Level Set Methods for Biomedical Imaging Level Set Methods for Biomedical Imaging Abstract of the Thesis Level Set Methods for Biomedical Imaging Table of Contents

OF THE THESIS Level Set Methods for Biomedical Imaging by Michelle M. Miller Master of Science in Applied Mathematics San Diego State University, 2008 Recently, insight regarding the internal structure of mitochondria and their integral role in many cellular processes has been gained through the examination of three-dimensional mitochondrial models. These models are constructed from electron tomograms where three dimensional images are calculated from a series of electron micrographs recorded at regular angular intervals over a wide angular range. The construction requires examining the tomogram as a sequence of two-dimensional images and identifying the mitochondrial inner, outer, and cristae membranes manually. The purpose of this project is to implement the level set method to identify the aforementioned mitochondrial structures numerically. The level set method, developed by Osher and Sethian, is an approach used for modeling propagating fronts that relies on the use of partial differential equations. This framework is especially useful in application to shape modeling because it requires no prior knowledge of the object shapes. The edges of the object are recovered through the propagation of an arbitrary initial function along its gradient field. In this project, the level set method is implemented, utilizing an initial level set composed of the positive distances to the initial contour, and applied to both synthetic images and mitochondrial images processed using total variation minimization noise reduction with fixed regularization. We then compare the efficiency and accuracy of a variety of initial fronts in identifying the object edges of interest.