Estimating the granularity coefficient of a Potts-Markov random field within an MCMC algorithm

This paper addresses the problem of estimating the Potts parameter B jointly with the unknown parameters of a Bayesian model within a Markov chain Monte Carlo (MCMC) algorithm. Standard MCMC methods cannot be applied to this problem because performing inference on B requires computing the intractable normalizing constant of the Potts model. In the proposed MCMC method the estimation of B is conducted using a likelihood-free Metropolis-Hastings algorithm. Experimental results obtained for synthetic data show that estimating B jointly with the other unknown parameters leads to estimation results that are as good as those obtained with the actual value of B. On the other hand, assuming that the value of B is known can degrade estimation performance significantly if this value is incorrect. To illustrate the interest of this method, the proposed algorithm is successfully applied to real bidimensional SAR and tridimensional ultrasound images

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

BiofilmQuant: A Computer-Assisted Tool for Dental Biofilm Quantification

Dental biofilm is the deposition of microbial material over a tooth substratum. Several methods have recently been reported in the literature for biofilm quantification; however, at best they provide a barely automated solution requiring significant input needed from the human expert. On the contrary, state-of-the-art automatic biofilm methods fail to make their way into clinical practice because of the lack of effective mechanism to incorporate human input to handle praxis or misclassified regions. Manual delineation, the current gold standard, is time consuming and subject to expert bias. In this paper, we introduce a new semi-automated software tool, BiofilmQuant, for dental biofilm quantification in quantitative light-induced fluorescence (QLF) images. The software uses a robust statistical modeling approach to automatically segment the QLF image into three classes (background, biofilm, and tooth substratum) based on the training data. This initial segmentation has shown a high degree of consistency and precision on more than 200 test QLF dental scans. Further, the proposed software provides the clinicians full control to fix any misclassified areas using a single click. In addition, BiofilmQuant also provides a complete solution for the longitudinal quantitative analysis of biofilm of the full set of teeth, providing greater ease of usability.Comment: 4 pages, 4 figures, 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2014

Statistical Region Based Segmentation of Ultrasound Images

Segmentation of ultrasound images is a challenging problem due to speckle, which corrupts the image and can result in weak or missing image boundaries, poor signal to noise ratio, and diminished contrast resolution. Speckle is a random interference pattern that is characterized by an asymmetric distribution as well as significant spatial correla- tion. These attributes of speckle are challenging to model in a segmentation approach, so many previous ultrasound segmentation methods simplify the problem by assuming that the speckle is white and/or Gaussian distributed. Unlike these methods, in this paper we present an ultrasound-specific segmentation approach that addresses both the spatial correlation of the data as well as its intensity distribution. We first decorrelate the image and then apply a region-based active contour whose motion is derived from an appropri- ate parametric distribution for maximum likelihood image segmentation. We consider zero-mean complex Gaussian, Rayleigh, and Fisher-Tippett flows, which are designed to model fully formed speckle in the in-phase/quadrature (IQ), envelope detected, and display (log compressed) images, respectively. We present experimental results demon- strating the effectiveness of our method, and compare the results to other parametric and non-parametric active contours

Bayesian Lattice Filters for Time-Varying Autoregression and Time-Frequency Analysis

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a wide range of processes is a subject of ongoing interest. We propose a novel approach to model-based time-frequency estimation using time-varying autoregressive models. In this context, we take a fully Bayesian approach and allow both the autoregressive coefficients and innovation variance to vary over time. Importantly, our estimation method uses the lattice filter and is cast within the partial autocorrelation domain. The marginal posterior distributions are of standard form and, as a convenient by-product of our estimation method, our approach avoids undesirable matrix inversions. As such, estimation is extremely computationally efficient and stable. To illustrate the effectiveness of our approach, we conduct a comprehensive simulation study that compares our method with other competing methods and find that, in most cases, our approach performs superior in terms of average squared error between the estimated and true time-varying spectral density. Lastly, we demonstrate our methodology through three modeling applications; namely, insect communication signals, environmental data (wind components), and macroeconomic data (US gross domestic product (GDP) and consumption).Comment: 49 pages, 16 figure

Local Variation as a Statistical Hypothesis Test

The goal of image oversegmentation is to divide an image into several pieces, each of which should ideally be part of an object. One of the simplest and yet most effective oversegmentation algorithms is known as local variation (LV) (Felzenszwalb and Huttenlocher 2004). In this work, we study this algorithm and show that algorithms similar to LV can be devised by applying different statistical models and decisions, thus providing further theoretical justification and a well-founded explanation for the unexpected high performance of the LV approach. Some of these algorithms are based on statistics of natural images and on a hypothesis testing decision; we denote these algorithms probabilistic local variation (pLV). The best pLV algorithm, which relies on censored estimation, presents state-of-the-art results while keeping the same computational complexity of the LV algorithm

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page