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Definition: A projection that minimizes the number of crossings is called a minimum crossing projection.
Although a regular projection of a set of line segments always exists, we are not lucky to get a crossing-free projection all the time. Therefore, obtaining the minimum crossing projection is desirable in some applications. As showed below, the images of the veins of the same brain appear more or less clear depending on the direction of projection; but the second one has fewer number of crossings and looks clearer than the first one in some sense.
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