OpenCV LSD算法详解：无参数直线检测的高精度实现

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OpenCV_LSD.pdf 是一篇发表于2012年3月24日的论文，专门介绍了OpenCV中的直线检测算法——LSD（Line Segment Detector）。该算法旨在提供亚像素级别的精度，并能够在无需参数调整的情况下应用于任何数字图像。LSD的特点在于其高效且控制着假阳性检测的数量，平均每张图像允许大约一个错误警报，从而确保了较高的准确度。论文的作者包括Rafael Grompone von Gioi、Jerémie Jakubowicz、Jean-Michel Morel以及Gregory Randall，他们分别来自法国的CMLA和ENSECachan、法国的TELECOM ParisTech以及乌拉圭的UdelaR。他们的研究受到了Burns、Hanson和Riseman方法[2]的启发，并借鉴了Desolneux、Moisan和Morel的理论[3,4]，采用反向验证方法进行线段检测。论文的核心部分详细介绍了LSD算法的工作原理，它基于像素级的特征匹配和边缘检测技术，通过连续的边缘跟踪来识别线段。该版本的算法可能包括改进的边缘检测算子、边缘跟踪策略以及一种有效的错误检测和修正机制，以减少误报并提高检测的可靠性。论文还提供了配套的在线材料，包括效果显著的图表和多个示例，使得读者能够直观地理解算法的性能和应用。此外，论文的在线资源还包括可供下载的软件工具、数据集和在线演示，这使得研究人员和开发者可以直接使用或进一步研究LSD算法。 OpenCV_LSD.pdf是一篇重要的IT文献，对于理解和实践计算机视觉中的直线检测任务，特别是那些对精度有较高要求的应用场景，如行人检测、车辆追踪或机器人导航等，具有很高的参考价值。掌握和利用LSD算法有助于提升图像处理和分析的效率与准确性。

LSD: a Line Segment Detector

This corresponds to the expected number of rectangles which have a suﬃcient number of aligned

points to be as rare as r under H

. When the NFA associated with an image rectangle is large, this

means that such an event is expected on the a contrario model, i.e., common and thus not a relevant

one. On the other hand, when the NFA value is small, the event is rare and probably a meaningful

one. A threshold ε is selected and when a rectangle has NFA(r, i) ≤ ε it is called ε-meaningful

rectangle and produces a detection.

Theorem 1

r∈R

NFA(r,I)<ε

≤ ε

where E is the expectation operator, 1 is the indicator function, R is the set of rectangles considered,

and I is a random image on H

The theorem states that the average number of ε-meaningful rectangles under the a contrario

model H

is less than ε. Thus, the number of detections on noise is controlled by ε and it can be

made as small as desired. In other words, this shows that LSD satisﬁes the Helmholtz principle.

This proof is given here because it was not given in the original article [1].

Proof We deﬁne

k(r) as

k(r) = min



κ ∈ N, P



k(r, I) ≥ κ



≤

(NM)

5/2



Then, NFA(r, i) ≤ ε is equivalent to k(r, i) ≥

k(r). Now,

r∈R

NFA(r,I)≤ε

r∈R



NFA(r, I) ≤ ε



r∈R

k(r, I) ≥

k(r)

But, by deﬁnition of

k(r) we know that

k(r, I) ≥

k(r)

≤

(NM)

5/2

and using that #R = (NM)

5/2

γ we get

r∈R

NFA(r,I)≤ε

≤

r∈R

(NM)

5/2

= ε

which concludes the proof. 

Following Desolneux, Moisan, and Morel [3, 4], we set ε = 1 once for all. This corresponds to

accepting on average one false detection per image in the a contrario model, which is reasonable.

Also, the detection result is not sensitive to the value of ε. Indeed, the detection limit (that is the

minimal number of aligned points that could lead to a ε-meaningful rectangle) varies like

√

−log ε.

Setting ε to any reasonable value would produce very similar results.

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