Diagonal quantization for the Hough transform

Hough transform modified by line connectivity and line thickness

“…Substituting the maximum likelihood estimate $ / p x n ij ij = in (6) and taking logarithm, we have the first part of (5). Since the proportion of the black pixels on a line is expected to be no less than the noise level, the minimum value of L in (6) should be one.…”

“…h h (2) with i = 1, ..., CU; j = 1, ..., CT, where CU and CT are predetermined class sizes, and {U i } and {T j } are monotonic sequences so that all the cells cover the whole range of U and T. The optimal sizes of these rectangles depend on discretization of pixels [5], [6], [7]. One way to avoid the two-dimensional (2D) quantization of the (U, T) plane is to solve two simultaneous equations (1) for each pair of points and then pick the clusters of these solutions in the (U, T) plane.…”

On the inverse Hough transform

“…6. The curves (6,13) and (3,14) in the right class of group in row CM 43. Note that, due to the modification of the sf value, the curve (4, 14) shown in Fig.…”

“…Most of researchers take the HT space to be equal in size to the image space. However, the most known quantization schemes proposed are the HiFi-quantization [29], Yuen's quantization [31], and the most favorable of them, the Diagonal quantization [14]. These quantization schemes permit a satisfactory calculation of the line parameters, but do not guarantee the inversion of the HT space and the determination of the positions of the line pixels.…”

An efficient algorithm for line extraction from laser scans

“…This not only impacts on the efficiency of the line detector but also the computational requirements [7]. These problems have been addressed in detail in [1], [4] and [5]. Further, the use of Hough transform is restricted to alignment detection; the Hough transform can only determine the polar parameters of the straight lines, not the exact position of the points constituting the line [8].…”