1,903 research outputs found
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
An interactive analysis of harmonic and diffusion equations on discrete 3D shapes
AbstractRecent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes
Nonparametric tests of structure for high angular resolution diffusion imaging in Q-space
High angular resolution diffusion imaging data is the observed characteristic
function for the local diffusion of water molecules in tissue. This data is
used to infer structural information in brain imaging. Nonparametric scalar
measures are proposed to summarize such data, and to locally characterize
spatial features of the diffusion probability density function (PDF), relying
on the geometry of the characteristic function. Summary statistics are defined
so that their distributions are, to first-order, both independent of nuisance
parameters and also analytically tractable. The dominant direction of the
diffusion at a spatial location (voxel) is determined, and a new set of axes
are introduced in Fourier space. Variation quantified in these axes determines
the local spatial properties of the diffusion density. Nonparametric hypothesis
tests for determining whether the diffusion is unimodal, isotropic or
multi-modal are proposed. More subtle characteristics of white-matter
microstructure, such as the degree of anisotropy of the PDF and symmetry
compared with a variety of asymmetric PDF alternatives, may be ascertained
directly in the Fourier domain without parametric assumptions on the form of
the diffusion PDF. We simulate a set of diffusion processes and characterize
their local properties using the newly introduced summaries. We show how
complex white-matter structures across multiple voxels exhibit clear
ellipsoidal and asymmetric structure in simulation, and assess the performance
of the statistics in clinically-acquired magnetic resonance imaging data.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS441 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Surface Laplacian Technique in EEG: Theory and Methods
This paper reviews the method of surface Laplacian differentiation to study
EEG. We focus on topics that are helpful for a clear understanding of the
underlying concepts and its efficient implementation, which is especially
important for EEG researchers unfamiliar with the technique. The popular
methods of finite difference and splines are reviewed in detail. The former has
the advantage of simplicity and low computational cost, but its estimates are
prone to a variety of errors due to discretization. The latter eliminates all
issues related to discretization and incorporates a regularization mechanism to
reduce spatial noise, but at the cost of increasing mathematical and
computational complexity. These and several others issues deserving further
development are highlighted, some of which we address to the extent possible.
Here we develop a set of discrete approximations for Laplacian estimates at
peripheral electrodes and a possible solution to the problem of multiple-frame
regularization. We also provide the mathematical details of finite difference
approximations that are missing in the literature, and discuss the problem of
computational performance, which is particularly important in the context of
EEG splines where data sets can be very large. Along this line, the matrix
representation of the surface Laplacian operator is carefully discussed and
some figures are given illustrating the advantages of this approach. In the
final remarks, we briefly sketch a possible way to incorporate finite-size
electrodes into Laplacian estimates that could guide further developments.Comment: 43 pages, 8 figure
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