Kanti V. Mardia

Matching of palmprints

This paper investigates the feasibility of person identification based on feature points extracted from palmprint images. Our approach first extracts a set of feature points along the prominent palm lines (and the associated line orientation) from a given palmprint image. Next we decide if two palmprints belong to the same hand by computing a matching score between the corresponding sets of feature points of the two palmprints. The two sets of feature points/ orientations are matched using our previously developed point matching technique which takes into account the non-linear deformations as well as the outlier points present in the two sets. The estimates of the matching score distributions for the genuine and imposter sets of palm pairs showed that palmprints have a good discrimination power. The overlap between the genuine and imposter distributions was found to be about 5%. Our preliminary results indicate that adding palmprint information may improve the identity verification provided by fingerprints in cases where fingerprint images cannot be properly acquired (e.g., due to dry skin).

A review of image-warping methods

Image warping is a transformation which maps all positions in one image plane to positions in a second plane. It arises in many image analysis problems, whether in order to remove optical distortions introduced by a camera or a particular viewing perspective, to register an image with a map or template, or to align two or more images. The choice of warp is a compromise between a smooth distortion and one which achieves a good match. Smoothness can be ensured by assuming a parametric form for the warp or by constraining it using differential equations. Matching can be specified by points to be brought into alignment, by local measures of correlation between images, or by the coincidence of edges. Parametric and non-parametric approaches to warping, and matching criteria, are reviewed.

Multi-dimensional multivariate Gaussian Markov random fields with application to image processing

Recently, numerous practical applications of multivariate Gaussian Markov random fields (GMRF) on a lattice have emerged. However, the theory is not satisfactorily developed. We give various properties of multivariate GMRF for multi-dimensional lattice. In particular, some multivariate MRF are given. We discuss estimation procedures and give a numerical example from the area of image processing.

A spatial thresholding method for image segmentation

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. >

The Kriged Kalman filter

In recent years there has been growing interest in spatial-temporal modelling, partly due to the potential of large scale data in pollution and global climate monitoring to answer important environmental questions. We consider the Kriged Kalman filter (KKF), a powerful modelling strategy which combines the two wellestablished approaches of (a) Kriging, in the field of spatial statistics, and (b) the Kalman filter, in general state space formulations of multivariate time series analysis. We give a brief introduction to the model and describe its various properties, and highlight that the model allows prediction in time as well as in space, simultaneously. Some special cases of the time series model are considered. We give some procedures to implement the model, also illustrated through a practical example. The paper concludes with a discussion.

Spatial classification using fuzzy membership models

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. >

A generative, probabilistic model of local protein structure

Despite significant progress in recent years, protein structure prediction maintains its status as one of the prime unsolved problems in computational biology. One of the key remaining challenges is an efficient probabilistic exploration of the structural space that correctly reflects the relative conformational stabilities. Here, we present a fully probabilistic, continuous model of local protein structure in atomic detail. The generative model makes efficient conformational sampling possible and provides a framework for the rigorous analysis of local sequence–structure correlations in the native state. Our method represents a significant theoretical and practical improvement over the widely used fragment assembly technique by avoiding the drawbacks associated with a discrete and nonprobabilistic approach.

A penalized likelihood approach to image warping

A warping is a function that deforms images by mapping between image domains. The choice of function is formulated statistically as maximum penalized likelihood, where the likelihood measures the similarity between images after warping and the penalty is a measure of distortion of a warping. The paper addresses two issues simultaneously, of how to choose the warping function and how to assess the alignment. A new, Fourier–von Mises image model is identified, with phase differences between Fourier‐transformed images having von Mises distributions. Also, new, null set distortion criteria are proposed, with each criterion uniquely minimized by a particular set of polynomial functions. A conjugate gradient algorithm is used to estimate the warping function, which is numerically approximated by a piecewise bilinear function. The method is motivated by, and used to solve, three applied problems: to register a remotely sensed image with a map, to align microscope images obtained by using different optics and to discriminate between species of fish from photographic images.

Omnibus tests of multinormality based on skewness and kurtosis

Measures of univariate skewness and kurtosis have long been used as a test of univariate normality, several omnibus test procedures based on a combination of the measures having been proposed, see Pearson, D’Agestino and Bowman (1977) and Mardia (1979). Mardia (1970) proposed measures of multivariate skewness and kurtosis, and constructed a test of multinormality based on these measures. we obtain the correlation between these measures and propose several omnibus tests using the two measures. The performances of these tests are compared by means of a Monte Carlo study.

SHAPE DISTRIBUTIONS FOR LANDMARK DATA

The paper obtains the exact distribution of Booksteins shape variables under his plausible model for landmark data. We consider its properties including invariances, marginal distributions and the relationship with Kendalls uniform measure. Particular cases for triangles and quadrilaterals are highlighted. A normal approximation to the distribution is obtained, extending Booksteins result for three landmarks. The adequacy of these approximations is also studied.