Abstracts Mathematics

Using Domain-Specific Information in Image Processing

by Brianna Rose Cash

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.