By Rafael Grompone von Gioi
The trustworthy detection of low-level snapshot constructions is an outdated and nonetheless hard challenge in machine imaginative and prescient. This ebook leads a close travel throughout the LSD set of rules, a line section detector designed to be absolutely automated. in accordance with the a contrario framework, the set of rules works successfully with no the necessity of any parameter tuning. The layout standards are completely defined and the algorithm's sturdy and undesirable effects are illustrated on actual and artificial photographs. the problems concerned, in addition to the techniques used, are universal to many geometrical constitution detection difficulties and a few attainable extensions are discussed.
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Extra info for A Contrario Line Segment Detection
11; a total of γ different values for p are tried. The total number of pixels in the rectangle is denoted by n and the number of p-aligned pixels is denoted by k (we drop r and x when they are implicit to simplify the notation). Then, the number of false alarms (NFA) associated with the rectangle r is NFA(r) = (NM)5/2 γ · B(n, k, p) , where N and M are the number of columns and rows of the image (after scaling), and B(n, k, p) is the tail of the binomial distribution, B(n, k, p) = n ∑ j=k n j p (1 − p)n− j .
As these two thin rectangles are aligned one to the other up to a tolerance τ , all the pixels of both rectangles are grouped into one line-support region. In LSD this problem is handled by detecting problematic line-support regions and cutting them into two smaller regions, hoping to cut the region at the right place to solve the problem. The criterion is described below. Once a region is cut, if the new one is accepted, the rectangle associated is recomputed and the algorithm is resumed. The detection of this “angle problem” is based on the density of aligned pixels in the rectangle.
J All in all, for each rectangle being evaluated and given a precision p, the numbers k and n are counted, and then the NFA value is computed by n NFA(r) = (NM)5/2 γ · ∑ j=k n j p (1 − p)n− j . 2) The rectangles with NFA(r) ≤ ε are validated as detections. As stated before and following Desolneux, Moisan, and Morel [19, 22], we set ε = 1 once for all. Here we will only show an experiment illustrating the stability of the result relative to ε value. 9 shows the input image and the result of LSD with ε = 1, ε = 10−1, and ε = 10−2 , respectively.