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.     

Stochastic Templates for Aquaculture Images and a Parallel Pattern Detector

A general statistical approach is presented for the identification of objects in digital images, motivated by an application in aquaculture involving underwater images of fish. Using Procrustes analysis, a point distribution model is fitted on a set of training images and used as a prior distribution for the shape of a deformable template. The likelihood of a proposed template is calculated in terms of the response from a feature detector along the boundary of the template. The posterior distribution of template variables is examined by using Markov chain Monte Carlo analysis. A key challenge in the aquaculture application is the variable nature of edges arising from the surface curvature of fish and the low contrast between the foreground and background. Conventional gradient-based edge detection proves inadequate, but a parallel pattern detector copes much better. Results are presented for a fully automated analysis of the database. The strengths and weaknesses of this approach are discussed and future developments are outlined.     

A fast wavelet approach for recovering damaged images

A wavelet method is proposed for recovering damaged images. The proposed method combines wavelet shrinkage with preprocessing based on a binning process and an imputation procedure that is designed to extend the scope of wavelet shrinkage to data with missing values and perturbed locations. The proposed algorithm, termed as the BTW algorithm is simple to implement and efficient for recovering an image. Furthermore, this algorithm can be easily applied to wavelet regression for one-dimensional (1-D) signal estimation with irregularly spaced data. Simulation studies and real examples show that the proposed method can produce substantially effective results.     

On Local Power Properties of Frequency Domain‐based Tests for Stationarity

A framework for the asymptotic analysis of local power properties of tests of stationarity in time series analysis is developed. Appropriate sequences of locally stationary processes are defined that converge at a controlled rate to a limiting stationary process as the length of the time series increases. Different interesting classes of local alternatives to the null hypothesis of stationarity are then considered, and the local power properties of some recently proposed, frequency domain‐based tests for stationarity are investigated. Some simulations illustrate our theoretical findings.     

Functional and dynamic magnetic resonance imaging using vector adaptive weights smoothing

We consider the problem of statistical inference for functional and dynamic magnetic resonance imaging (MRI). A new approach is proposed which extends the adaptive weights smoothing procedure of Polzehl and Spokoiny that was originally designed for image denoising. We demonstrate how the adaptive weights smoothing method can be applied to time series of images, which typically occur in functional and dynamic MRI. It is shown how signal detection in functional MRI and the analysis of dynamic MRI can benefit from spatially adaptive smoothing. The performance of the procedure is illustrated by using real and simulated data.     

Statistical dimension estimation in singular spectrum analysis

Summary Singular spectrum analysis has been proposed in the field of nonlinear dynamical systems as filtering method. In this paper a criterion to choose the number of components which leads to the best filtering is proposed. The selection is made by minimizing the prediction error.     

Random sliced inverse regression

Sliced Inverse Regression (SIR; 1991) is a dimension reduction method for reducing the dimension of the predictors without losing regression information. The implementation of SIR requires inverting the covariance matrix of the predictors—which has hindered its use to analyze high-dimensional data where the number of predictors exceed the sample size. We propose random sliced inverse regression (rSIR) by applying SIR to many bootstrap samples, each using a subset of randomly selected candidate predictors. The final rSIR estimate is obtained by aggregating these estimates. A simple variable selection procedure is also proposed using these bootstrap estimates. The performance of the proposed estimates is studied via extensive simulation. Application to a dataset concerning myocardial perfusion diagnosis from cardiac Single Proton Emission Computed Tomography (SPECT) images is presented.     

On shape detection in noisy images with particular reference to ultrasonography

We discuss the detection of a connected shape in a noisy image. Two types of image are considered: in the first a degraded outline of the shape is visible, while in the second the data are a corrupted version of the shape itself. In the first type the shape is defined by a thin outline of pixels with records that are different from those at pixels inside and outside the shape, while in the second type the shape is defined by its edge and pixels inside and outside the shape have different records. Our motivation is the identification of cross-sectional head shapes in ultrasound images of human fetuses. We describe and discuss a new approach to detecting shapes in images of the first type that uses a specially designed filter function that iteratively identifies the outline pixels of the head. We then suggest a way based on the cascade algorithm introduced by Jubb and Jennison (1991) of improving and considerably increasing the speed of a method proposed by Storvik (1994) for detecting edges in images of the second type.     

Confocal fluorescence microscopy of leaf cells: an application of Bayesian image analysis

Confocal fluorescence microscopy is a recent and important imaging tool for visualizing three-dimensional specimens without the need for physical sectioning, so that changes in living cells can be studied over time. The application of interest here is a study of the changes in the stomatal guard cells of plant leaves during their opening and closing response sequences. Quantitative estimates of the size and shape of these cells rely on accurate classification (or segmentation) of the images into areas which are parts of cells and areas which are background. This segmentation is complicated in confocal microscopy because the images appear to be 'smudged' or 'dirty'; this degradation is due largely to diffraction and attenuation of the recorded signal caused by the specimen itself. Correcting for this degradation is difficult without knowing the specimen-dependent parameters involved in the degradation process. A fully Bayesian approach is proposed for tackling this problem of blind deconvolution, i.e. of concurrently estimating the degradation parameters while segmenting two-dimensional sections. The end-products are interval estimates of size and shape which acknowledge some of the uncertainty involved in the segmentation. The results are promising, generating credible intervals which are sufficiently narrow to be useful in practice.     

Statistical methods for noisy images with discontinuities

In this paper, we describe a new statistical method for images which contain discontinuities. The method tries to improve the quality of a 'measured' image, which is degraded by the presence of random distortions. This is achieved by using knowledge about the degradation process and a priori information about the main characteristics of the underlying ideal image. Specifically, the method uses information about the discontinuity patterns in small areas of the 'true' image. Some auxiliary labels 'explicitly' describe the location of discontinuities in the true image. A Bayesian model for the image grey levels and the discontinuity labels is built. The maximum a posteriori estimator is considered. The iterated conditional modes algorithm is used to find a (local) maximum of the posterior distribution. The proposed method has been successfully applied to both artificial and real magnetic resonance images. A comparison of the results with those obtained from three other known methods also has been performed. Finally, the connection between Bayesian 'explicity and 'implicit' models is studied. In implicit modelling, there is no use of any set of labels explicitly describing the location of discontinuities. For these models, we derive some constraints of the function by which the presence of the discontinuities is taken into account.     

Bayesian analysis of dynamic magnetic resonance breast images

Summary.  We describe an integrated methodology for analysing dynamic magnetic resonance images of the breast. The problems that motivate this methodology arise from a collaborative study with a tumour institute. The methods are developed within the Bayesian framework and comprise image restoration and classification steps. Two different approaches are proposed for the restoration. Bayesian inference is performed by means of Markov chain Monte Carlo algorithms. We make use of a Metropolis algorithm with a specially chosen proposal distribution that performs better than more commonly used proposals. The classification step is based on a few attribute images yielded by the restoration step that describe the essential features of the contrast agent variation over time. Procedures for hyperparameter estimation are provided, so making our method automatic. The results show the potential of the methodology to extract useful information from acquired dynamic magnetic resonance imaging data about tumour morphology and internal pathophysiological features.     

Factored principal components analysis, with applications to face recognition

A dimension reduction technique is proposed for matrix data, with applications to face recognition from images. In particular, we propose a factored covariance model for the data under study, estimate the parameters using maximum likelihood, and then carry out eigendecompositions of the estimated covariance matrix. We call the resulting method factored principal components analysis. We also develop a method for classification using a likelihood ratio criterion, which has previously been used for evaluating the strength of forensic evidence. The methodology is illustrated with applications in face recognition.     

Gaussian Regularized Sliced Inverse Regression

Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity between these predictors or small sample sizes compared to the dimension, the inversion is not possible and a regularization technique has to be used. Our approach is based on a Fisher Lecture given by R.D. Cook where it is shown that SIR axes can be interpreted as solutions of an inverse regression problem. We propose to introduce a Gaussian prior distribution on the unknown parameters of the inverse regression problem in order to regularize their estimation. We show that some existing SIR regularizations can enter our framework, which permits a global understanding of these methods. Three new priors are proposed leading to new regularizations of the SIR method. A comparison on simulated data as well as an application to the estimation of Mars surface physical properties from hyperspectral images are provided.     

A finite mixture model for image segmentation

In this paper, we propose a model for image segmentation based on a finite mixture of Gaussian distributions. For each pixel of the image, prior probabilities of class memberships are specified through a Gibbs distribution, where association between labels of adjacent pixels is modeled by a class-specific term allowing for different interaction strengths across classes. We show how model parameters can be estimated in a maximum likelihood framework using Mean Field theory. Experimental performance on perturbed phantom and on real benchmark images shows that the proposed method performs well in a wide variety of empirical situations.     

Combining noisy images of small crystalline domains in high resolution electron microscopy

A technique is presented for enhancing and combining electron microscope images of small clystalline areas. Phases obtained by Fourier transforming electron micrographs are merged with available more precise amplitudes, in a Fourier synthesis, to obtain a final estimated image. The procedure is illustrated with 42 individual images of the purple membrane from Halobacterium halobium. To show the power of combination, results based on 1, 2, 4, 8, 16, 32 and 42 images are presented. An estimate based solely on the micrograph data, i.e. ignoring the precise amplitudes, is also presented and is seen to be notably poorer. The level of uncertainty of the final image is assessed by stimulating 10 final images and superposing the results.     

Tracking multiple moving objects in images using Markov Chain Monte Carlo

A new Bayesian state and parameter learning algorithm for multiple target tracking models with image observations are proposed. Specifically, a Markov chain Monte Carlo algorithm is designed to sample from the posterior distribution of the unknown time-varying number of targets, their birth, death times and states as well as the model parameters, which constitutes the complete solution to the specific tracking problem we consider. The conventional approach is to pre-process the images to extract point observations and then perform tracking, i.e. infer the target trajectories. We model the image generation process directly to avoid any potential loss of information when extracting point observations using a pre-processing step that is decoupled from the inference algorithm. Numerical examples show that our algorithm has improved tracking performance over commonly used techniques, for both synthetic examples and real florescent microscopy data, especially in the case of dim targets with overlapping illuminated regions.