28,019 research outputs found
Minkowski Functionals of SDSS galaxies I : Analysis of Excursion Sets
We present a first morphometric investigation of a preliminary sample from
the SDSS of 154287 galaxies with apparent magnitude 14.5<m_r<17.5 and redshift
0.001<z<0.4. We measure the Minkowski Functionals, which are a complete set of
morphological descriptors. To account for the complicated wedge--like geometry
of the present survey data, we construct isodensity contour surfaces from the
galaxy positions in redshift space and employ two complementary methods of
computing the Minkowski Functionals. We find that the observed Minkowski
Functionals for SDSS galaxies are consistent with the prediction of a
Lambda--dominated spatially--flat Cold Dark Matter model with random--Gaussian
initial conditions, within the cosmic variance estimated from the corresponding
mock catalogue. We expect that future releases of the SDSS survey will allow us
to distinguish morphological differences in the galaxy distribution with regard
to different morphological type and luminosity ranges.Comment: 35 pages, 13 figures, accepted for publication in PASJ. For preprint
with higher-resolution PS files, see
http://www.a.phys.nagoya-u.ac.jp/~hikage/MFs/mf_sdss.ps.g
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
SurfelMeshing: Online Surfel-Based Mesh Reconstruction
We address the problem of mesh reconstruction from live RGB-D video, assuming
a calibrated camera and poses provided externally (e.g., by a SLAM system). In
contrast to most existing approaches, we do not fuse depth measurements in a
volume but in a dense surfel cloud. We asynchronously (re)triangulate the
smoothed surfels to reconstruct a surface mesh. This novel approach enables to
maintain a dense surface representation of the scene during SLAM which can
quickly adapt to loop closures. This is possible by deforming the surfel cloud
and asynchronously remeshing the surface where necessary. The surfel-based
representation also naturally supports strongly varying scan resolution. In
particular, it reconstructs colors at the input camera's resolution. Moreover,
in contrast to many volumetric approaches, ours can reconstruct thin objects
since objects do not need to enclose a volume. We demonstrate our approach in a
number of experiments, showing that it produces reconstructions that are
competitive with the state-of-the-art, and we discuss its advantages and
limitations. The algorithm (excluding loop closure functionality) is available
as open source at https://github.com/puzzlepaint/surfelmeshing .Comment: Version accepted to IEEE Transactions on Pattern Analysis and Machine
Intelligenc
Anatomical curve identification
Methods for capturing images in three dimensions are now widely available, with stereo-photogrammetry and laser scanning being two common approaches. In anatomical studies, a number of landmarks are usually identified manually from each of these images and these form the basis of subsequent statistical analysis. However, landmarks express only a very small proportion of the information available from the images. Anatomically defined curves have the advantage of providing a much richer expression of shape. This is explored in the context of identifying the boundary of breasts from an image of the female torso and the boundary of the lips from a facial image. The curves of interest are characterised by ridges or valleys. Key issues in estimation are the ability to navigate across the anatomical surface in three-dimensions, the ability to recognise the relevant boundary and the need to assess the evidence for the presence of the surface feature of interest. The first issue is addressed by the use of principal curves, as an extension of principal components, the second by suitable assessment of curvature and the third by change-point detection. P-spline smoothing is used as an integral part of the methods but adaptations are made to the specific anatomical features of interest. After estimation of the boundary curves, the intermediate surfaces of the anatomical feature of interest can be characterised by surface interpolation. This allows shape variation to be explored using standard methods such as principal components. These tools are applied to a collection of images of women where one breast has been reconstructed after mastectomy and where interest lies in shape differences between the reconstructed and unreconstructed breasts. They are also applied to a collection of lip images where possible differences in shape between males and females are of interest
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
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
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