In humans, there is clear evidence of an association between hip fracture risk and femoral neck bone mineral density, and some evidence of an association between fracture risk and the shape of the proximal femur. Here, we investigate whether the femoral cortex plays a role in these associations: do particular morphologies predispose to weaker cortices? To answer this question, we used cortical bone mapping to measure the distribution of cortical mass surface density (CMSD, mg/cm 2 ) in a cohort of 125 females. Principal component analysis of the femoral surfaces identified three modes of shape variation accounting for 65% of the population variance. We then used statistical parametric mapping (SPM) to locate regions of the cortex where CMSD depends on shape, allowing for age. Our principal findings were increased CMSD with increased gracility over much of the proximal femur; and decreased CMSD at the superior femoral neck, coupled with increased CMSD at the calcar femorale, with increasing neck-shaft angle. In obtaining these results, we studied the role of spatial normalization in SPM, identifying systematic misregistration as a major impediment to the joint analysis of CMSD and shape. Through a series of experiments on synthetic data, we evaluated a number of registration methods for spatial normalization, concluding that only those predicated on an explicit set of homologous landmarks are suitable for this kind of analysis. The emergent methodology amounts to an extension of Geometric Morphometric Image Analysis to the domain of textured surfaces, alongside a protocol for labelling homologous landmarks in clinical CT scans of the human proximal femur.

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm(2)) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex.

The distribution of cortical bone in the proximal femur is believed to be a critical component in determining fracture resistance. Current CT technology is limited in its ability to measure cortical thickness, especially in the sub-millimetre range which lies within the point spread function of today's clinical scanners. In this paper, we present a novel technique that is capable of producing unbiased thickness estimates down to 0.3mm. The technique relies on a mathematical model of the anatomy and the imaging system, which is fitted to the data at a large number of sites around the proximal femur, producing around 17,000 independent thickness estimates per specimen. In a series of experiments on 16 cadaveric femurs, estimation errors were measured as -0.01+/-0.58mm (mean+/-1std.dev.) for cortical thicknesses in the range 0.3-4mm. This compares with 0.25+/-0.69mm for simple thresholding and 0.90+/-0.92mm for a variant of the 50% relative threshold method. In the clinically relevant sub-millimetre range, thresholding increasingly fails to detect the cortex at all, whereas the new technique continues to perform well. The many cortical thickness estimates can be displayed as a colour map painted onto the femoral surface. Computation of the surfaces and colour maps is largely automatic, requiring around 15min on a modest laptop computer.

Displacement estimation is a key step in the evaluation of tissue elasticity by quasistatic strain imaging. An efficient approach may incorporate a tracking strategy whereby each estimate is initially obtained from its neighbours' displacements and then refined through a localized search. This increases the accuracy and reduces the computational expense compared with exhaustive search. However, simple tracking strategies fail when the target displacement map exhibits complex structure. For example, there may be discontinuities and regions of indeterminate displacement caused by decorrelation between the pre- and post-deformation radio frequency (RF) echo signals. This paper introduces a novel displacement tracking algorithm, with a search strategy guided by a data quality indicator. Comparisons with existing methods show that the proposed algorithm is more robust when the displacement distribution is challenging.

A freehand scanning protocol is the only way to acquire arbitrary large volumes of three-dimensional ultrasound (US) data. For some applications, multiple freehand sweeps are required to cover the area of interest. Aligning these multiple sweeps is difficult, typically requiring nonrigid image-based registration as well as the readings from the spatial locator attached to the US probe. Conventionally, nonrigid warps are achieved through general elastic spline deformations, which are expensive to compute and difficult to constrain. This paper presents an alternative registration technique, where the warp's degrees of freedom are carefully linked to the mechanics of the freehand scanning process. The technique is assessed through an extensive series of in vivo experiments, which reveal a registration precision of a few pixels with comparatively little computational load.

We show that a hierarchical Bayesian modeling approach allows us to perform regularization in sequential learning. We identify three inference levels within this hierarchy: model selection, parameter estimation, and noise estimation. In environments where data arrive sequentially, techniques such as cross validation to achieve regularization or model selection are not possible. The Bayesian approach, with extended Kalman filtering at the parameter estimation level, allows for regularization within a minimum variance framework. A multilayer perceptron is used to generate the extended Kalman filter nonlinear measurements mapping. We describe several algorithms at the noise estimation level that allow us to implement on-line regularization. We also show the theoretical links between adaptive noise estimation in extended Kalman filtering, multiple adaptive learning rates, and multiple smoothing regularization coefficients.

We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent sampling importance resampling algorithm (HySIR). In terms of computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimization strategy that allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving on-line, nonlinear, and nongaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the one-step-ahead probability density functions of the options prices.

The ability to estimate a surface from a set of cross sections allows calculation of the enclosed volume and the display of the surface in three-dimensions. This process has increasingly been used to derive useful information from medical data. However, extracting the cross sections (segmenting) can be very difficult, and automatic segmentation methods are not sufficiently robust to handle all situations. Hence, it is an advantage if the surface reconstruction algorithm can work effectively on a small number of cross sections. In addition, cross sections of medical data are often quite complex. Shape-based interpolation is a simple and elegant solution to this problem, although it has known limitations when handling complex shapes. In this paper, the shape-based interpolation paradigm is extended to interpolate a surface through sparse, complex cross sections, providing a significant improvement over our previously published maximal disc-guided interpolation. The performance of this algorithm is demonstrated on various types of medical data (X-ray computed tomography, magnetic resonance imaging and three-dimensional ultrasound). Although the correspondence problem in general remains unsolved, it is demonstrated that correct surfaces can be estimated from a limited amount of real data, through the use of region rather than object correspondence.

We propose a novel sequential algorithm for training neural networks in non-stationary environments. The approach is based on a Monte Carlo method known as the sampling-importance resampling simulation algorithm. We derive our algorithm using a Bayesian framework, which allows us to learn the probability density functions of the network weights and outputs. Consequently, it is possible to compute various statistical estimates including centroids, modes, confidence intervals and kurtosis. The algorithm performs a global search for minima in parameter space by monitoring the errors and gradients at several points in the error surface. This global optimisation strategy is shown to perform better than local optimisation paradigms such as the extended Kalman filter.

A common authoring technique involves making annotations on a printed draft and then typing the corrections into a computer at a later date. In this paper, we describe a system that goes some way towards automating this process. The author simply passes the annotated documents through a sheetfeed scanner and then brings up the electronic document in a text editor. The system then works out where the annotated words are and allows the author to skip from one annotation to the next at the touch of a key. At the heart of the system lies a procedure for reliably establishing correspondences between printed words and their electronic counterparts, without performing optical character recognition. This procedure might have interesting applications in document database retrieval, since it allows an electronic document to be indexed by a printed version of itself.

Volume intersection algorithms are used to reconstruct incomplete objects from their silhouettes. An imagined light source is moved about the data and the cumulative amount of "light" seen at each point an space is interpreted as indicating the likelihood that the point is inside the object. The object data need not be uniformly distributed nor exclusively surface data. Explicit distinction between noise, surface and interior data is avoided. The novel concept of a localised viewing region is introduced to overcome the inherent inability of volume intersection algorithms to reconstruct concave surfaces. Algorithms for 2D pixel and 3D voxel data are described and applied to 3D ultrasound data.

One of the most promising applications of 3-D ultrasound lies in the visualisation and volume estimation of internal 3-D structures. Unfortunately, artifacts and speckle make automatic analysis of the data difficult. In this paper we investigate the use of 3-D spatial compounding to improve data quality, and find that accurate registration is the key. A correlation-based registration technique is applied to 3-D ultrasound data acquired from in-vivo examinations of a human gall bladder. We find that the registration technique performs well, and visualisation and segmentation of the compounded data are clearly improved.

We propose a novel strategy for training neural networks using sequential Monte Carlo algorithms. This global optimisation strategy allows us to learn the probability distribution of the network weights in a sequential framework. It is well suited to applications involving on-line, nonlinear or non-stationary signal processing. We show how the new algorithms can outperform extended Kalman filter (EKF) training.

3-D ultrasound is a new medical imaging technique which can quickly and non-invasively deliver clinically useful renderings of internal structures. The technique is vulnerable to tissue motion during the scan which can result in an inconsistent 3-D data set. This paper describes an algorithm which corrects for tissue motion and other errors that cause mis-registration during a scan. The resulting 3-D data sets are clearer and of enhanced diagnostic utility. The registration is achieved by applying visual tracking techniques outside their traditional area of application. The algorithm is automatic, incremental and easily incorporated into existing 3-D ultrasound systems.

Feedback neural networks enjoy considerable popularity as a means of approximately solving combinatorial optimization problems. It is now well established how to map problems onto networks so that invalid solutions are never found. It is not as clear how the networks' solutions compare in terms of quality with those obtained using other optimization techniques; such issues are addressed in this paper. A linearized analysis of annealed network dynamics allows a prototypical network solution to be identified in a pertinent eigenvector basis. It is possible to predict the likely quality of this solution by examining optimal solutions in the same basis. Applying this methodology to traveling salesman problems, it appears that neural networks are well suited to the solution of Euclidean but not random problems; this is confirmed by extensive experiments. The failure of a network to adequately solve even 10-city problems is highly significant.

Current approaches to gaze tracking tend to be highly intrusive: the subject must either remain perfectly still, or wear cumbersome headgear to maintain a constant separation between the sensor and the eye. This paper describes a more flexible vision-based approach, which can estimate the direction of gaze from a single, monocular view of a face. The technique makes minimal assumptions about the structure of the face, requires very few image measurements, and produces a useful estimate of the facial orientation. The computational requirements are insignificant, so with automatic tracking of a few facial features it is possible to produce real-time gaze estimates.

The often disappointing performance of optimizing neural networks can be partly attributed to the rather ad hoc manner in which problems are mapped onto them for solution. In this paper a rigorous mapping is described for quadratic 0-1 programming problems with linear equality and inequality constraints, this being the most general class of problem such networks can solve. The problem's constraints define a polyhedron P containing all the valid solution points, and the mapping guarantees strict confinement of the network's state vector to P. However, forcing convergence to a 0-1 point within P is shown to be generally intractable, rendering the Hopfield and similar models inapplicable to the vast majority of problems. A modification of the tabu learning technique is presented as a more coherent approach to general problem solving with neural networks. When tested on a collection of knapsack problems, the modified dynamics produced some very encouraging results.