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Vessel segmentation algorithms are critical components of circulatory blood vessel analysis systems. We present a survey of vessel extraction techniques and algorithms, putting the various approaches and techniques in perspective by means of a classification of the existing research. While we target mainly the extraction of blood vessels, neurovascular structure in particular we also review some of the segmentation methods for the tubular objects that show similar characteristics to vessels. We divide vessel segmentation algorithms and techniques into six main categories: (1) pattern recognition techniques, (2) model-based approaches, (3) tracking-based approaches, (4) artificial intelligence-based approaches, (5) neural network-based approaches, and (6) miscellaneous tube-like object detection approaches. Some of these categories are further divided into sub-categories. A table compares the papers against such criteria as dimensionality, input type, preprocessing, user interaction, and result type.