PDE-based image processing for segmentation and image restoration

Abstract

We propose noble ideas and formulations based on nonlinear partial differential equations (PDEs) in image segmentation and image restoration. Two algorithms which have different perspectives on taking initial contours are proposed in image segmentation. The first is to place initial contours arbitrarily for the purpose of capturing multiple junctions and holes of object in image. The second is to place those close to boundaries of objects for the purpose of fine segmentation. In the image restoration, we propose a nonlinear PDE for regularizing a tensor which contains first derivative information of image such as strength of edges and parallel direction to the gradient of image. It improves the quality of result in many low level topics in computer vision, which need the first derivative information of image. In the first segmentation algorithm, noble forces based on active contours models are proposed for capturing objects in the image. Contemplating the common functionality of forces in previous active contours models, we propose the geometric attraction-driven flow (GADF), the binary edge function, and the binary balloon forces to detect objects in difficult cases such as varying illumination and complex shapes. The orientation of GADF is orthogonally aligned with the boundary of object and has the opposite direction across the boundary. It prevents the leakage on the weak edge. To reduce the interference from other forces, we design the binary edge function using the property of orientation in GADF. We also design the binary balloon force based on the four-color theorem. Combining with initial dual level set functions, the proposed model captures holes in objects and multiple junctions from different colors. The result does not depend on positions of initial contours. In the second segmentation algorithm, we propose fine segmentation in order to extract objects in an image without loss of detailed shapes. The image has simple background colors or si...