Minimal Path Methods for Segmentation and Analysis of 2D and 3D Line Structures

Image segmentation plays a vital role in many applications of computer vision. Segmentation is not only an important task in its own right, but also a prerequisite for many further image analysis steps. Consequently, segmentation is one of the most active research areas of computer vision. In this thesis, line structures are considered, which have quite different characteristics compared to common objects in natural 2D images: Line structures are much thinner and longer, and often they have little color or texture information such as blood vessels in medical images. To cope with these challenges, minimal path methods are commonly used. In this thesis, two new methods are introduced which are extensions of existing minimal path methods. The first method is a novel hybrid approach for automatic 3D segmentation and quantification of high-resolution 7 Tesla magnetic resonance angiography (MRA) images of the human cerebral vasculature. Our approach consists of two main steps. First, a 3D model-based approach is used to segment and quantify thick vessels and most parts of thin vessels. Second, remaining vessel gaps of the first step in low-contrast and noisy regions are completed using a 3D minimal path approach, which exploits directional information. We present two novel minimal path approaches: The first is an explicit approach based on energy minimization using probabilistic sampling, and the second is an implicit approach based on fast marching with anisotropic directional prior. The second method we introduce is a novel minimal path method for the segmentation of 2D and 3D line structures. Minimal path methods perform propagation of a wavefront emanating from a start point at a speed derived from image features, followed by path extraction using backtracing. Usually, the computation of the speed and the propagation of the wave are two separate steps, and point features are used to compute a static speed. We introduce a new continuous minimal path method which steers the wave propagation progressively using dynamic speed based on path features. We present three instances of our method, using an appearance feature of the path, a geometric feature based on the curvature of the path, and a joint appearance and geometric feature based on the tangent of the wavefront. Such features have not been used in previous continuous minimal path methods. We compute the features dynamically during the wave propagation, and also efficiently using a fast numerical scheme and a low-dimensional parameter space. Our method does not suffer from discretization or metrication errors. We conducted quantitative and qualitative experimental evaluations of our methods using 2D and 3D images from different application areas, including synthetic images, retinal images, satellite images of streets, rivers, and bridges, and 3D 7T MRA images of human brain vessels