We propose 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. These 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 performed qualitative and quantitative evaluations using 2D and 3D images from different application areas.

We propose 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. We conducted an extensive evaluation with over 2300 3D synthetic images and 40 real 3D 7 Tesla MRA images. Quantitative and qualitative evaluation shows that our approach achieves superior results compared with a previous minimal path approach. Furthermore, our approach was successfully used in two clinical studies on stroke and vascular dementia.

We introduce a new model-based approach for automatic quantification of colocalizations in multichannel 3D microscopy images. The approach uses different 3D parametric intensity models in conjunction with a model fitting scheme to localize and quantify subcellular structures with high accuracy. The central idea is to determine colocalizations between different channels based on the estimated geometry of the subcellular structures as well as to differentiate between different types of colocalizations. A statistical analysis was performed to assess the significance of the determined colocalizations. This approach was used to successfully analyze about 500 three-channel 3D microscopy images of human soft tissue tumors and controls.

We introduce a new approach for 3-D segmentation and quantification of vessels. The approach is based on a 3-D cylindrical parametric intensity model, which is directly fitted to the image intensities through an incremental process based on a Kalman filter. Segmentation results are the vessel centerline and shape, i.e., we estimate the local vessel radius, the 3-D position and 3-D orientation, the contrast, as well as the fitting error. We carried out an extensive validation using 3-D synthetic images and also compared the new approach with an approach based on a Gaussian model. In addition, the new model has been successfully applied to segment vessels from 3-D MRA and computed tomography angiography image data. In particular, we compared our approach with an approach based on the randomized Hough transform. Moreover, a validation of the segmentation results based on ground truth provided by a radiologist confirms the accuracy of the new approach. Our experiments show that the new model yields superior results in estimating the vessel radius compared to previous approaches based on a Gaussian model as well as the Hough transform.