This project will develop, analyze, and apply new models for solving three fundamental problems in image processing: (1) edge-preserving noise removal; (2) image decomposition into objects plus textures; (3) recovery of lost information through image interpolation (or 'image inpainting'). The main feature of this new class of models is their ability to isolate and detect in natural scenes target objects that are obstructed by noise, textures, or other occluding objects, without generating erroneous or misleading features in the process. The identification and/or development of false object boundaries has long been a challenge for edge-preserving image processing models; this project seeks to find a universal approach for solving this problem. These new models are based on variational methods and partial differential equations. The investigator will establish their mathematical validity, determine properties of their solutions, develop efficient and accurate numerical schemes for their implementation, and directly apply these models to solve critical problems in the sciences and engineering.
Through existing collaborations with researchers in medical imaging, materials science, geology, pharmaceuticals, and optical character recognition, the investigator and undergraduate students will use these new models to solve key issues in science and technology. These problems include removing noise while isolating key medical features in highly degraded magnetic resonance images, identifying and analyzing the grain structure of nanoscale materials for optimizing high technology metals, and identifying land cover regions that are at high risk for hazards such as wildfires or flooding in remotely sensed images where the boundaries of these regions are obstructed by textures such as roads or topography. Currently, the only reliable methods for treating each of these problems depend on hand-drawn object boundaries. This is prohibitively time consuming on large data sets, so automating the boundary detection process will greatly enhance the state of the art. False object detection can be devastating in any one of these applications, so existing automated methods cannot be directly applied. This project seeks to find theoretically sound approaches that avoid this drawback while removing obstructions and accurately identifying target objects.
