119,664 research outputs found
Posterior shape models
We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a "posterior shape model", which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness
Multivariate texture discrimination using a principal geodesic classifier
A new texture discrimination method is presented for classification and retrieval of colored textures represented in the wavelet domain. The interband correlation structure is modeled by multivariate probability models which constitute a Riemannian manifold. The presented method considers the shape of the class on the manifold by determining the principal geodesic of each class. The method, which we call principal geodesic classification, then determines the shortest distance from a test texture to the principal geodesic of each class. We use the Rao geodesic distance (GD) for calculating distances on the manifold. We compare the performance of the proposed method with distance-to-centroid and knearest neighbor classifiers and of the GD with the Euclidean distance. The principal geodesic classifier coupled with the GD yields better results, indicating the usefulness of effectively and concisely quantifying the variability of the classes in the probabilistic feature space
Conditional Transformation Models
The ultimate goal of regression analysis is to obtain information about the
conditional distribution of a response given a set of explanatory variables.
This goal is, however, seldom achieved because most established regression
models only estimate the conditional mean as a function of the explanatory
variables and assume that higher moments are not affected by the regressors.
The underlying reason for such a restriction is the assumption of additivity of
signal and noise. We propose to relax this common assumption in the framework
of transformation models. The novel class of semiparametric regression models
proposed herein allows transformation functions to depend on explanatory
variables. These transformation functions are estimated by regularised
optimisation of scoring rules for probabilistic forecasts, e.g. the continuous
ranked probability score. The corresponding estimated conditional distribution
functions are consistent. Conditional transformation models are potentially
useful for describing possible heteroscedasticity, comparing spatially varying
distributions, identifying extreme events, deriving prediction intervals and
selecting variables beyond mean regression effects. An empirical investigation
based on a heteroscedastic varying coefficient simulation model demonstrates
that semiparametric estimation of conditional distribution functions can be
more beneficial than kernel-based non-parametric approaches or parametric
generalised additive models for location, scale and shape
The Development And Application Of A Statistical Shape Model Of The Human Craniofacial Skeleton
Biomechanical investigations involving the characterization of biomaterials or improvement of implant design often employ finite element (FE) analysis. However, the contemporary method of developing a FE mesh from computed tomography scans involves much manual intervention and can be a tedious process. Researchers will often focus their efforts on creating a single highly validated FE model at the expense of incorporating variability of anatomical geometry and material properties, thus limiting the applicability of their findings. The goal of this thesis was to address this issue through the use of a statistical shape model (SSM). A SSM is a probabilistic description of the variation in the shape of a given class of object. (Additional scalar data, such as an elastic constant, can also be incorporated into the model.) By discretizing a sample (i.e. training set) of unique objects of the same class using a set of corresponding nodes, the main modes of shape variation within that shape class are discovered via principal component analysis. By combining the principal components using different linear combinations, new shape instances are created, each with its own unique geometry while retaining the characteristics of its shape class. In this thesis, FE models of the human craniofacial skeleton (CFS) were first validated to establish their viability. A mesh morphing procedure was then developed to map one mesh onto the geometry of 22 other CFS models forming a training set for a SSM of the CFS. After verifying that FE results derived from morphed meshes were no different from those obtained using meshes created with contemporary methods, a SSM of the human CFS was created, and 1000 CFS FE meshes produced. It was found that these meshes accurately described the geometric variation in human population, and were used in a Monte Carlo analysis of facial fracture, finding past studies attempting to characterize the fracture probability of the zygomatic bone are overly conservative
Statistical inference for multivariate extremes via a geometric approach
A geometric representation for multivariate extremes, based on the shapes of
scaled sample clouds in light-tailed margins and their so-called limit sets,
has recently been shown to connect several existing extremal dependence
concepts. However, these results are purely probabilistic, and the geometric
approach itself has not been fully exploited for statistical inference. We
outline a method for parametric estimation of the limit set shape, which
includes a useful non/semi-parametric estimate as a pre-processing step. More
fundamentally, our approach provides a new class of asymptotically-motivated
statistical models for the tails of multivariate distributions, and such models
can accommodate any combination of simultaneous or non-simultaneous extremes
through appropriate parametric forms for the limit set shape. Extrapolation
further into the tail of the distribution is possible via simulation from the
fitted model. A simulation study confirms that our methodology is very
competitive with existing approaches, and can successfully allow estimation of
small probabilities in regions where other methods struggle. We apply the
methodology to two environmental datasets, with diagnostics demonstrating a
good fit
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