Convergence of adaptive morphological filters in the context of Markov chains

A typical parameterized r-opening *r is a filter defined as a union of openings by a collection of compact, convex structuring elements, each of which is governed by a parameter vector r. It reduces to a single parameter r-opening filter by a set of structuring elements when r is a scalar sizing parameter. The parameter vector is adjusted by a set of adaptation rules according to whether the re construction Ar derived from r correctly or incorrectly passes the signal and noise grains sampled from the image. Applied to the signal-union-noise model, the optimization problem is to find the vector of r that minimizes the Mean-Absolute-Error between the filtered and ideal image processes. The adaptive r-opening filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. For a single parameter r-opening filter, we proved that there exists a stationary distribution governing the parameter in the steady state and convergence is characterized in terms of the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. Steady-state behavior is compared to the optimal solution for the uniform model, for which it is possible to derive a closed-form solution for the optimal filter. We also developed the Markov adaptation system for multiparameter opening filters and provided numerical solutions to some special cases. For multiparameter r-opening filters, various adaptive models derived from various assumptions on the form of the filter have been studied. Although the state-probability increment equations can be derived from the appropriate Chapman-Kolmogorov equations, the closed-form representation of steady-state distributions is mathematically problematic due to the support geometry of the boundary states and their transitions. Therefore, numerical methods are employed to approximate for steady state probability distributions. The technique developed for conventional opening filters is also applied to bandpass opening filters. In present thesis study, the concept of signal and noise pass sets plays a central role throughout the adaptive filter analysis. The pass set reduces to the granulometric measure (or {&r}-measure) of the signal and noise grain. Optimization and adaptation are characterized in terms of the distribution of the granulometric measures for single parameter filters, or in terms of the multivariate distribution of the signal and noise pass sets. By introducing these concepts, this thesis study also provides some optimal opening filter error equations. It has been shown in the case of the uniform distribution of single sizing parameter that there is a strong agreement between the adaptive filter and optimal filter based on analytic error minimization. This agreement has been also demonstrated in various r-opening filters. Furthermore, the probabilistic interpretation has a close connection to traditional linear adaptive filter theory. The method has been applied to the classical grain separation (clutter removal) problem. *See content for correct numerical representation

Evaluation of methods for detection of fluorescence labeled subcellular objects in microscope images

<p>Abstract</p> <p>Background</p> <p>Several algorithms have been proposed for detecting fluorescently labeled subcellular objects in microscope images. Many of these algorithms have been designed for specific tasks and validated with limited image data. But despite the potential of using extensive comparisons between algorithms to provide useful information to guide method selection and thus more accurate results, relatively few studies have been performed.</p> <p>Results</p> <p>To better understand algorithm performance under different conditions, we have carried out a comparative study including eleven spot detection or segmentation algorithms from various application fields. We used microscope images from well plate experiments with a human osteosarcoma cell line and frames from image stacks of yeast cells in different focal planes. These experimentally derived images permit a comparison of method performance in realistic situations where the number of objects varies within image set. We also used simulated microscope images in order to compare the methods and validate them against a ground truth reference result. Our study finds major differences in the performance of different algorithms, in terms of both object counts and segmentation accuracies.</p> <p>Conclusions</p> <p>These results suggest that the selection of detection algorithms for image based screens should be done carefully and take into account different conditions, such as the possibility of acquiring empty images or images with very few spots. Our inclusion of methods that have not been used before in this context broadens the set of available detection methods and compares them against the current state-of-the-art methods for subcellular particle detection.</p

Multi-scale texture segmentation of synthetic aperture radar images

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Post-mortem analysis of cortical thickness and neuronal morphometry in autism.

Autism Spectrum Disorders (ASD) are a group of conditions characterized by a broad spectrum of deficiencies related to social communication, both verbal and non-verbal, as well as repetitive behaviors such as rocking back and forth, or arm flapping. This devastating group of disorders affects millions of people regardless of their socioeconomic, ethnic and racial backgrounds. Among other issues such as migraines, sensory deficits and intense aggression, epilepsy is a major neurological disorder very highly associated with ASD; roughly one third of all ASD patients are diagnosed with epilepsy, and a much higher proportion suffer from at least one seizure in their lifetime. Past neuropathological studies have suggested various deformities in the brains of ASD patients, ranging from abnormal brain volume, and head circumference, to the presence of atrophy and cortical dysplasias, such as heterotopias. Other more cellular abnormalities have also been speculated, including neurotransmitter imbalances, as well as neuron proliferation and organization disturbances. Though many intricate techniques have been attempted in order to investigate the etiology and potential treatments of ASD pathology, the results have been inconclusive and highly arguable. This especially applies to magnetic resonance imaging (MRI) studies of cortical thickness, which have produced highly questionable and inconsistent information; researchers have attributed this to the potential instability of the mode of research. Due to the limitations on the resolution of MRI, it is difficult to directly compute the location of the pial surface, which creates difficulty in delineating the cortical gray matter from the subcortical white matter. The goal of our study was to indentify cortical dysplasias, and then to analyze the neuromorphology of the same areas. In order to accomplish this, we retrieved post-mortem tissue from the Autism Tissue Program, and measured the cortical thickness by solving the Laplace equation, followed by the application of the Boolean model and granulometry to determine the potential abnormalities of ASD neuronal morphometry. We found multiple dysplasias in various brain regions, predominantly within the pre-frontal cortex, which correlated nicely with the symptomology of ASD. The anterior commissure (AC) served as the landmark to delineate the prefrontal cortex; when compared with neurotypical tissue, the ASD tissue was thinner surrounding the AC. Upon further analysis of the dysplastic processes, our findings confirmed the presence of smaller, but more numerous pyramidal neurons in the ASD brain when compared with neurotypicals. These findings are also substantial in terms of explaining two of the more prominent issues associated with ASD: aggressive behavior and frequent seizures. Overall, the findings of the current study do support several previous reports and provides further evidence of problematic cortical development and ASD symptom manifestation

Image enhancement techniques applied to solar feature detection

This dissertation presents the development of automatic image enhancement techniques for solar feature detection. The new method allows for detection and tracking of the evolution of filaments in solar images. Series of H-alpha full-disk images are taken in regular time intervals to observe the changes of the solar disk features. In each picture, the solar chromosphere filaments are identified for further evolution examination. The initial preprocessing step involves local thresholding to convert grayscale images into black-and-white pictures with chromosphere granularity enhanced. An alternative preprocessing method, based on image normalization and global thresholding is presented. The next step employs morphological closing operations with multi-directional linear structuring elements to extract elongated shapes in the image. After logical union of directional filtering results, the remaining noise is removed from the final outcome using morphological dilation and erosion with a circular structuring element. Experimental results show that the developed techniques can achieve excellent results in detecting large filaments and good detection rates for small filaments. The final chapter discusses proposed directions of the future research and applications to other areas of solar image processing, in particular to detection of solar flares, plages and sunspots

Image Analysis Algorithms for Single-Cell Study in Systems Biology

With the contiguous shift of biology from a qualitative toward a quantitative field of research, digital microscopy and image-based measurements are drawing increased interest. Several methods have been developed for acquiring images of cells and intracellular organelles. Traditionally, acquired images are analyzed manually through visual inspection. The increasing volume of data is challenging the scope of manual analysis, and there is a need to develop methods for automated analysis. This thesis examines the development and application of computational methods for acquisition and analysis of images from single-cell assays. The thesis proceeds with three different aspects.First, a study evaluates several methods for focusing microscopes and proposes a novel strategy to perform focusing in time-lapse imaging. The method relies on the nature of the focus-drift and its predictability. The study shows that focus-drift is a dynamical system with a small randomness. Therefore, a prediction-based method is employed to track the focus-drift overtime. A prototype implementation of the proposed method is created by extending the Nikon EZ-C1 Version 3.30 (Tokyo, Japan) imaging platform for acquiring images with a Nikon Eclipse (TE2000-U, Nikon, Japan) microscope.Second, a novel method is formulated to segment individual cells from a dense cluster. The method incorporates multi-resolution analysis with maximum-likelihood estimation (MAMLE) for cell detection. The MAMLE performs cell segmentation in two phases. The initial phase relies on a cutting-edge filter, edge detection in multi-resolution with a morphological operator, and threshold decomposition for adaptive thresholding. It estimates morphological features from the initial results. In the next phase, the final segmentation is constructed by boosting the initial results with the estimated parameters. The MAMLE method is evaluated with de novo data sets as well as with benchmark data from public databases. An empirical evaluation of the MAMLE method confirms its accuracy.Third, a comparative study is carried out on performance evaluation of state-ofthe-art methods for the detection of subcellular organelles. This study includes eleven algorithms developed in different fields for segmentation. The evaluation procedure encompasses a broad set of samples, ranging from benchmark data to synthetic images. The result from this study suggests that there is no particular method which performs superior to others in the test samples. Next, the effect of tetracycline on transcription dynamics of tetA promoter in Escherichia coli (E. coli ) cells is studied. This study measures expressions of RNA by tagging the MS2d-GFP vector with a target gene. The RNAs are observed as intracellular spots in confocal images. The kernel density estimation (KDE) method for detecting the intracellular spots is employed to quantify the individual RNA molecules.The thesis summarizes the results from five publications. Most of the publications are associated with different methods for imaging and analysis of microscopy. Confocal images with E. coli cells are targeted as the primary area of application. However, potential applications beyond the primary target are also made evident. The findings of the research are confirmed empirically

Detection and Classification of Diabetic Retinopathy Pathologies in Fundus Images

Diabetic Retinopathy (DR) is a disease that affects up to 80% of diabetics around the world. It is the second greatest cause of blindness in the Western world, and one of the leading causes of blindness in the U.S. Many studies have demonstrated that early treatment can reduce the number of sight-threatening DR cases, mitigating the medical and economic impact of the disease. Accurate, early detection of eye disease is important because of its potential to reduce rates of blindness worldwide. Retinal photography for DR has been promoted for decades for its utility in both disease screening and clinical research studies. In recent years, several research centers have presented systems to detect pathology in retinal images. However, these approaches apply specialized algorithms to detect specific types of lesion in the retina. In order to detect multiple lesions, these systems generally implement multiple algorithms. Furthermore, some of these studies evaluate their algorithms on a single dataset, thus avoiding potential problems associated with the differences in fundus imaging devices, such as camera resolution. These methodologies primarily employ bottom-up approaches, in which the accurate segmentation of all the lesions in the retina is the basis for correct determination. A disadvantage of bottom-up approaches is that they rely on the accurate segmentation of all lesions in order to measure performance. On the other hand, top-down approaches do not depend on the segmentation of specific lesions. Thus, top-down methods can potentially detect abnormalities not explicitly used in their training phase. A disadvantage of these methods is that they cannot identify specific pathologies and require large datasets to build their training models. In this dissertation, I merged the advantages of the top-down and bottom-up approaches to detect DR with high accuracy. First, I developed an algorithm based on a top-down approach to detect abnormalities in the retina due to DR. By doing so, I was able to evaluate DR pathologies other than microaneurysms and exudates, which are the main focus of most current approaches. In addition, I demonstrated good generalization capacity of this algorithm by applying it to other eye diseases, such as age-related macular degeneration. Due to the fact that high accuracy is required for sight-threatening conditions, I developed two bottom-up approaches, since it has been proven that bottom-up approaches produce more accurate results than top-down approaches for particular structures. Consequently, I developed an algorithm to detect exudates in the macula. The presence of this pathology is considered to be a surrogate for clinical significant macular edema (CSME), a sight-threatening condition of DR. The analysis of the optic disc is usually not taken into account in DR screening systems. However, there is a pathology called neovascularization that is present in advanced stages of DR, making its detection of crucial clinical importance. In order to address this problem, I developed an algorithm to detect neovascularization in the optic disc. These algorithms are based on amplitude-modulation and frequency-modulation (AM-FM) representations, morphological image processing methods, and classification algorithms. The methods were tested on a diverse set of large databases and are considered to be the state-of the art in this field