579,106 research outputs found
Sparse Modeling of Landmark and Texture Variability using the Orthomax Criterion
In the past decade, statistical shape modeling has been widely popularized in the medical image analysis community. Predominantly, principal component analysis (PCA) has been employed to model biological shape variability. Here, a reparameterization with orthogonal basis vectors is obtained such that the variance of the input data is maximized. This property drives models toward global shape deformations and has been highly successful in fitting shape models to new images. However, recent literature has indicated that this uncorrelated basis may be suboptimal for exploratory analyses and disease characterization. This paper explores the orthomax class of statistical methods for transforming variable loadings into a simple structure which is more easily interpreted by favoring sparsity. Further, we introduce these transformations into a particular framework traditionally based on PCA; the Active Appearance Models (AAMs). We note that the orthomax transformations are independent of domain dimensionality (2D/3D etc.) and spatial structure. Decompositions of both shape and texture models are carried out. Further, the issue of component ordering is treated by establishing a set of relevant criteria. Experimental results are given on chest radiographs, magnetic resonance images of the brain, and face images. Since pathologies are typically spatially localized, either with respect to shape or texture, we anticipate many medical applications where sparse parameterizations are preferable to the conventional global PCA approach
ICA vs. PCA Active Appearance Models: Application to Cardiac MR Segmentation
Abstract. Statistical shape models generally use Principal Component Analysis (PCA) to describe the main directions of shape variation in a training set of ex-ample shapes. However, PCA has the restriction that the input data must be drawn from a Gaussian distribution and is only able to describe global shape variations. In this paper we evaluate the use of an alternative shape decomposi-tion, Independent Component Analysis (ICA), for two reasons. ICA does not require a Gaussian distribution of the input data and is able to describe localized shape variations. With ICA however, the resulting vectors are not ordered, therefore a method for ordering the Independent Components is presented in this paper. To evaluate ICA-based Active Appearance Models (AAMs), 10 leave-15-out models were trained on a set of 150 short-axis cardiac MR Images with PCA-based as well as ICA-based AAMs. The median values for the aver-age and maximal point-to-point distances between the expert drawn and auto-matically segmented contours for the PCA-based AAM were 2.95 and 8.39 pix-els. For the ICA-based AAM these distances were 1.86 and 5.01 pixels respec-tively. From this, we conclude that the use of ICA results in a substantial im-provement in border localization accuracy over a PCA-based model.
Estimation of probability distribution on multiple anatomical objects and evaluation of statistical shape models
The estimation of shape probability distributions of anatomic structures is a major research area in medical image analysis. The statistical shape descriptions estimated from training samples provide means and the geometric shape variations of such structures. These are key components in many applications. This dissertation presents two approaches to the estimation of a shape probability distribution of a multi-object complex. Both approaches are applied to objects in the male pelvis, and show improvement in the estimated shape distributions of the objects. The first approach is to estimate the shape variation of each object in the complex in terms of two components: the object's variation independent of the effect of its neighboring objects; and the neighbors' effect on the object. The neighbors' effect on the target object is interpreted using the idea on which linear mixed models are based. The second approach is to estimate a conditional shape probability distribution of a target object given its neighboring objects. The estimation of the conditional probability is based on principal component regression. This dissertation also presents a measure to evaluate the estimated shape probability distribution regarding its predictive power, that is, the ability of a statistical shape model to describe unseen members of the population. This aspect of statistical shape models is of key importance to any application that uses shape models. The measure can be applied to PCA-based shape models and can be interpreted as a ratio of the variation of new data explained by the retained principal directions estimated from training data. This measure was applied to shape models of synthetic warped ellipsoids and right hippocampi. According to two surface distance measures and a volume overlap measure it was empirically verified that the predictive measure reflects what happens in the ambient space where the model lies
Exact Dimensionality Selection for Bayesian PCA
We present a Bayesian model selection approach to estimate the intrinsic
dimensionality of a high-dimensional dataset. To this end, we introduce a novel
formulation of the probabilisitic principal component analysis model based on a
normal-gamma prior distribution. In this context, we exhibit a closed-form
expression of the marginal likelihood which allows to infer an optimal number
of components. We also propose a heuristic based on the expected shape of the
marginal likelihood curve in order to choose the hyperparameters. In
non-asymptotic frameworks, we show on simulated data that this exact
dimensionality selection approach is competitive with both Bayesian and
frequentist state-of-the-art methods
Finding Young Stellar Populations in Elliptical Galaxies from Independent Components of Optical Spectra
Elliptical galaxies are believed to consist of a single population of old
stars formed together at an early epoch in the Universe, yet recent analyses of
galaxy spectra seem to indicate the presence of significant younger populations
of stars in them. The detailed physical modelling of such populations is
computationally expensive, inhibiting the detailed analysis of the several
million galaxy spectra becoming available over the next few years. Here we
present a data mining application aimed at decomposing the spectra of
elliptical galaxies into several coeval stellar populations, without the use of
detailed physical models. This is achieved by performing a linear independent
basis transformation that essentially decouples the initial problem of joint
processing of a set of correlated spectral measurements into that of the
independent processing of a small set of prototypical spectra. Two methods are
investigated: (1) A fast projection approach is derived by exploiting the
correlation structure of neighboring wavelength bins within the spectral data.
(2) A factorisation method that takes advantage of the positivity of the
spectra is also investigated. The preliminary results show that typical
features observed in stellar population spectra of different evolutionary
histories can be convincingly disentangled by these methods, despite the
absence of input physics. The success of this basis transformation analysis in
recovering physically interpretable representations indicates that this
technique is a potentially powerful tool for astronomical data mining.Comment: 12 Pages, 7 figures; accepted in SIAM 2005 International Conference
on Data Mining, Newport Beach, CA, April 200
A stochastic algorithm for probabilistic independent component analysis
The decomposition of a sample of images on a relevant subspace is a recurrent
problem in many different fields from Computer Vision to medical image
analysis. We propose in this paper a new learning principle and implementation
of the generative decomposition model generally known as noisy ICA (for
independent component analysis) based on the SAEM algorithm, which is a
versatile stochastic approximation of the standard EM algorithm. We demonstrate
the applicability of the method on a large range of decomposition models and
illustrate the developments with experimental results on various data sets.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS499 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions
The probability density function of the acoustic field amplitude scattered by
the seafloor was measured in a rocky environment off the coast of Norway using
a synthetic aperture sonar system, and is reported here in terms of the
probability of false alarm. Interpretation of the measurements focused on
finding appropriate class of statistical models (single versus two-component
mixture models), and on appropriate models within these two classes. It was
found that two-component mixture models performed better than single models.
The two mixture models that performed the best (and had a basis in the physics
of scattering) were a mixture between two K distributions, and a mixture
between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used
to estimate the probability density function of the mixture model parameters.
It was found that the K-K mixture exhibits significant correlation between its
parameters. The mixture between the Rayleigh and generalized Pareto
distributions also had significant parameter correlation, but also contained
multiple modes. We conclude that the mixture between two K distributions is the
most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical
Society of Americ
Hierarchical Graphical Models for Multigroup Shape Analysis using Expectation Maximization with Sampling in Kendall's Shape Space
This paper proposes a novel framework for multi-group shape analysis relying
on a hierarchical graphical statistical model on shapes within a population.The
framework represents individual shapes as point setsmodulo translation,
rotation, and scale, following the notion in Kendall shape space.While
individual shapes are derived from their group shape model, each group shape
model is derived from a single population shape model. The hierarchical model
follows the natural organization of population data and the top level in the
hierarchy provides a common frame of reference for multigroup shape analysis,
e.g. classification and hypothesis testing. Unlike typical shape-modeling
approaches, the proposed model is a generative model that defines a joint
distribution of object-boundary data and the shape-model variables.
Furthermore, it naturally enforces optimal correspondences during the process
of model fitting and thereby subsumes the so-called correspondence problem. The
proposed inference scheme employs an expectation maximization (EM) algorithm
that treats the individual and group shape variables as hidden random variables
and integrates them out before estimating the parameters (population mean and
variance and the group variances). The underpinning of the EM algorithm is the
sampling of pointsets, in Kendall shape space, from their posterior
distribution, for which we exploit a highly-efficient scheme based on
Hamiltonian Monte Carlo simulation. Experiments in this paper use the fitted
hierarchical model to perform (1) hypothesis testing for comparison between
pairs of groups using permutation testing and (2) classification for image
retrieval. The paper validates the proposed framework on simulated data and
demonstrates results on real data.Comment: 9 pages, 7 figures, International Conference on Machine Learning 201
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