Level set methods are a popular way to solve the image segmentation problem. The solution contour is found by solving an optimization problem where a cost functional is minimized. Gradient descent methods are often used to solve this optimization problem since they are very easy to implement and applicable to general nonconvex functionals. They are, however, sensitive to local minima and often display slow convergence. Traditionally, cost functionals have been modified to avoid these problems. In this paper, we instead propose using two modified gradient descent methods, one using a momentum term and one based on resilient propagation. These methods are commonly used in the machine learning community. In a series of 2-D/3-D-experiments using real and synthetic data with ground truth, the modifications are shown to reduce the sensitivity for local optima and to increase the convergence rate. The parameter sensitivity is also investigated. The proposed methods are very simple modifications of the basic method, and are directly compatible with any type of level set implementation. Downloadable reference code with examples is available online.

Computed Tomography Angiography (CTA) is commonly used in clinical routine for diagnosing vascular diseases. The procedure involves the injection of a contrast agent into the blood stream to increase the contrast between the blood vessels and the surrounding tissue in the image data. CTA is often visualized with Direct Volume Rendering (DVR) where the enhanced image contrast is important for the construction of Transfer Functions (TFs). For increased efficiency, clinical routine heavily relies on preset TFs to simplify the creation of such visualizations for a physician. In practice, however, TF presets often do not yield optimal images due to variations in mixture concentration of contrast agent in the blood stream. In this paper we propose an automatic, optimization-based method that shifts TF presets to account for general deviations and local variations of the intensity of contrast enhanced blood vessels. Some of the advantages of this method are the following. It computationally automates large parts of a process that is currently performed manually. It performs the TF shift locally and can thus optimize larger portions of the image than is possible with manual interaction. The method is based on a well known vesselness descriptor in the definition of the optimization criterion. The performance of the method is illustrated by clinically relevant CT angiography datasets displaying both improved structural overviews of vessel trees and improved adaption to local variations of contrast concentration.

Many applications in image analysis include the problem of linear structure detection, e.g. segmentation of blood vessels in medical images, roads in satellite images, etc. A simple and efficient solution is to apply linear filters tuned to the structures of interest and extract line and edge positions from the filter output. However, if the filter is not carefully designed, artifacts such as ringing can distort the results and hinder a robust detection. In this paper, we study the ringing effects using a common Gabor filter for linear structure detection, and suggest a method for generating non-ring filters in 2D and 3D. The benefits of the non-ring design are motivated by results on both synthetic and natural images.

The segmentation and analysis of blood vessels has received much attention in the research community. The results aid numerous applications for diagnosis and treatment of vascular diseases. Here we use level set propagation with local phase information to capture the boundaries of vessels. The basic notion is that local phase, extracted using quadrature filters, allows us to distinguish between lines and edges in an image. Noting that vessels appear either as lines or edge pairs, we integrate multiple scales and capture information about vessels of varying width. The outcome is a ¿global¿ phase which can be used to drive a contour robustly towards the vessel edges. We show promising results in 2D and 3D. Comparison with a related method gives similar or even better results and at a computational cost several orders of magnitude less. Even with very sparse initializations, our method captures a large portion of the vessel tree.