Anisotropic Mesh Adaptation for Image Segmentation based on Partial Differential Equations

Title from PDF of title page viewed January 12, 2021Dissertation advisor: Xianping LiVitaIncludes bibliographical references (pages 69-85)Thesis (Ph.D.)--Department of Mathematics and Statistics and School of Computing and Engineering. University of Missouri--Kansas City, 2020As the resolution of digital images increases significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this dissertation, we consider image segmentation by solving a partial differential equation (PDE) model based on the Mumford-Shah functional. We first, develop a new anisotropic mesh adaptation (AMA) framework to improve segmentation efficiency and accuracy. In the AMA framework, we incorporate an anisotropic mesh adaptation for image representation and a nite element method for solving the PDE model. Comparing to traditional algorithms solved by the finnite difference method, our AMA framework provides faster and better results without the need for re-sizing the images to lower quality. We also extend the algorithm to segment images with multiple regions. We also improve the well-known Chan-Vese model by developing a locally enhanced Chan-Vese (LECV) model. Our LECV model incorporates a newly define signed pressure force (SPF) function, which is built upon the local image information. The SPF function helps to attract the contour curve to the object boundaries for images with inhomogeneous intensities. The proposed LECV model, together with the AMA segmentation framework can successfully segment the image with or without inhomogeneous intensities. While most other segmentation methods only work on low-resolution images, our LECV model is successfully applied to high-resolution images, with improved efficiency and accuracy.Introduction -- PDE-Based Image Segmentation -- Background and Literature review -- AMA Segmentation Method -- LECV Model for Image Segmentation -- Conclusion and discussio

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

Automatic BIRAD scoring of breast cancer mammograms

A computer aided diagnosis system (CAD) is developed to fully characterize and classify mass to benign and malignancy and to predict BIRAD (Breast Imaging Reporting and Data system) scores using mammographic image data. The CAD includes a preprocessing step to de-noise mammograms. This is followed by an active counter segmentation to deforms an initial curve, annotated by a radiologist, to separate and define the boundary of a mass from background. A feature extraction scheme wasthen used to fully characterize a mass by extraction of the most relevant features that have a large impact on the outcome of a patient biopsy. For this thirty-five medical and mathematical features based on intensity, shape and texture associated to the mass were extracted. Several feature selection schemes were then applied to select the most dominant features for use in next step, classification. Finally, a hierarchical classification schemes were applied on those subset of features to firstly classify mass to benign (mass with BIRAD score 2) and malignant mass (mass with BIRAD score over 4), and secondly to sub classify mass with BIRAD score over 4 to three classes (BIRAD with score 4a,4b,4c). Accuracy of segmentation performance were evaluated by calculating the degree of overlapping between the active counter segmentation and the manual segmentation, and the result was 98.5%. Also reproducibility of active counter 3 using different manual initialization of algorithm by three radiologists were assessed and result was 99.5%. Classification performance was evaluated using one hundred sixty masses (80 masses with BRAD score 2 and 80 mass with BIRAD score over4). The best result for classification of data to benign and malignance was found using a combination of sequential forward floating feature (SFFS) selection and a boosted tree hybrid classifier with Ada boost ensemble method, decision tree learner type and 100 learners’ regression tree classifier, achieving 100% sensitivity and specificity in hold out method, 99.4% in cross validation method and 98.62 % average accuracy in cross validation method. For further sub classification of eighty malignance data with BIRAD score of over 4 (30 mass with BIRAD score 4a,30 masses with BIRAD score 4b and 20 masses with BIRAD score 4c), the best result achieved using the boosted tree with ensemble method bag, decision tree learner type with 200 learners Classification, achieving 100% sensitivity and specificity in hold out method, 98.8% accuracy and 98.41% average accuracy for ten times run in cross validation method. Beside those 160 masses (BIRAD score 2 and over 4) 13 masses with BIRAD score 3 were gathered. Which means patient is recommended to be tested in another medical imaging technique and also is recommended to do follow-up in six months. The CAD system was trained with mass with BIRAD score 2 and over 4 also 4 it was further tested using 13 masses with a BIRAD score of 3 and the CAD results are shown to agree with the radiologist’s classification after confirming in six months follow up. The present results demonstrate high sensitivity and specificity of the proposed CAD system compared to prior research. The present research is therefore intended to make contributions to the field by proposing a novel CAD system, consists of series of well-selected image processing algorithms, to firstly classify mass to benign or malignancy, secondly sub classify BIRAD 4 to three groups and finally to interpret BIRAD 3 to BIRAD 2 without a need of follow up study

Deep Learning of Unified Region, Edge, and Contour Models for Automated Image Segmentation

Image segmentation is a fundamental and challenging problem in computer vision with applications spanning multiple areas, such as medical imaging, remote sensing, and autonomous vehicles. Recently, convolutional neural networks (CNNs) have gained traction in the design of automated segmentation pipelines. Although CNN-based models are adept at learning abstract features from raw image data, their performance is dependent on the availability and size of suitable training datasets. Additionally, these models are often unable to capture the details of object boundaries and generalize poorly to unseen classes. In this thesis, we devise novel methodologies that address these issues and establish robust representation learning frameworks for fully-automatic semantic segmentation in medical imaging and mainstream computer vision. In particular, our contributions include (1) state-of-the-art 2D and 3D image segmentation networks for computer vision and medical image analysis, (2) an end-to-end trainable image segmentation framework that unifies CNNs and active contour models with learnable parameters for fast and robust object delineation, (3) a novel approach for disentangling edge and texture processing in segmentation networks, and (4) a novel few-shot learning model in both supervised settings and semi-supervised settings where synergies between latent and image spaces are leveraged to learn to segment images given limited training data.Comment: PhD dissertation, UCLA, 202

Computer aided assessment of CT scans of traumatic brain injury patients

A thesis submitted in partial fulfilment for the degree of Doctor of PhilosophyOne of the serious public health problems is the Traumatic Brain Injury, also known as silent epidemic, affecting millions every year. Management of these patients essentially involves neuroimaging and noncontrast CT scans are the first choice amongst doctors. Significant anatomical changes identified on the neuroimages and volumetric assessment of haemorrhages and haematomas are of critical importance for assessing the patients’ condition for targeted therapeutic and/or surgical interventions. Manual demarcation and annotation by experts is still considered gold standard, however, the interpretation of neuroimages is fraught with inter-observer variability and is considered ’Achilles heel’ amongst radiologists. Errors and variability can be attributed to factors such as poor perception, inaccurate deduction, incomplete knowledge or the quality of the image and only a third of doctors confidently report the findings. The applicability of computer aided dianosis in segmenting the apposite regions and giving ’second opinion’ has been positively appraised to assist the radiologists, however, results of the approaches vary due to parameters of algorithms and manual intervention required from doctors and this presents a gap for automated segmentation and estimation of measurements of noncontrast brain CT scans. The Pattern Driven, Content Aware Active Contours (PDCAAC) Framework developed in this thesis provides robust and efficient segmentation of significant anatomical landmarks, estimations of their sizes and correlation to CT rating to assist the radiologists in establishing the diagnosis and prognosis more confidently. The integration of clinical profile of the patient into image segmentation algorithms has significantly improved their performance by highlighting characteristics of the region of interest. The modified active contour method in the PDCAAC framework achieves Jaccard Similarity Index (JI) of 0.87, which is a significant improvement over the existing methods of active contours achieving JI of 0.807 with Simple Linear Iterative Clustering and Distance Regularized Level Set Evolution. The Intraclass Correlation Coefficient of intracranial measurements is >0.97 compared with radiologists. Automatic seeding of the initial seed curve within the region of interest is incorporated into the method which is a novel approach and alleviates limitation of existing methods. The proposed PDCAAC framework can be construed as a contribution towards research to formulate correlations between image features and clinical variables encompassing normal development, ageing, pathological and traumatic cases propitious to improve management of such patients. Establishing prognosis usually entails survival but the focus can also be extended to functional outcomes, residual disability and quality of life issues

Mathematical Approaches for Image Enhancement Problems

This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics

Biometric iris image segmentation and feature extraction for iris recognition

PhD ThesisThe continued threat to security in our interconnected world today begs for urgent solution. Iris biometric like many other biometric systems provides an alternative solution to this lingering problem. Although, iris recognition have been extensively studied, it is nevertheless, not a fully solved problem which is the factor inhibiting its implementation in real world situations today. There exists three main problems facing the existing iris recognition systems: 1) lack of robustness of the algorithm to handle non-ideal iris images, 2) slow speed of the algorithm and 3) the applicability to the existing systems in real world situation. In this thesis, six novel approaches were derived and implemented to address these current limitation of existing iris recognition systems. A novel fast and accurate segmentation approach based on the combination of graph-cut optimization and active contour model is proposed to define the irregular boundaries of the iris in a hierarchical 2-level approach. In the first hierarchy, the approximate boundary of the pupil/iris is estimated using a method based on Hough’s transform for the pupil and adapted starburst algorithm for the iris. Subsequently, in the second hierarchy, the final irregular boundary of the pupil/iris is refined and segmented using graph-cut based active contour (GCBAC) model proposed in this work. The segmentation is performed in two levels, whereby the pupil is segmented first before the iris. In order to detect and eliminate noise and reflection artefacts which might introduce errors to the algorithm, a preprocessing technique based on adaptive weighted edge detection and high-pass filtering is used to detect reflections on the high intensity areas of the image while exemplar based image inpainting is used to eliminate the reflections. After the segmentation of the iris boundaries, a post-processing operation based on combination of block classification method and statistical prediction approach is used to detect any super-imposed occluding eyelashes/eyeshadows. The normalization of the iris image is achieved though the rubber sheet model. In the second stage, an approach based on construction of complex wavelet filters and rotation of the filters to the direction of the principal texture direction is used for the extraction of important iris information while a modified particle swam optimization (PSO) is used to select the most prominent iris features for iris encoding. Classification of the iriscode is performed using adaptive support vector machines (ASVM). Experimental results demonstrate that the proposed approach achieves accuracy of 98.99% and is computationally about 2 times faster than the best existing approach.Ebonyi State University and Education Task Fund, Nigeri

Improved modeling of segmented earthquake rupture informed by enhanced signal analysis of seismic and geodetic observations

Earthquake source modeling has emerged from the need to be able to describe and quantifythe mechanism and physical properties of earthquakes. Investigations of earthquake ruptureand fault geometry requires the testing of a large number of such potential sets of earthquakesources models. Earthquakes often rupture across more than one fault segment. If such rupturesegmentation occurs on a significant scale, a simple model may not represent the rupture processwell. This thesis focuses on the data-driven inclusion of earthquake rupture segmentation intoearthquake source modeling. The developed tools and the modeling are based on the jointuse of seismological waveform far-field and geodetic Interferometric Synthetic Aperture Radarnear-field surface displacement maps to characterise earthquake sources robustly with rigorousconsideration of data and modeling errors.A strategy based on information theory is developed to determine the appropriate modelcomplexity to represent the available observations in a data-driven way. This is done inconsideration of the uncertainties in the determined source mechanisms by investigating theinferences of the full Bayesian model ensemble. Application on the datasets of four earthquakesindicated that the inferred source parameters are systematically biased by the choice of modelcomplexity. This might have effects on follow-up analyses, e. g. regional stress field inversionsand seismic hazard assessments.Further, two methods were developed to provide data-driven model-independent constraints toinform a kinematic earthquake source optimization about earthquake source parameter priorestimates. The first method is a time-domain multi-array backprojection of teleseismic datawith empirical traveltime corrections to infer the spatio-temporal evolution of the rupture. Thisenables detection of potential rupture segmentation based on the occurrence of coherent high-frequency sources during the rupture process. The second developed method uses image analysismethods on satellite radar measured surface displacement maps to infer modeling constraints onrupture characteristics (e.g. strike and length) and the number of potential segments. These twomethods provide model-independent constraints on fault location, dimension, orientation andrupture timing. The inferred source parameter constraints are used to constrain an inversion forthe source mechanism of the 2016 Muji Mw 6.6 earthquake, a segmented and bilateral strike-slipearthquake.As a case study to further investigate a depth-segmented fault system and occurrence of co-seismic rupture segmentation in such a system the 2008-2009 Qaidam sequence with co-seismicand post-seismic displacements is investigated. The Qaidam 2008-2009 earthquake sequence innortheast Tibet involved two reverse-thrust earthquakes and a postseismic signal of the 2008earthquake. The 2008 Qaidam earthquake is modeled as a deep shallow dipping earthquakewith no indication of rupture segmentation. The 2009 Qaidam earthquake is modeled on threedistinct south-dipping high-angle thrusts, with a bilateral and segmented rupture process. Agood agreement between co-seismic surface displacement measurements and coherent seismicenergy emission in the backprojection results is determined.Finally, a combined framework is proposed which applies all the developed methods and tools inan informed parallel modeling of several earthquake source model complexities. This frameworkallows for improved routine determination of earthquake source modeling under considerationof rupture segmentation. This thesis provides overall an improvement for earthquake sourceanalyses and the development of modeling standards for robust determination of second-orderearthquake source parameters