This project focuses on two important image analysis problems. One is on image registration, which is to match up images or image volumes for structure localization, difference detection, and other purposes. It is widely used in medical imaging, remote sensing, finger print or face recognition, and so forth. The second major focus is on 3-D image denoising with edges and major edge features preserved. Because of fast progress in image acquisition techniques, 3-D images become increasingly popular in magnetic resonance imaging (MRI), functional MRI (fMRI), and other applications. However, observed 3-D images often contain noise, due to hardware imperfection and other reasons, which should be removed beforehand so that subsequent image analyses would be more reliable. In the literature, existing image registration (IR) methods can be roughly classified into two categories: feature-based IR methods and intensity-based IR methods. Because feature selection is often a time-consuming and challenging process, intensity-based IR methods have become popular in various applications. However, most existing intensity-based IR methods require a parametric model for describing the image matching transformation, which is often difficult to verify in practice. In this project, the investigator and his colleagues propose an intensity-based IR procedure without imposing any parametric form on the matching transformation. Therefore, the proposed method has the potential to greatly improve the intensity-based IR techniques and greatly broaden their applications. In the literature, most existing image denoising methods are for analyzing 2-D images. They often have certain ability to preserve planar parts of the edges, but cannot preserve angular parts of the edges well. Their direct extensions to 3-D cases generally cannot handle 3-D images efficiently, because the structure of 3-D images is often substantially more complicated than that of 2-D images. This project proposes a novel 3-D image denoising method which can preserve edges and major edge features well. Therefore, it would provide a reliable tool for 3-D image denoising.

Images are used everywhere in our society, ranging from medical diagnostics by CT, MRI, and other medical imaging techniques to satellite monitoring of global environmental changes. This project aims to improve image registration and 3-D image denoising techniques, which are used broadly in various imaging applications. Thus, it will have broader impacts on our society through its direct impact on improvement of medical diagnostics, security systems involving fingerprint and face recognition, remote sensing techniques, and so forth. This project also aims to contribute to the development of human resources in science and engineering through its educational activities. For instance, the investigator offers an advanced topics course on image analysis, from which graduate students from various departments can receive systematic training in scientific research. Several graduate students are doing their thesis research with the investigator on image processing. Some computer software packages developed by the investigator and his graduate students would be posted on a project web page for other researchers to download and use. The major research results obtained from this project would be presented in national and international conferences, and be submitted for publication in academic journals.

Project Report

This project focuses on two image processing problems that are important in many image applications. One is on image registration (IR), which is for matching one image to one or more other images of a same or similar scene, in order to combine information from different images. IR is widely used in medical imaging, remote sensing, face and finger image recognition, and so forth. The second problem is about 3-D image denoising with edges and major edge features preserved. Because of the fast progress in image acquisition techniques, 3-D images become increasingly popular in magnetic resonance imaging (MRI), functional MRI (fMRI), and other applications. Consequently, 3-D image denoising is an important task in such applications. In this project, we systematically studied the major properties of the geometrical transformation T involved in IR, and found that the IR problem was ill-posed in the sense that T could not be properly defined at certain places, including places where the image intensity functions of the two related images were linear. To describe the ill-posed nature of the IR problem, several concepts, including the 2-D degenerate pixels, 2-D partial degenerate pixels, 1-D degenerate pixels, and 1-D partial degenerate pixels, were proposed for describing the local properties of T. The relationship among these concepts was also studied. Based on this study about T, a local smoothing method was proposed for solving the intensity-based IR problem. It was shown that this method performed well, compared to some state-of-the-art IR methods. Regarding 3-D image denoising, in this project, we proposed a novel 3-D image denoising procedure which could preserve edges and major edge features well. Our proposed procedure consists of three major steps. First, edge voxels are detected using a 3-D edge detector. Second, in a neighborhood of a given voxel, the underlying edge surface is approximated by a surface template chosen from a pre-specified surface template family. The surface template family is specified in a way that major features of the edge surfaces can be accommodated well by its surface templates, which makes it possible for us to preserve edges and major edge features in 3-D image denoising. Third, the true image intensity at the given voxel is estimated by a weighted average of the observed image intensities in the neighborhood whose voxels are located on the same side of the chosen surface template as the given voxel. Both numerical and theoretical arguments showed that this method worked well in various applications. During the grant period, the PI offered an advanced topics course on image processing and jump regression analysis. Results from this project were covered by the course. Graduate students from various departments across the campus of University of Minnesota, including departments of Computer Sciences, Mathematics, Material Sciences, Neuroscience, and Statistics, registered for this course. Students taking the course got systematic training in research plan development, literature search, scientific writing, presentation, and so forth. Furthermore, two of the PI's former Ph.D. students finished their thesis research in 2011 and 2012 on image registration and 3-D image denoising, respectively. The academic training they got from their thesis research should make them well prepared for their current jobs and their future careers. This NSF award results in one book chapter, ten journal papers and two refereed conference papers.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
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Gabor Szekely
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University of Minnesota Twin Cities
United States
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