6,358 research outputs found
3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries
Recent advances in electron microscopy have enabled the imaging of single
cells in 3D at nanometer length scale resolutions. An uncharted frontier for in
silico biology is the ability to simulate cellular processes using these
observed geometries. Enabling such simulations requires watertight meshing of
electron micrograph images into 3D volume meshes, which can then form the basis
of computer simulations of such processes using numerical techniques such as
the Finite Element Method. In this paper, we describe the use of our recently
rewritten mesh processing software, GAMer 2, to bridge the gap between poorly
conditioned meshes generated from segmented micrographs and boundary marked
tetrahedral meshes which are compatible with simulation. We demonstrate the
application of a workflow using GAMer 2 to a series of electron micrographs of
neuronal dendrite morphology explored at three different length scales and show
that the resulting meshes are suitable for finite element simulations. This
work is an important step towards making physical simulations of biological
processes in realistic geometries routine. Innovations in algorithms to
reconstruct and simulate cellular length scale phenomena based on emerging
structural data will enable realistic physical models and advance discovery at
the interface of geometry and cellular processes. We posit that a new frontier
at the intersection of computational technologies and single cell biology is
now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies
available upon reques
Semantically Informed Multiview Surface Refinement
We present a method to jointly refine the geometry and semantic segmentation
of 3D surface meshes. Our method alternates between updating the shape and the
semantic labels. In the geometry refinement step, the mesh is deformed with
variational energy minimization, such that it simultaneously maximizes
photo-consistency and the compatibility of the semantic segmentations across a
set of calibrated images. Label-specific shape priors account for interactions
between the geometry and the semantic labels in 3D. In the semantic
segmentation step, the labels on the mesh are updated with MRF inference, such
that they are compatible with the semantic segmentations in the input images.
Also, this step includes prior assumptions about the surface shape of different
semantic classes. The priors induce a tight coupling, where semantic
information influences the shape update and vice versa. Specifically, we
introduce priors that favor (i) adaptive smoothing, depending on the class
label; (ii) straightness of class boundaries; and (iii) semantic labels that
are consistent with the surface orientation. The novel mesh-based
reconstruction is evaluated in a series of experiments with real and synthetic
data. We compare both to state-of-the-art, voxel-based semantic 3D
reconstruction, and to purely geometric mesh refinement, and demonstrate that
the proposed scheme yields improved 3D geometry as well as an improved semantic
segmentation
Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates
The study of cerebral anatomy in developing neonates is of great importance for
the understanding of brain development during the early period of life. This
dissertation therefore focuses on three challenges in the modelling of cerebral
anatomy in neonates during brain development. The methods that have been
developed all use Magnetic Resonance Images (MRI) as source data.
To facilitate study of vascular development in the neonatal period, a set of image
analysis algorithms are developed to automatically extract and model cerebral
vessel trees. The whole process consists of cerebral vessel tracking from
automatically placed seed points, vessel tree generation, and vasculature
registration and matching. These algorithms have been tested on clinical Time-of-
Flight (TOF) MR angiographic datasets.
To facilitate study of the neonatal cortex a complete cerebral cortex segmentation
and reconstruction pipeline has been developed. Segmentation of the neonatal
cortex is not effectively done by existing algorithms designed for the adult brain
because the contrast between grey and white matter is reversed. This causes pixels
containing tissue mixtures to be incorrectly labelled by conventional methods. The
neonatal cortical segmentation method that has been developed is based on a novel
expectation-maximization (EM) method with explicit correction for mislabelled
partial volume voxels. Based on the resulting cortical segmentation, an implicit
surface evolution technique is adopted for the reconstruction of the cortex in
neonates. The performance of the method is investigated by performing a detailed
landmark study.
To facilitate study of cortical development, a cortical surface registration algorithm
for aligning the cortical surface is developed. The method first inflates extracted
cortical surfaces and then performs a non-rigid surface registration using free-form
deformations (FFDs) to remove residual alignment. Validation experiments using
data labelled by an expert observer demonstrate that the method can capture local
changes and follow the growth of specific sulcus
Second-order Shape Optimization for Geometric Inverse Problems in Vision
We develop a method for optimization in shape spaces, i.e., sets of surfaces
modulo re-parametrization. Unlike previously proposed gradient flows, we
achieve superlinear convergence rates through a subtle approximation of the
shape Hessian, which is generally hard to compute and suffers from a series of
degeneracies. Our analysis highlights the role of mean curvature motion in
comparison with first-order schemes: instead of surface area, our approach
penalizes deformation, either by its Dirichlet energy or total variation.
Latter regularizer sparks the development of an alternating direction method of
multipliers on triangular meshes. Therein, a conjugate-gradients solver enables
us to bypass formation of the Gaussian normal equations appearing in the course
of the overall optimization. We combine all of the aforementioned ideas in a
versatile geometric variation-regularized Levenberg-Marquardt-type method
applicable to a variety of shape functionals, depending on intrinsic properties
of the surface such as normal field and curvature as well as its embedding into
space. Promising experimental results are reported
3D time series analysis of cell shape using Laplacian approaches
Background:
Fundamental cellular processes such as cell movement, division or food uptake critically depend on cells being able to change shape. Fast acquisition of three-dimensional image time series has now become possible, but we lack efficient tools for analysing shape deformations in order to understand the real three-dimensional nature of shape changes.
Results:
We present a framework for 3D+time cell shape analysis. The main contribution is three-fold: First, we develop a fast, automatic random walker method for cell segmentation. Second, a novel topology fixing method is proposed to fix segmented binary volumes without spherical topology. Third, we show that algorithms used for each individual step of the analysis pipeline (cell segmentation, topology fixing, spherical parameterization, and shape representation) are closely related to the Laplacian operator. The framework is applied to the shape analysis of neutrophil cells.
Conclusions:
The method we propose for cell segmentation is faster than the traditional random walker method or the level set method, and performs better on 3D time-series of neutrophil cells, which are comparatively noisy as stacks have to be acquired fast enough to account for cell motion. Our method for topology fixing outperforms the tools provided by SPHARM-MAT and SPHARM-PDM in terms of their successful fixing rates. The different tasks in the presented pipeline for 3D+time shape analysis of cells can be solved using Laplacian approaches, opening the possibility of eventually combining individual steps in order to speed up computations
Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images
We present a novel kernel regression framework for smoothing scalar surface
data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel
constructed from the eigenfunctions, we formulate a new bivariate kernel
regression framework as a weighted eigenfunction expansion with the heat kernel
as the weights. The new kernel regression is mathematically equivalent to
isotropic heat diffusion, kernel smoothing and recently popular diffusion
wavelets. Unlike many previous partial differential equation based approaches
involving diffusion, our approach represents the solution of diffusion
analytically, reducing numerical inaccuracy and slow convergence. The numerical
implementation is validated on a unit sphere using spherical harmonics. As an
illustration, we have applied the method in characterizing the localized growth
pattern of mandible surfaces obtained in CT images from subjects between ages 0
and 20 years by regressing the length of displacement vectors with respect to
the template surface.Comment: Accepted in Medical Image Analysi
The Spine of the Cosmic Web
We present the SpineWeb framework for the topological analysis of the Cosmic
Web and the identification of its walls, filaments and cluster nodes. Based on
the watershed segmentation of the cosmic density field, the SpineWeb method
invokes the local adjacency properties of the boundaries between the watershed
basins to trace the critical points in the density field and the separatrices
defined by them. The separatrices are classified into walls and the spine, the
network of filaments and nodes in the matter distribution. Testing the method
with a heuristic Voronoi model yields outstanding results. Following the
discussion of the test results, we apply the SpineWeb method to a set of
cosmological N-body simulations. The latter illustrates the potential for
studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version:
http://skysrv.pha.jhu.edu/~miguel/SpineWeb
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