Vascular Bifurcation Detection in Scale-Space Daniel-Marian Baboiu and Ghassan Hamarneh Simon Fraser University Burnaby BC, Canada, V5A 1S6 dba28@alumni.sfu.ca Abstract Several methods have been proposed over the years for segmentation of vessels, many of them based on scale- space. However, none of the existing methods for blood vessel segmentation is appropriate for extension to bifur- cation detection. Other existing bifurcation detection al- gorithms use an inherently serial “track and detect” ap- proach, which also requires a seed point. We present for the first time a comprehensive scale-space analysis of vascular bifurcations, resulting in a simple, novel algorithm for di- rect detection of blood vessel bifurcation points based not only on spatial variation across scales, but also on the vari- ation at a single spatial point across scales, without requir- ing training data or seed points. We present an analytical model for the bifurcation evolution with increasing scale, which was combined with eigenvalue analysis to create a bifurcation-Ness filter. We reveal, for the first time, a hybrid structure of bifurcations in scale-space. The algorithm was tested for validation in both 2D and 3D, with synthetic data as well as medical and non-medical images. 1. Introduction While significant progress has been made over the years in the segmentation of the vessels themselves, automatic de- tection of bifurcation points remains a significant difficulty. Several approaches have been proposed, for example based on centerline extraction [13] or on active models (snakes [11] and vessel crawlers [12]). However, the centerline- based methods either do not handle bifurcations (in some cases because the response function tracked decreases at bi- furcations) or have difficulties ensuring continuity at vessel junctions. A comprehensive review [6] groups vessel extraction techniques in six families, including artificial intelligence approaches. These appear to be the most promising in terms of sensitivity and accuracy ([16] reports success rate of 97%). However, methods based on artificial intelligence are computationally expensive and require training data, and even [16] uses a track-and-detect approach, requiring a seed. A more recent review [8] states that bifurcation detection is still one of the most challenging tasks in au- tomated blood vessel segmentation, with only a handful of papers specifically dedicated to bifurcation detection. All these approaches are inherently serial, appropriate for com- puters with only a few cores, with parallelism used only for processing local data. From an image feature point of view, blood vessels are ridges, and the corresponding descriptors can be used. Most notably, the scale-space Hessian analysis [3] results in a ves- selness operator, based on Gaussian penalties for deviations from ideal values. This approach does not detect the bifur- cation points; in fact, the vesselness measure defined drops significantly at bifurcation points (although not to 0), lead- ing to disconnected vessel segments. The approach we propose is a simple and direct method, based on the scale space behavior of bifurcations. This ap- proach uses the scale-space transform not only to find the maximum across scales, but also for extracting additional information from the rate of change across scales (the first scale-space approach to do so). It is intended to be used mainly as a “first line” filter for more complex, area-based filters, although its performance is good enough to be used by itself. Unlike the the serial approach of track-and-detect methods, the filter we propose processes the whole image in parallel, and thus is able to take full advantage of modern massively multicore computer architectures. As a result of using scale-space – a smoothing of the initial image with a set of Gaussians with progressively increasing widths – the method proposed is robust to relatively small amounts of noise. Only basic image processing techniques, such as background subtraction and contrast stretching, were used. Most of the tests of the algorithm were done with 2D im- ages (synthetic as well as clinical), but the results are gen- eral, and the theoretical model is valid for volumetric data as well. There is no loss of generality in testing, since theo- retical models of bifurcations show that the branches of the vessels in a bifurcation should lie in the same plane [5]. This is confirmed by an extensive experimental study made using 41