Modelling digital straight lines

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 quantisation. 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