Algorithms are presented for rapid, automatic, robust, adaptive, and accurate tracing of retinal vasculature and analysis of intersections and crossovers. This method improves upon prior work in several ways: automatic adaptation from frame to frame without manual initialization/adjustment, with few tunable parameters; robust operation on image sequences exhibiting natural variability, poor and varying imaging conditions, including over/under-exposure, low contrast, and artifacts such as glare; does not require the vasculature to be connected, so it can handle partial views; and operation is efficient enough for use on unspecialized hardware, and amenable to deadline-driven computing, being able to produce a rapidly and monotonically improving sequence of usable partial results. Increased computation can be traded for superior tracing performance. Its efficiency comes from direct processing on gray-level data without any preprocessing, and from processing only a minimally necessary fraction of pixels in an exploratory manner, avoiding low-level image-wide operations such as thresholding, edge detection, and morphological processing. These properties make the algorithm suited to real-time, on-line (live) processing and is being applied to computer-assisted laser retinal surgery.