C. A. Glasbey

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.

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.

A latent Gaussian Markov random-field model for spatiotemporal rainfall disaggregation

Summary. Rainfall data are often collected at coarser spatial scales than required for input into hydrology and agricultural models. We therefore describe a spatiotemporal model which allows multiple imputation of rainfall at fine spatial resolutions, with a realistic dependence structure in both space and time and with the total rainfall at the coarse scale consistent with that observed. The method involves the transformation of the fine scale rainfall to a thresholded Gaussian process which we model as a Gaussian Markov random field. Gibbs sampling is then used to generate realizations of rainfall efficiently at the fine scale. Results compare favourably with previous, less elegant methods.

SPICY: towards automated phenotyping of large pepper plants in the greenhouse

Most high-throughput systems for automated plant phenotyping involve a fixed recording cabinet to which plants are transported. However, important greenhouse plants like pepper are too tall to be transported. In this research we developed a system to automatically measure plant characteristics of tall pepper plants in the greenhouse. With a device equipped with multiple cameras, images of plants are recorded at a 5cm interval over a height of 3m. Two types of features are extracted: (1) features from a 3D reconstruction of the plant canopy; and (2) statistical features derived directly from RGB images. The experiment comprised 151 genotypes of a recombinant inbred population of pepper, to examine the heritability and quantitative trait loci (QTL) of the features. Features extracted from the 3D reconstruction of the canopy were leaf size and leaf angle, with heritabilities of 0.70 and 0.56 respectively. Three QTL were found for leaf size, and one for leaf angle. From the statistical features, plant height showed a good correlation (0.93) with manual measurements, and QTL were in accordance with QTL of manual measurements. For total leaf area, the heritability was 0.55, and two of the three QTL found by manual measurement were found by image analysis.

Combinatorial image analysis of DNA microarray features

MOTIVATION DNA and protein microarrays have become an established leading-edge technology for large-scale analysis of gene and protein content and activity. Contact-printed microarrays has emerged as a relatively simple and cost effective method of choice but its reliability is especially susceptible to quality of pixel information obtained from digital scans of spotted features in the microarray image. RESULTS We address the statistical computation requirements for optimizing data acquisition and processing of digital scans. We consider the use of median filters to reduce noise levels in images and top-hat filters to correct for trends in background values. We also consider, as alternative estimators of spot intensity, discs of fixed radius, proportions of histograms and k-means clustering, either with or without a square-root intensity transformation and background subtraction. We identify, using combinatoric procedures, optimal filter and estimator parameters, in achieving consistency among the replicates of a gene on each microarray. Our results, using test data from microarrays of HCMV, indicate that a highly effective approach for improving reliability and quality of microarray data is to apply a 21 by 21 top-hat filter, then estimate spot intensity as the mean of the largest 20% of pixel values in the target region, after a square-root transformation, and corrected for background, by subtracting the mean of the smallest 70% of pixel values. AVAILABILITY Fortran90 subroutines implementing these methods are available from the authors, or at http://www.bioss.ac.uk/~chris.

The analysis of data from germination tests

The development of statistically sound methods of summarizing the results from germination tests appears to have been neglected. This paper reviews the literature critically, proposes the use of maximum likelihood techniques to summarize such data and develops an appropriate routine, available as a computer program ‘DISTGERM’.

Spatio-temporal variability of solar energy across a region: a statistical modelling approach

Abstract Solar energy collected at a number of discrete sites, which are dispersed over a geographical area, will exhibit both spatial and temporal variability. Being able to model this variability will have many applications, for example in controlling an electricity system that is supplied by decentralised PV arrays. This paper describes a statistical modelling study of solar data that were recorded over 2 years at a total of 22 sites in the city of Edinburgh, Scotland, and in the nearby Pentland hills. A spatio-temporal model is proposed for global irradiation on a horizontal plane: this incorporates the sum of two exponentials to model the decrease in covariance between sites with time lag, and a space–time term to model the combined dependence of covariance on time lag and easterly distance.

The responses of growing pigs to a chronic-intermittent stress treatment

Many of the stressor treatments used in animal models of depression have parallels in the normal experiences of domestic pigs. The experiment described here aimed to assess whether a chronic-intermittent stress regime caused behavioural or physiological changes, indicative of depression, in domestic pigs. Ten juvenile male pigs were exposed to a social and environmental stress regime. Over the stressor period, weight gain was significantly lower in test pigs than in control pigs. Stress treatment had a significant effect on salivary cortisol levels, with test pigs having a higher salivary cortisol concentration than control pigs after the stress treatment but not before. Test pigs showed less ventral lying than control pigs in the post-stress observation. A detrended fluctuation analysis (DFA) of postural behavioural organisation showed that test pigs had a more structured pattern of activity than controls in the post-stress observation and a tendency towards a more structured pattern in the pre-stress observation. There were no major behavioural differences between the two groups during three repeated open field tests. The results suggest that the stressor treatment did create a mild chronic stress, as indicated by the hypercortisolaemia and lower weight gain in the test pigs. However, no unambiguous behavioural indicators of depression were seen. The behavioural analysis did show that fractal techniques, such as DFA, could be applied to pig behaviour and that they can reveal extra novel information about the structure of an individuals behavioural organisation and how it changes in response to complex environmental stressors.

Statistical estimation of gene expression using multiple laser scans of microarrays

UNLABELLED We propose a statistical model for estimating gene expression using data from multiple laser scans at different settings of hybridized microarrays. A functional regression model is used, based on a non-linear relationship with both additive and multiplicative error terms. The function is derived as the expected value of a pixel, given that values are censored at 65 535, the maximum detectable intensity for double precision scanning software. Maximum likelihood estimation based on a Cauchy distribution is used to fit the model, which is able to estimate gene expressions taking account of outliers and the systematic bias caused by signal censoring of highly expressed genes. We have applied the method to experimental data. Simulation studies suggest that the model can estimate the true gene expression with negligible bias. AVAILABILITY FORTRAN 90 code for implementing the method can be obtained from the authors.

Detrended fluctuation analysis of behavioural responses to mild acute stressors in domestic hens

Fractal analysis provides a novel measure of behavioural complexity and has previously revealed subtle alterations in behaviour under biologically costly conditions, such as parasitism or disease. The analysis is based upon the temporal pattern of behaviour that, although rarely considered in behavioural studies, may provide information in addition to standard measures of duration and frequency. Such information could be useful in assessing the welfare of confined animals. Using ISA Brown pullets, we wished to test the hypothesis that fractal analysis reveals novel behavioural alterations during stress. The behaviour of undisturbed birds in their home pen was compared to the behaviour of the same birds: (1) in a novel arena, (2) in their home pen following blood withdrawal and (3) in their home pen following 5 min of mechanical restraint plus blood withdrawal. Detrended fluctuation analysis (DFA), which calculates fractal complexity measures for time series data, was applied to sequences of vigilance behaviour and walking. These two behavioural parameters where chosen because they are relatively simple to measure and might be expected to alter under stress. When compared to home pen behaviour, complexity in vigilance behaviour increased in the novel arena ( P< 0.001) and following restraint and blood sampling ( P< 0.05) but was unaltered following blood withdrawal only (P = 0.36). Total time spent vigilant was increased in the novel arena (P = 0.001) but not following restraint (P = 0.45) or blood withdrawal (P = 0.11). The complexity of walking patterns and the total time spent walking were similar in all situations. In conclusion, DFA provides a novel measure of temporal behavioural complexity in chickens. In contrast to studies of chronic situations in other animals, acute stress caused an increase in behavioural complexity in the present experiment. This increased complexity occurred independently of changes