the non-obtuse angle condition that requires the dihedral
angles of mesh elements to be non-obtuse. In this paper, a generalization of
the condition, the so-called anisotropic non-obtuse angle condition, is
developed for the finite element solution of heterogeneous anisotropic
diffusion problems. The new condition is essentially the same as the existing
one except that the dihedral angles are now measured in a metric depending on
the diffusion matrix of the underlying problem. Several variants of the new
condition are obtained. Based on one of them, two metric tensors for use in
anisotropic mesh generation are developed to account for DMP satisfaction and
the combination of DMP satisfaction and mesh adaptivity. Numerical examples are
given to demonstrate the features of the linear finite element method for
anisotropic meshes generated with the metric tensors.Comment: 34 page
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