Influence of discretization in image space on Hough transform

Accuracy of the straight line Hough Transform: The non-voting approach

“…Parameter quantization impact on the vote spreading has been a subject of numerous publications; see e.g., [3,4,12,11,13,9]. It is important to note that the vote spreading severity is inversely proportional to Dq; the larger Dq the more likely the condition (3) to hold.…”

“…Suppose y = 0 under h = ip/4; i = 1, 3; then the condition turns into a simple: round (x cos h) = -round (x cos h + cosh) which holds for x = 0, 3, 6, 7, 10, etc. The anisotropic nature of the SHT was previously addressed in [20,21,12].…”

“…Implementation-wise, only the starting pixel is a subject to rotation using Eq. (12), while all the remaining coordinates after rotation can be derived from the chain-codes of the trace. New (x ht , y ht ) coordinates are derived from the original (x 0 , y 0 ) by rotating by angle h t :…”

On the inverse Hough transform

“…It should be noted that there are some schemes proposed for the proper quantization of the standard HT in order to ensure that the peak values of the accumulator array give the correct parameters of the line segments [15], [26], [27], [28], [29], [30]. Svalbe [26] derived properties of a set of natural lines able to be formed on a discrete grid and examined their relation with the parameters of the discrete HT.…”

“…Soffer and Kyryati [28] introduced conditions that ensure the convergence of the HT to the global maximum. Guo and Chutatape [30] examined the case of straight lines with one pixel width and showed that the efficiency of the HT is quite different for straight lines with different slopes. Also, it is shown that the type of the short line segments of a line influences the performance of the HT.…”