Extended principal component analysis and its applications to image analysis

The objectives of this research are to analyze and develop a modified Principal Component Analysis (PCA) and to develop a two-dimensional PCA with applications in image processing. PCA is a classical multivariate technique where its mathematical treatment is purely based on the eigensystem of positive-definite symmetric matrices. Its main function is to statistically transform a set of correlated variables to a new set of uncorrelated variables over $\IR\sp{n}$ by retaining most of the variations present in the original variables.^ The variances of the Principal Components (PCs) obtained from the modified PCA form a correlation matrix of the original variables. The decomposition of this correlation matrix into a diagonal matrix produces a set of orthonormal basis that can be used to linearly transform the given PCs. It is this linear transformation that reproduces the original variables. The two-dimensional PCA can be devised as a two successive of one-dimensional PCA. It can be shown that, for an $m\times n$ matrix, the PCs obtained from the two-dimensional PCA are the singular values of that matrix.^ In this research, several applications for image analysis based on PCA are developed, i.e., edge detection, feature extraction, and multi-resolution PCA decomposition and reconstruction. ^

Rigid and non-rigid point-based medical image registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

Fractal analysis of flocs formed in edible oil -water emulsions by image analysis techniques

Edible oil is an important contaminant in water and wastewater. Oil droplets smaller than 40 μm may remain in effluent as an emulsion and combine with other contaminants in water. Coagulation/flocculation processes are used to remove oil droplets from water and wastewater. By adding a polymer at proper dose, small oil droplets can be flocculated and separated from water. The purpose of this study was to characterize and analyze the morphology of flocs and floc formation in edible oil-water emulsions by using microscopic image analysis techniques. The fractal dimension, concentration of polymer, effect of pH and temperature are investigated and analyzed to develop a fractal model of the flocs. Three types of edible oil (corn, olive, and sunflower oil) at concentrations of 600 ppm (by volume) were used to determine the optimum polymer dosage and effect of pH and temperature. To find the optimum polymer dose, polymer was added to the oil-water emulsions at concentration of 0.5, 1.0, 1.5, 2.0, 3.0 and 3.5 ppm (by volume). The clearest supernatants obtained from flocculation of corn, olive, and sunflower oil were achieved at polymer dosage of 3.0 ppm producing turbidities of 4.52, 12.90, and 13.10 NTU, respectively. This concentration of polymer was subsequently used to study the effect of pH and temperature on flocculation. The effect of pH was studied at pH 5, 7, 9, and 11 at 30°C. Microscopic image analysis was used to investigate the morphology of flocs in terms of fractal dimension, radius of oil droplets trapped in floc, floc size, and histograms of oil droplet distribution. Fractal dimension indicates the density of oil droplets captured in flocs. By comparison of fractal dimensions, pH was found to be one of the most important factors controlling droplet flocculation. Neutral pH or pH 7 showed the highest degree of flocculation, while acidic (pH 5) and basic pH (pH 9 and pH 11) showed low efficiency of flocculation. The fractal dimensions achieved from flocculation of corn, olive, and sunflower oil at pH 7 and temperature 30°C were 1.2763, 1.3592, and 1.4413, respectively. The effect of temperature was explored at temperatures 20°, 30°, and 40°C and pH 7. The results of flocculation of oil at pH 7 and different temperatures revealed that temperature significantly affected flocculation. The fractal dimension of flocs formed in corn, olive and sunflower oil emulsion at pH 7 and temperature 20°, 30°, and 40°C were 1.82, 1.28, 1.29, 1.62, 1.36, 1.42, 1.36, 1.44, and 1.28, respectively. After comparison of fractal dimension, radius of oil droplets captured, and floc length in each oil type, the optimal flocculation temperature was determined to be 30°C. ^

Rigid and Non-rigid Point-based Medical Image Registration

The primary goal of this dissertation is to develop point-based rigid and non-rigid image registration methods that have better accuracy than existing methods. We first present point-based PoIRe, which provides the framework for point-based global rigid registrations. It allows a choice of different search strategies including (a) branch-and-bound, (b) probabilistic hill-climbing, and (c) a novel hybrid method that takes advantage of the best characteristics of the other two methods. We use a robust similarity measure that is insensitive to noise, which is often introduced during feature extraction. We show the robustness of PoIRe using it to register images obtained with an electronic portal imaging device (EPID), which have large amounts of scatter and low contrast. To evaluate PoIRe we used (a) simulated images and (b) images with fiducial markers; PoIRe was extensively tested with 2D EPID images and images generated by 3D Computer Tomography (CT) and Magnetic Resonance (MR) images. PoIRe was also evaluated using benchmark data sets from the blind retrospective evaluation project (RIRE). We show that PoIRe is better than existing methods such as Iterative Closest Point (ICP) and methods based on mutual information. We also present a novel point-based local non-rigid shape registration algorithm. We extend the robust similarity measure used in PoIRe to non-rigid registrations adapting it to a free form deformation (FFD) model and making it robust to local minima, which is a drawback common to existing non-rigid point-based methods. For non-rigid registrations we show that it performs better than existing methods and that is less sensitive to starting conditions. We test our non-rigid registration method using available benchmark data sets for shape registration. Finally, we also explore the extraction of features invariant to changes in perspective and illumination, and explore how they can help improve the accuracy of multi-modal registration. For multimodal registration of EPID-DRR images we present a method based on a local descriptor defined by a vector of complex responses to a circular Gabor filter.

Scheduling medical application workloads on virtualized computing systems

This dissertation presents and evaluates a methodology for scheduling medical application workloads in virtualized computing environments. Such environments are being widely adopted by providers of "cloud computing" services. In the context of provisioning resources for medical applications, such environments allow users to deploy applications on distributed computing resources while keeping their data secure. Furthermore, higher level services that further abstract the infrastructure-related issues can be built on top of such infrastructures. For example, a medical imaging service can allow medical professionals to process their data in the cloud, easing them from the burden of having to deploy and manage these resources themselves. In this work, we focus on issues related to scheduling scientific workloads on virtualized environments. We build upon the knowledge base of traditional parallel job scheduling to address the specific case of medical applications while harnessing the benefits afforded by virtualization technology. To this end, we provide the following contributions: (1) An in-depth analysis of the execution characteristics of the target applications when run in virtualized environments. (2) A performance prediction methodology applicable to the target environment. (3) A scheduling algorithm that harnesses application knowledge and virtualization-related benefits to provide strong scheduling performance and quality of service guarantees. In the process of addressing these pertinent issues for our target user base (i.e. medical professionals and researchers), we provide insight that benefits a large community of scientific application users in industry and academia. Our execution time prediction and scheduling methodologies are implemented and evaluated on a real system running popular scientific applications. We find that we are able to predict the execution time of a number of these applications with an average error of 15%. Our scheduling methodology, which is tested with medical image processing workloads, is compared to that of two baseline scheduling solutions and we find that it outperforms them in terms of both the number of jobs processed and resource utilization by 20–30%, without violating any deadlines. We conclude that our solution is a viable approach to supporting the computational needs of medical users, even if the cloud computing paradigm is not widely adopted in its current form.