On a parameter estimation method for Gibbs-Markov random fields

Cataloged from PDF version of article.This correspondence is about a Gibbs-Markov random field (GMRF) parameter estimation technique proposed by Derin and Elliott. We will refer to this technique as the histogramming (H) method. First, the relation of the H method to the (conditional) maximum likelihood (ML) method is considered. Second, a bias-reduction based modification of the H method is proposed to improve its performance, especially in the case of small amounts of image data

On a Parameter Estimation Method For Gibbs-Markov Random Fields

This correspondence is about a Gibbs-Markov random field (GMRF) parameter estimation technique proposed by Derin and Elliott. We will refer to this technique as the histogramming (H) method. First, the relation of the H method to the (conditional) maximum likelihood (ML) method is considered. Second, a bias-reduction based modification of the H method is proposed to improve its performance, especially in the case of small amounts of image data. © 1994 IEE

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

Bayesian inference for structured additive regression models for large-scale problems with applications to medical imaging

In der angewandten Statistik können Regressionsmodelle mit hochdimensionalen Koeffizienten auftreten, die sich nicht mit gewöhnlichen Computersystemen schätzen lassen. Dies betrifft unter anderem die Analyse digitaler Bilder unter Berücksichtigung räumlich-zeitlicher Abhängigkeiten, wie sie innerhalb der medizinisch-biologischen Forschung häufig vorkommen. In der vorliegenden Arbeit wird ein Verfahren formuliert, das in der Lage ist, Regressionsmodelle mit hochdimensionalen Koeffizienten und nicht-normalverteilten Zielgrößen unter moderaten Anforderungen an die benötigte Hardware zu schätzen. Hierzu wird zunächst im Rahmen strukturiert additiver Regressionsmodelle aufgezeigt, worin die Limitationen aktueller Inferenzansätze bei der Anwendung auf hochdimensionale Problemstellungen liegen, sowie Möglichkeiten diskutiert, diese zu umgehen. Darauf basierend wird ein Algorithmus formuliert, dessen Stärken und Schwächen anhand von Simulationsstudien analysiert werden. Darüber hinaus findet das Verfahren Anwendung in drei verschiedenen Bereichen der medizinisch-biologischen Bildgebung und zeigt dadurch, dass es ein vielversprechender Kandidat für die Beantwortung hochdimensionaler Fragestellungen ist.In applied statistics regression models with high-dimensional coefficients can occur which cannot be estimated using ordinary computers. Amongst others, this applies to the analysis of digital images taking spatio-temporal dependencies into account as they commonly occur within bio-medical research. In this thesis a procedure is formulated which allows to fit regression models with high-dimensional coefficients and non-normal response values requiring only moderate computational equipment. To this end, limitations of different inference strategies for structured additive regression models are demonstrated when applied to high-dimensional problems and possible solutions are discussed. Based thereon an algorithm is formulated whose strengths and weaknesses are subsequently analyzed using simulation studies. Furthermore, the procedure is applied to three different fields of bio-medical imaging from which can be concluded that the algorithm is a promising candidate for answering high-dimensional problems

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

A VISION-BASED QUALITY INSPECTION SYSTEM FOR FABRIC DEFECT DETECTION AND CLASSIFICATION

Published ThesisQuality inspection of textile products is an important issue for fabric manufacturers. It is desirable to produce the highest quality goods in the shortest amount of time possible. Fabric faults or defects are responsible for nearly 85% of the defects found by the garment industry. Manufacturers recover only 45 to 65% of their profits from second or off-quality goods. There is a need for reliable automated woven fabric inspection methods in the textile industry. Numerous methods have been proposed for detecting defects in textile. The methods are generally grouped into three main categories according to the techniques they use for texture feature extraction, namely statistical approaches, spectral approaches and model-based approaches. In this thesis, we study one method from each category and propose their combinations in order to get improved fabric defect detection and classification accuracy. The three chosen methods are the grey level co-occurrence matrix (GLCM) from the statistical category, the wavelet transform from the spectral category and the Markov random field (MRF) from the model-based category. We identify the most effective texture features for each of those methods and for different fabric types in order to combine them. Using GLCM, we identify the optimal number of features, the optimal quantisation level of the original image and the optimal intersample distance to use. We identify the optimal GLCM features for different types of fabrics and for three different classifiers. Using the wavelet transform, we compare the defect detection and classification performance of features derived from the undecimated discrete wavelet and those derived from the dual-tree complex wavelet transform. We identify the best features for different types of fabrics. Using the Markov random field, we study the performance for fabric defect detection and classification of features derived from different models of Gaussian Markov random fields of order from 1 through 9. For each fabric type we identify the best model order. Finally, we propose three combination schemes of the best features identified from the three methods and study their fabric detection and classification performance. They lead generally to improved performance as compared to the individual methods, but two of them need further improvement

Diffusion-based spatial priors for imaging.

We describe a Bayesian scheme to analyze images, which uses spatial priors encoded by a diffusion kernel, based on a weighted graph Laplacian. This provides a general framework to formulate a spatial model, whose parameters can be optimised. The standard practice using the software statistical parametric mapping (SPM) is to smooth imaging data using a fixed Gaussian kernel as a pre-processing step before applying a mass-univariate statistical model (e.g., a general linear model) to provide images of parameter estimates (Friston et al., 2006). This entails the strong assumption that data are generated smoothly throughout the brain. An alternative is to include smoothness in a multivariate statistical model (Penny et al., 2005). The advantage of the latter is that each parameter field is smoothed automatically, according to a measure of uncertainty, given the data. Explicit spatial priors enable formal model comparison of different prior assumptions, e.g. that data are generated from a stationary (i.e. fixed throughout the brain) or non-stationary spatial process. We describe the motivation, background material and theory used to formulate diffusion-based spatial priors for fMRI data and apply it to three different datasets, which include standard and high-resolution data. We compare mass-univariate ordinary least squares estimates of smoothed data and three Bayesian models spatially independent, stationary and non-stationary spatial models of non-smoothed data. The latter of which can be used to preserve boundaries between functionally selective regional responses of the brain, thereby increasing the spatial detail of inferences about cortical responses to experimental input

Bayesian inference for structured additive regression models for large-scale problems with applications to medical imaging

In der angewandten Statistik können Regressionsmodelle mit hochdimensionalen Koeffizienten auftreten, die sich nicht mit gewöhnlichen Computersystemen schätzen lassen. Dies betrifft unter anderem die Analyse digitaler Bilder unter Berücksichtigung räumlich-zeitlicher Abhängigkeiten, wie sie innerhalb der medizinisch-biologischen Forschung häufig vorkommen. In der vorliegenden Arbeit wird ein Verfahren formuliert, das in der Lage ist, Regressionsmodelle mit hochdimensionalen Koeffizienten und nicht-normalverteilten Zielgrößen unter moderaten Anforderungen an die benötigte Hardware zu schätzen. Hierzu wird zunächst im Rahmen strukturiert additiver Regressionsmodelle aufgezeigt, worin die Limitationen aktueller Inferenzansätze bei der Anwendung auf hochdimensionale Problemstellungen liegen, sowie Möglichkeiten diskutiert, diese zu umgehen. Darauf basierend wird ein Algorithmus formuliert, dessen Stärken und Schwächen anhand von Simulationsstudien analysiert werden. Darüber hinaus findet das Verfahren Anwendung in drei verschiedenen Bereichen der medizinisch-biologischen Bildgebung und zeigt dadurch, dass es ein vielversprechender Kandidat für die Beantwortung hochdimensionaler Fragestellungen ist.In applied statistics regression models with high-dimensional coefficients can occur which cannot be estimated using ordinary computers. Amongst others, this applies to the analysis of digital images taking spatio-temporal dependencies into account as they commonly occur within bio-medical research. In this thesis a procedure is formulated which allows to fit regression models with high-dimensional coefficients and non-normal response values requiring only moderate computational equipment. To this end, limitations of different inference strategies for structured additive regression models are demonstrated when applied to high-dimensional problems and possible solutions are discussed. Based thereon an algorithm is formulated whose strengths and weaknesses are subsequently analyzed using simulation studies. Furthermore, the procedure is applied to three different fields of bio-medical imaging from which can be concluded that the algorithm is a promising candidate for answering high-dimensional problems