Modern medical imaging techniques have revolutionized health care over the last decades, providing clinicians with high-resolution 3D images of the inside of the patient's body without the need for invasive procedures. Detailed images of the vascular anatomy can be captured by angiography, providing a valuable source of information when deciding whether a vascular intervention is needed, for planning treatment, and for analyzing the success of therapy. However, increasing level of detail in the images, together with a wide availability of imaging devices, lead to an urgent need for automated techniques for image segmentation and analysis in order to assist the clinicians in performing a fast and accurate examination. To reduce the need for user interaction and increase the speed of vascular segmentation,  we propose a fast and fully automatic vascular skeleton extraction algorithm. This algorithm first analyzes the volume's intensity histogram in order to automatically adapt the internal parameters to each patient and then it produces an approximate skeleton of the patient's vasculature. The skeleton can serve as a seed region for subsequent surface extraction algorithms. Further improvements of the skeleton extraction algorithm include the expansion to detect the skeleton of diseased arteries and the design of a convolutional neural network classifier that reduces false positive detections of vascular cross-sections. In addition to the complete skeleton extraction algorithm, the thesis presents a segmentation algorithm based on modified onion-kernel region growing. It initiates the growing from the previously extracted skeleton and provides a rapid binary segmentation of tubular structures. To provide the possibility of extracting precise measurements from this segmentation we introduce a method for obtaining a segmentation with subpixel precision out of the binary segmentation and the original image. This method is especially suited for thin and elongated structures, such as vessels, since it does not shrink the long protrusions. The method supports both 2D and 3D image data. The methods were validated on real computed tomography datasets and are primarily intended for applications in vascular segmentation, however, they are robust enough to work with other anatomical tree structures after adequate parameter adjustment, which was demonstrated on an airway-tree segmentation.