One of the major stumbling blocks in the use of standard directional distributions is difficulty in implementing the well-established maximum likelihood estimation method. The root of the problem is that their normalizing constants are complicated. To circumvent this problem, sometimes a member from a non-exponential family is used and then a relevant member from the exponential family is matched. These alternative distributions have simple moment estimators though the matching can be somewhat arbitrary. Firstly, we resolve the estimation problem by introducing the score matching estimators for directional distributions. Secondly, we resolve the matching problem optimally by introducing the score matching approximation. We give some insight into these proposals through the basic directional distributions, though the results are optimal and universally applicable for distributions on compact manifolds.

The increasing importance of non-coding RNA in biology and medicine has led to a growing interest in the problem of RNA 3-D structure prediction. As is the case for proteins, RNA 3-D structure prediction methods require two key ingredients: an accurate energy function and a conformational sampling procedure. Both are only partly solved problems. Here, we focus on the problem of conformational sampling. The current state of the art solution is based on fragment assembly methods, which construct plausible conformations by stringing together short fragments obtained from experimental structures. However, the discrete nature of the fragments necessitates the use of carefully tuned, unphysical energy functions, and their non-probabilistic nature impairs unbiased sampling. We offer a solution to the sampling problem that removes these important limitations: a probabilistic model of RNA structure that allows efficient sampling of RNA conformations in continuous space, and with associated probabilities. We show that the model captures several key features of RNA structure, such as its rotameric nature and the distribution of the helix lengths. Furthermore, the model readily generates native-like 3-D conformations for 9 out of 10 test structures, solely using coarse-grained base-pairing information. In conclusion, the method provides a theoretical and practical solution for a major bottleneck on the way to routine prediction and simulation of RNA structure and dynamics in atomic detail.

MOTIVATION: The large-scale comparison of protein-ligand binding sites is problematic, in that measures of structural similarity are difficult to quantify and are not easily understood in terms of statistical similarity that can ultimately be related to structure and function. We present a binding site matching score the Poisson Index (PI) based upon a well-defined statistical model. PI requires only the number of matching atoms between two sites and the size of the two sites-the same information used by the Tanimoto Index (TI), a comparable and widely used measure for molecular similarity. We apply PI and TI to a previously automatically extracted set of binding sites to determine the robustness and usefulness of both scores. RESULTS: We found that PI outperforms TI; moreover, site similarity is poorly defined for TI at values around the 99.5% confidence level for which PI is well defined. A difference map at this confidence level shows that PI gives much more meaningful information than TI. We show individual examples where TI fails to distinguish either a false or a true site paring in contrast to PI, which performs much better. TI cannot handle large or small sites very well, or the comparison of large and small sites, in contrast to PI that is shown to be much more robust. Despite the difficulty of determining a biological 'ground truth' for binding site similarity we conclude that PI is a suitable measure of binding site similarity and could form the basis for a binding site classification scheme comparable to existing protein domain classification schema.

BACKGROUND: Matching functional sites is a key problem for the understanding of protein function and evolution. The commonly used graph theoretic approach, and other related approaches, require adjustment of a matching distance threshold a priori according to the noise in atomic positions. This is difficult to pre-determine when matching sites related by varying evolutionary distances and crystallographic precision. Furthermore, sometimes the graph method is unable to identify alternative but important solutions in the neighbourhood of the distance based solution because of strict distance constraints. We consider the Bayesian approach to improve graph based solutions. In principle this approach applies to other methods with strict distance matching constraints. The Bayesian method can flexibly incorporate all types of prior information on specific binding sites (e.g. amino acid types) in contrast to combinatorial formulations. RESULTS: We present a new meta-algorithm for matching protein functional sites (active sites and ligand binding sites) based on an initial graph matching followed by refinement using a Markov chain Monte Carlo (MCMC) procedure. This procedure is an innovative extension to our recent work. The method accounts for the 3-dimensional structure of the site as well as the physico-chemical properties of the constituent amino acids. The MCMC procedure can lead to a significant increase in the number of significant matches compared to the graph method as measured independently by rigorously derived p-values. CONCLUSION: MCMC refinement step is able to significantly improve graph based matches. We apply the method to matching NAD(P)(H) binding sites within single Rossmann fold families, between different families in the same superfamily, and in different folds. Within families sites are often well conserved, but there are examples where significant shape based matches do not retain similar amino acid chemistry, indicating that even within families the same ligand may be bound using substantially different physico-chemistry. We also show that the procedure finds significant matches between binding sites for the same co-factor in different families and different folds.

Based on deformable templates, the paper formulates an integrated and flexible Bayesian recognition system of multiple occluded objects. Various local dependence properties of the model are obtained to reduce the computational cost with the increase in the number of objects. Numerical results for a synthetic image and for a real image of mushrooms are discussed.

Ridge curves are important features in human vision (see Koenderink, 1990, p.295). In this paper we apply a simple algebraic criterion of Porteous (1994) to the problem of finding ridge curves in machine vision. This work provides a simpler approach than other existing methods (see for example, Thirion and Gourdon, 1992, and Hosaka, 1992). To identify ridge curves in practice on surface data it is necessary first to smooth the data, which we do using thin-plate splines and related kriging procedures. After validating our methodology, we illustrate its use on a set of laser range data of the human head. 1 Introduction Intuitively ridge curves on a surface occur at points where the curvature is changing most rapidly. There is some evidence that the human eye picks out ridge curves when looking at a surface. For example, for the human face the ridge curves seem to correspond to prominent anatomical features. It is claimed that ridge curves "usually appear, along with edges of ...

In many applications in computer vision and signal processing, it is necessary to assimilate data from multiple sources. This is a particularly important issue in medical imaging, where information on a patient may be available from a number of different modalities. As a result, there has been much recent research interest in this area. The authors suggest an additional Bayesian method which generates a segmented classification concurrently with improving reconstructions of a set of registered images. A synthetic example is used to demonstrate the subjectives and benefits of this proposed approach. Two medical applications, one fusing computed tomography (CT) and single photon emission computed tomography (SPECT) brain scans, and the other magnetic resonance (MR) images at two different resolutions, are considered.

The Bayesian reconstruction of the shape of an object in image sequences using deformable template techniques is considered. The object shape is represented by a prototype outline which is deformed under constraints of continuity and rigidity. The deformation of the template retains consistent shape characteristics whilst allowing variation and evolution of object shape over time. The reconstruction of single images using deformable templates allows incorporation of more detailed prior knowledge of expected image features than a simple local pixel dependence model. An application to a sequence of CCD animated digital images is given.>

In the usual statistical approach to spatial classification, it is assumed that each pixel belongs to precisely one of a small number of known groups. This framework is extended to include mixed-pixel data; then, only a proportion of each pixel belongs to each group. Two models based on multivariate Gaussian random fields are proposed to model this fuzzy membership process. The problems of predicting the group membership and estimating the parameters are discussed. Some simulations are presented to study the properties of this approach, and an example is given using Landsat remote-sensing data.>

Several model-based algorithms for threshold selection are presented, concentrating on the two-population univariate case in which an image contains an object and background. It is shown how the main ideas behind two important nonspatial thresholding algorithms follow from classical discriminant analysis. Novel thresholding algorithms that make use of available local/spatial information are then given. It is found that an algorithm using alternating mean thresholding and median filtering provides an acceptable method when the image is relatively highly contaminated, and seems to depend less on initial values than other procedures. The methods are also applicable to multispectral k-population images.>