Mathematics
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Item Using Domain-Specific Information in Image Processing(2014) Cash, Brianna Rose; O'Leary, Dianne P; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)With the increasing availability of high resolution imaging tools, even in our pockets (i.e. smartphones), everyday users can do far more than simply digitally capturing a family moment. The ease of new applications available in these portable forms, linked with users who have expert knowledge about the images and tasks, opens the door to new possibilities. With this in mind we propose two new approaches that utilize the user's knowledge for improved results. We apply these approaches to real life problems in medical and scientific image applications. In the first approach, we introduce a class of linear and nonlinear methods which we call Domain-Specific Grayscale (DSGS) methods. A DSGS method transforms a color image into an image analogous to a grayscale image, where user-specified information is used to optimize a specified image processing task and reduce the computational complexity. We introduce new methods based on projection into the space of single-coordinate images, and we adapt support vector machines by using their scores to create a DSGS image. We apply these methods to applications in dermatology, analyzing images of skin tests and skin lesions, and demonstrate their usefulness. In the second approach, we introduce a tool for improved image deblurring that safeguards against bias that can easily be introduced by a user favoring a particular result. This is particularly important in scientific and medical applications used for discovery or diagnosis. We provide real-time results of choices of regularization methods and parameter selection, and we check the statistical plausibility of the results, using three statistical diagnostics, allowing a user to see the results of the choices. Our work demonstrates the utility of domain-specific information, supplied by the user, in improving the results of image processing algorithms.Item Measuring Deformations and Illumination Changes in Images with Applications to Face Recognition(2012) Jorstad, Anne; Jacobs, David; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This thesis explores object deformation and lighting change in images, proposing methods that account for both variabilities within a single framework. We construct a deformation- and lighting-insensitive metric that assigns a cost to a pair of images based on their similarity. The primary applications discussed will be in the domain of face recognition, because faces provide a good and important example of highly structured yet deformable objects with readily available datasets. However, our methods can be applied to any domain with deformations and lighting change. In order to model variations in expression, establishing point correspondences between faces is essential, and a primary goal of this thesis is to determine dense correspondences between pairs of face images, assigning a cost to each point pairing based on a novel image metric. We show that an image manifold can be defined to model deformations and illumination changes. Images are considered as points on a high-dimensional manifold given local structure by our new metric, where costs are based on changes in shape and intensity. Curves on this manifold describe transformations such as deformations and lighting changes to connect nearby images, or larger identity changes connecting images far apart. This allows deformations to be introduced gradually over the course of several images, where correspondences are well-defined between every pair of adjacent images along a path. The similarity between two images on the manifold can be defined as the length of the geodesic that connects them. The new local metric is validated in an optical flow-like framework where it is used to determine a dense correspondence vector field between pairs of images. We then demonstrate how to find geodesics between pairs of images on a Riemannian image manifold. The new lighting-insensitive metric is described in the wavelet domain where it is able to handle moderate amounts of deformation, and allows us to derive an algorithm where the analytic geodesics between images can be computed extremely efficiently. To handle larger deformations in addition to changes in illumination, we consider an algorithmic framework where deformations are modeled with diffeomorphisms. We present preliminary implementations of the diffeomorphic framework, and suggest how this work can be extended for further applications.