2,063 research outputs found
Dynamics of the Boxy Elliptical Galaxy NGC 1600
We use three--integral models to infer the distribution function (DF) of the
boxy E3-E4 galaxy NGC 1600 from surface brightness and line profile data on the
minor and major axes. We assume axisymmetry and that the mass-to-light ratio is
constant in the central ~1 R_e. Stars in the resulting gravitational potential
move mainly on regular orbits. We use an approximate third integral K from
perturbation theory, and write the DF as a sum of basis functions in the three
integrals E, L_z and K. We then fit the projected moments of these basis
functions to the kinematic observables and deprojected density, using a
non-parametric algorithm.
The deduced dynamical structure is radially anisotropic, with
sigma_theta/sigma_r ~ sigma_phi/sigma_r ~ 0.7 on the major axis. Both on the
minor axis and near the centre the velocity distribution is more isotropic;
thus the model is flattened by equatorial radial orbits. The kinematic data is
fit without need for a central black hole; the central mass determined
previously from ground-based data therefore overestimates the actual black hole
mass. The mass-to-light ratio of the stars is M/L_V = 6 h_50.
The anisotropy structure of NGC 1600 with a radially anisotropic main body
and more nearly isotropic centre is similar to that found recently in NGC 1399,
NGC 2434, NGC 3379 and NGC 6703, suggesting that this pattern may be common
amongst massive elliptical galaxies. We discuss a possible merger origin of NGC
1600 in the light of these results.Comment: 14 pages, 9 figures, re-submitted to Monthly Notice
Re-growth of stellar disks in mature galaxies: The two component nature of NGC 7217 revisited with VIRUS-W
Previous studies have reported the existence of two counter-rotating stellar
disks in the early-type spiral galaxy NGC7217. We have obtained high-resolution
optical spectroscopic data (R ~ 9000) with the new fiber-based Integral Field
Unit instrument VIRUS-W at the 2.7m telescope of the McDonald Observatory in
Texas. Our analysis confirms the existence of two components. However, we find
them to be co-rotating. The first component is the more luminous (~ 77% of the
total light), has the higher velocity dispersion (~ 170 km/s) and rotates
relatively slowly (projected = 50 km/s). The lower luminosity second
component, (~ 23% of the total light), has a low velocity dispersion (~ 20
km/s) and rotates quickly (projected = 150 km/s). The difference in
the kinematics of the two stellar components allows us to perform a kinematic
decomposition and to measure the strengths of their Mg and Fe Lick indices
separately. The rotational velocities and dispersions of the less luminous and
faster component are very similar to those of the interstellar gas as measured
from the [OIII] emission. Morphological evidence of active star formation in
this component further suggests that NGC7217 may be in the process of
(re)growing a disk inside a more massive and higher dispersion stellar halo.
The kinematically cold and regular structure of the gas disk in combination
with the central almost dust-free morphology allows us to compare the dynamical
mass inside of the central 500pc with predictions from a stellar population
analysis. We find agreement between the two if a Kroupa stellar initial mass
function is assumed.Comment: accepted for publication by MNRA
Non parametric reconstruction of distribution functions from observed galactic disks
A general inversion technique for the recovery of the underlying distribution
function for observed galactic disks is presented and illustrated. Under the
assumption that these disks are axi-symmetric and thin, the proposed method
yields the unique distribution compatible with all the observables available.
The derivation may be carried out from the measurement of the azimuthal
velocity distribution arising from positioning the slit of a spectrograph along
the major axis of the galaxy. More generally, it may account for the
simultaneous measurements of velocity distributions corresponding to slits
presenting arbitrary orientations with respect to the major axis. The approach
is non-parametric, i.e. it does not rely on a particular algebraic model for
the distribution function. Special care is taken to account for the fraction of
counter-rotating stars which strongly affects the stability of the disk. An
optimisation algorithm is devised -- generalising the work of Skilling & Bryan
(1984) -- to carry this truly two-dimensional ill-conditioned inversion
efficiently. The performances of the overall inversion technique with respect
to the noise level and truncation in the data set is investigated with
simulated data. Reliable results are obtained up to a mean signal to noise
ratio of~5 and when measurements are available up to . A discussion of
the residual biases involved in non parametric inversions is presented.
Prospects of application to observed galaxies and other inversion problems are
discussed.Comment: 11 pages, 13 figures; accepted for publication by MNRA
Uncertainty quantification in non-rigid image registration via stochastic gradient Markov chain Monte Carlo
We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backpropagation and the variational inference by backpropagation frameworks, in order to efficiently draw samples from the posterior distribution of transformation parameters. To address the modelling issues, we formulate a Bayesian model for image registration that overcomes the existing barriers when using a dense, high-dimensional, and diffeomorphic transformation parametrisation. This results in improved calibration of uncertainty estimates. We compare the model in terms of both image registration accuracy and uncertainty quantification to VoxelMorph, a state-of-the-art image registration model based on deep learning
Dynamical models and machine learning for supervised segmentation
This thesis is concerned with the problem of how to outline regions of interest in medical images, when
the boundaries are weak or ambiguous and the region shapes are irregular. The focus on machine learning
and interactivity leads to a common theme of the need to balance conflicting requirements. First,
any machine learning method must strike a balance between how much it can learn and how well it
generalises. Second, interactive methods must balance minimal user demand with maximal user control.
To address the problem of weak boundaries,methods of supervised texture classification are investigated
that do not use explicit texture features. These methods enable prior knowledge about the image to
benefit any segmentation framework. A chosen dynamic contour model, based on probabilistic boundary
tracking, combines these image priors with efficient modes of interaction. We show the benefits of the
texture classifiers over intensity and gradient-based image models, in both classification and boundary
extraction.
To address the problem of irregular region shape, we devise a new type of statistical shape model
(SSM) that does not use explicit boundary features or assume high-level similarity between region
shapes. First, the models are used for shape discrimination, to constrain any segmentation framework
by way of regularisation. Second, the SSMs are used for shape generation, allowing probabilistic segmentation
frameworks to draw shapes from a prior distribution. The generative models also include
novel methods to constrain shape generation according to information from both the image and user
interactions.
The shape models are first evaluated in terms of discrimination capability, and shown to out-perform
other shape descriptors. Experiments also show that the shape models can benefit a standard type of
segmentation algorithm by providing shape regularisers. We finally show how to exploit the shape
models in supervised segmentation frameworks, and evaluate their benefits in user trials
Gaussian Process Morphable Models
Statistical shape models (SSMs) represent a class of shapes as a normal
distribution of point variations, whose parameters are estimated from example
shapes. Principal component analysis (PCA) is applied to obtain a
low-dimensional representation of the shape variation in terms of the leading
principal components. In this paper, we propose a generalization of SSMs,
called Gaussian Process Morphable Models (GPMMs). We model the shape variations
with a Gaussian process, which we represent using the leading components of its
Karhunen-Loeve expansion. To compute the expansion, we make use of an
approximation scheme based on the Nystrom method. The resulting model can be
seen as a continuous analogon of an SSM. However, while for SSMs the shape
variation is restricted to the span of the example data, with GPMMs we can
define the shape variation using any Gaussian process. For example, we can
build shape models that correspond to classical spline models, and thus do not
require any example data. Furthermore, Gaussian processes make it possible to
combine different models. For example, an SSM can be extended with a spline
model, to obtain a model that incorporates learned shape characteristics, but
is flexible enough to explain shapes that cannot be represented by the SSM. We
introduce a simple algorithm for fitting a GPMM to a surface or image. This
results in a non-rigid registration approach, whose regularization properties
are defined by a GPMM. We show how we can obtain different registration
schemes,including methods for multi-scale, spatially-varying or hybrid
registration, by constructing an appropriate GPMM. As our approach strictly
separates modelling from the fitting process, this is all achieved without
changes to the fitting algorithm. We show the applicability and versatility of
GPMMs on a clinical use case, where the goal is the model-based segmentation of
3D forearm images
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