LSD: 精确的线段检测器算法详解

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LSD: A Line Segment Detector 是一篇发表于2012年3月24日的Image Processing Online上的论文，作者是Rafael Grompone von Gioi、Jérémie Jakubowicz、Jean-Michel Morel和Gregory Randall。该研究专注于设计一种能够在无需参数调整的情况下，对任何数字图像进行亚像素精度线段检测的算法。LSD方法的主要目标是提供精确的结果，同时保持低假阳性率，平均而言，每个图像仅允许一个假警报。论文基于Burns、Hanson和Riseman的方法论，但在此基础上进行了创新。它采用了一种反向验证策略，这是根据Desolneux、Moisan和Morel的理论构建的。LSD版本的亮点在于其自适应性，能够在处理各种图像时展现出稳定且高效的性能，无需针对特定场景进行优化。本文的贡献包括一个详细的算法描述，可能包括对边缘检测、特征提取、候选线段生成、以及验证和筛选过程的深入分析。此外，作者还提供了在线附录、软件工具、数据集和在线演示，以便研究人员和开发者能够直接应用或进一步研究LSD技术。doi:10.5201/ipol.2012.gjmr-lsd是一个指向完整资源的链接，用户可以通过这个链接获取更多信息。 LSD的优势在于其普遍适用性和精度，这对于计算机视觉、图像处理、机器人导航等领域具有重要意义，因为它能帮助系统在实时或近实时的环境下准确识别和理解图像中的线段结构。这项工作可能启发了后续研究者开发更为高效和鲁棒的线段检测算法，以及在诸如自动驾驶、医学图像分析等实际应用中的优化。LSD是一个值得深入学习和实践的重要IT技术。

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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