Anisotropic Mesh Adaptation for Image Segmentation based on Partial Differential Equations

Abstract

As the resolution of digital images increases significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this dissertation, we consider image segmentation by solving a partial differential equation (PDE) model based on the Mumford-Shah functional. We first, develop a new anisotropic mesh adaptation (AMA) framework to improve segmentation efficiency and accuracy. In the AMA framework, we incorporate an anisotropic mesh adaptation for image representation and a nite element method for solving the PDE model. Comparing to traditional algorithms solved by the finnite difference method, our AMA framework provides faster and better results without the need for re-sizing the images to lower quality. We also extend the algorithm to segment images with multiple regions. We also improve the well-known Chan-Vese model by developing a locally enhanced Chan-Vese (LECV) model. Our LECV model incorporates a newly define signed pressure force (SPF) function, which is built upon the local image information. The SPF function helps to attract the contour curve to the object boundaries for images with inhomogeneous intensities. The proposed LECV model, together with the AMA segmentation framework can successfully segment the image with or without inhomogeneous intensities. While most other segmentation methods only work on low-resolution images, our LECV model is successfully applied to high-resolution images, with improved efficiency and accuracy.