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### LSD: 一种线段检测器 #### 概述 LSD（Line Segment Detector）是一种高效、精确且自适应的线段检测算法，能够在任何数字图像中检测出亚像素精度的线段。该方法由Rafael Grompone von Gioi、Jérémie Jakubowicz、Jean-Michel Morel 和 Gregory Randall 四位学者共同研发，并在2012年发表于《Image Processing On Line》期刊上。 #### 算法原理与特点 LSD算法的设计理念在于提供一个无需参数调整即可应用于各种不同图像环境中的线段检测方案，并能够有效控制误报率，在每张图像中平均只允许出现一次误报。该算法的基础来自于Burns、Hanson和Riseman提出的方法，并结合了Desolneux、Moisan以及Morel的理论中关于a contrario验证方法的思想。 **核心算法**：LSD的核心在于对边缘像素进行分析，通过追踪可能的线段结构并对其进行优化，最终确定线段的位置和长度。其具体步骤包括： 1. **边缘检测**：首先利用Canny边缘检测器或其他方法获取图像中的边缘像素。 2. **线段追踪**：从每个边缘像素出发，追踪可能构成线段的方向，直到满足停止条件为止。 3. **优化与验证**：对于每一条追踪得到的潜在线段，进一步优化其位置和长度，并利用a contrario原则来验证该线段是否为真正的线段特征。 **a contrario验证**：这是一种统计方法，用于评估特定模式或结构在随机噪声背景下的显著性。在LSD算法中，通过对随机噪声中可能出现的线段分布进行模拟，可以设置阈值来判断检测到的线段是否显著地超出随机噪声水平，从而减少误报。 #### 实现细节 - **版本更新**：文中提到的LSD版本1.6是经过同行评审并通过IPOL接受的版本。相比原版文章中描述的版本1.0，1.6版本在准确性和性能上有所提升。 - **代码实现**：LSD的源代码采用ANSIC语言编写，支持在线演示。此外，还提供了早期版本1.0和1.5的代码供参考。 - **补充材料**：除了算法本身，作者还提供了视频帧级应用示例以及其他版本的LSD代码作为补充材料，这些资料可在IPOL网页上获取。 - **应用场景**：LSD算法不仅适用于静态图像中的线段检测，还可以扩展应用于视频序列的实时处理中，为计算机视觉领域的多个应用领域提供了有力的支持。 #### 结论 LSD算法因其高效性、精确性和广泛的适用性而成为线段检测领域的重要贡献之一。它不仅能够应对复杂的图像背景，还能够在不调整参数的情况下实现稳定的检测效果，为后续的图像分析和处理提供了坚实的基础。无论是学术研究还是实际应用，LSD都展现出了其独特的优势和价值。

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Published in Image Processing On Line on 2012–03–24.

Submitted on 2012–00–00, accepted on 2012–00–00.

ISSN 2105–1232

 2012 IPOL & the authors CC–BY–NC–SA

This article is available online with supplementary materials,

software, datasets and online demo at

http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd

2014/07/01 v0.5 IPOL article class

LSD: a Line Segment Detector

Rafael Grompone von Gioi

, J´er´emie Jakubowicz

, Jean-Michel Morel

Gregory Randall

CMLA, ENS Cachan, France (grompone@cmla.ens-cachan.fr)

TELECOM ParisTech, France (jakubowi@telecom-paristech.fr)

CMLA, ENS Cachan, France (morel@cmla.ens-cachan.fr)

IIE, UdelaR, Uruguay (randall@fing.edu.uy)

Abstract

LSD is a linear-time Line Segment Detector giving subpixel accurate results. It is designed

to work on any digital image without parameter tuning. It controls its own number of false

detections: on average, one false alarm is allowed per image [1]. The method is based on Burns,

Hanson, and Riseman’s method [2], and uses an a contrario validation approach according to

Desolneux, Moisan, and Morel’s theory [3, 4]. The version described here includes some further

improvement over the one described in our original article [1].

Source Code

The ANSI C implementation of LSD version 1.6 is the one which has been peer reviewed and

accepted by IPOL. The source co de, the code documentation, and the online demo are accessible

at the IPOL web page of this article

Supplementary Material

Also available at the IPOL web page of this article

are two older implementations of LSD,

versions 1.0 and 1.5, as well as an example of applying LSD, frame by frame, to a video.

The version 1.0 of LSD code corresponds better to the algorithm described in our original

article [1], and does not include the further improvements described here and included in the

current version; they can be compiled, both, as a C language program or using the Megawave2

framework. Versions 1.0 and 1.5 of the code are non reviewed material.

Keywords: line segment detection, a contrario method

Rafael Grompone von Gioi, J

emie Jakubowicz, Jean-Michel Morel, Gregory Randall, LSD: a Line Segment Detector, Image

Processing On Line, 2 (2012), pp. 35–55. http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd

Rafael Grompone von Gioi, J

emie Jakubowicz, Jean-Michel Morel, Gregory Randall

Figure 1: Image gradient and level-lines.

1 Introduction

LSD is aimed at detecting locally straight contours on images. This is what we call line segments.

Contours are zones of the image where the gray level is changing fast enough from dark to light or

the opposite. Thus, the gradient and level-lines of the image are key concepts and are illustrated in

ﬁgure 1.

The algorithm starts by computing the level-line angle at each pixel to produce a level-line ﬁeld,

i.e., a unit vector ﬁeld such that all vectors are tangent to the level line going through their base

point. Then, this ﬁeld is segmented into connected regions of pixels that share the same level-line

angle up to a certain tolerance τ. These connected regions are called line support regions, see ﬁgure 2.

Image Level-line Field Line Support Regions

Figure 2: Line Support Regions.

Each line support region (a set of pixels) is a candidate for a line segment. The corresponding

geometrical object (a rectangle in this case) must be associated with it. The principal inertial axis

of the line support region is used as main rectangle direction; the size of the rectangle is chosen to

cover the full region, see ﬁgure 3.

Each rectangle is subject to a validation procedure. The pixels in the rectangle whose level-line

angle corresponds to the angle of the rectangle up to a tolerance τ are called aligned points, see

ﬁgure 4. The total number of pixels in the rectangle, n, and its number of aligned points, k, are

counted and used to validate or not the rectangle as a detected line segment.

The validation step is based on the a contrario approach and the Helmholtz principle proposed by

Desolneux, Moisan, and Morel [3, 4]. The so-called Helmholtz principle states that no perception (or

detection) should be produced on an image of noise. Accordingly, the a contrario approach proposes

http://dx.doi.org/10.5201/ipol.2012.gjmr-lsd

http://megawave.cmla.ens-cachan.fr/

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