NSF Award
0093105
Pollak ABSTRACT<br/><br/>This research addresses various problems of extracting information from digital signals and images. A prototypical example is that of image segmentation: given a picture stored on a computer as an array of numbers (e.g., a medical image), the objective is to design an algorithm to automatically partition the image into meaningful regions (e.g., into a tumor and healthy tissue). More generally, this research is motivated by many applications---for example, in the areas of medical imaging and remote sensing---which are characterized by high complexity and poor quality of images (due to, for instance, noise, blurring, or clutter, which are caused by imperfections of the imaging process).Extracting and restoring objects from such images are challenging and important problems. Since good models of the intervening degradations are often very complex or even unavailable, these problems must be addressed in such a way that the resulting algorithms are insensitive to the precise structure of degradations. When precise modeling is possible, however, the algorithms should be flexible enough to take advantage of it. In addition, the large quantity of data in many applications of interest makes methods that are fast particularly valuable.<br/><br/>This project is developing develop a novel scale-space estimation framework applicable to such problems. Built on the foundation of recent non-linear scale-space approaches to image analysis, it is making important links with optimal estimation and sliding-mode control, thereby producing efficient methods for segmentation and restoration of 1-D signals and 2-D images. Theoretical analysis of these methods reveals their robustness, their applicability to a wide range of problems, and the fact that they admit fast numerical schemes. A number of practical image processing problems are being pursued, in particular, analysis of dermatoscopic imagery (magnified pictures of skin lesions used to improve the accuracy of screening for skin cancer).
