We propose a minimal path method to simultaneously compute segmentation masks and extract centerlines of tubular structures with line-topology. Minimal path methods are commonly used for the segmentation of tubular structures in a wide variety of applications. Recent methods use features extracted by CNNs, and often outperform methods using hand-tuned features. However, for CNN-based methods, the samples used for training may be generated inappropriately, so that they can be very different from samples encountered during inference. We approach this discrepancy by introducing a novel iterative training scheme, which enables generating better training samples specifically tailored for the minimal path methods without changing existing annotations. In our method, segmentation masks and centerlines are not determined after one another by post-processing, but obtained using the same steps. Our method requires only very few annotated training images. Comparison with seven previous approaches on three public datasets, including satellite images and medical images, shows that our method achieves state-of-the-art results both for segmentation masks and centerlines.

We propose Path-CNN, a method for the segmentation of centerlines of tubular structures by embedding convolutional neural networks (CNNs) into the progressive minimal path method. Minimal path methods are widely used for topology-aware centerline segmentation, but usually these methods rely on weak, hand-tuned image features. In contrast, CNNs use strong image features which are learned automatically from images. But CNNs usually do not take the topology of the results into account, and often require a large amount of annotations for training. We integrate CNNs into the minimal path method, so that both techniques benefit from each other: CNNs employ learned image features to improve the determination of minimal paths, while the minimal path method ensures the correct topology of the segmented centerlines, provides strong geometric priors to increase the performance of CNNs, and reduces the amount of annotations for the training of CNNs significantly. Our method has lower hardware requirements than many recent methods. Qualitative and quantitative comparison with other methods shows that Path-CNN achieves better performance, especially when dealing with tubular structures with complex shapes in challenging environments.

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.