A Realistic Digitization Model of Straight Lines

Understanding digital lines comprises two components: i) determining whether a given digital set is a digital line segment, i.e. whether there exists a real straight line in IR2 that digitizes to it, and ii) recovering the space of straight lines which digitize to a given digital line segment. Although these problems have been extensively studied by researchers in computer vision and digital geometry, the primary digitization model that has been used is object boundary quantization which is not a realistic sensor model in computer vision.In this paper, we present a realistic mathematical model of a digitized edge which handles both blurring and arbitrary thresholding. We show that a thresholded digital image of a blurred half-plane obtained for some unknown threshold value is equal to the image of a perfectly focused half-plane with the same slope obtained by object boundary quantization. This result implies that recovering the slope of a blurred half-plane, given its image obtained for some unknown threshold value, reduces to recovering the slope of a perfectly focused half-plane under object boundary quantization. Therefore, the previous results and algorithms for the recovery of straight lines, which mainly assumed object boundary quantization, are also valid if we assume this more realistic digitization model.