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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

This article is available online with supple mentary materials,

software, datasets and online demo at

https://doi.org/10.5201/ipol.2012.gjmr-lsd

2015/06/16 v0.5.1 IPOL article class

LSD: a Line Segment Detector

R G  G

, J´´ J

, J-M M

G R

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

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

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

IIE, UdelaR, Uruguay (r andall@fing.edu.uy)

Communicated by Lionel Moisan Demo edited by Rafael Grompone

Abstract

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

to work on any digital image wit hout parameter tuning. It controls its own number of false

detections: on average, one false alarm is allowed per image [

1]. The met hod 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 C ode

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

accepted by IPOL. The sou rce code, 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 fr ame, to a vide o.

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 de scribed he re and included in the

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

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

Keywords: line segment detection, a contrario method

Rafael Grompone von Gioi, J

emie Jakubowicz, Jean-Michel Morel, Gregory Ran dall, LSD: a Line Segment D etector, Image

Processing On Line, 2 (2012), pp. 35–55. https:/ /doi.org/10.5201/ip ol.2012.gjmr-lsd

Rafael Grompone von Gioi, J

emie Jakubowicz, Jean-Michel More l, Gregory Randall

F 1: I   -.

1 Introduction

LSD         . T     line segments.

C                  

 . T,    -          

 1.

T      -        level-line eld,

..,                  

. T,              -

      τ . T     line support regions,   2.

Image Level-line Field Line Support Regions

F 2: L S R.

E line support region (   )      line segment. T 

  (    )     . T   

  line su pport region      ;        

   ,   3 .

E       . T      -

            τ   align ed points, 

 4. T       , n,     aligned points, k, 

            line segment.

T       a contrario    H   

D, M,  M [3, 4]. T - H      (

)        . A,  a contrario  

https://doi.org/ 10.5201/ipol.201 2.gjmr-lsd

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

LSD: a Line Segment Detector

F 3: R     .

2τ

8 aligned points

F 4: A .

   noise  a contrario  H

      . T,  

                  a contrario

. I  ,          a contrario .

I    line segments,        aligned points. W  

   line segment   a contrario        ,   

 line segment. G   i    r,    k(r, i)    aligned

points  n(r)       r. T,        

     

test

· P

[k(r, I) ≥ k(r, i)] (1)

  number of te sts N

test

        , P

 

   a contrario  H

(   ),  I     

. T H

           k(r, I), 

       -    I. T  H

   

            .

N  k(r, I)       I          level-line

eld  H

. N,      k(r, I)     

.

T a contrario  H

  line segment       

   level-line eld    :

• LLA(j)

j∈P ixels

     

• LLA(j)     [0, 2π]

Rafael Grompone von Gioi, J

emie Jakubowicz, Jean-Michel More l, Gregory Randall

 LLA(j)   -    j. U  H

,      

 a contrario    aligned point 

p =

,           LLA(j), k(r, I)   

. T,    P

[k(r, I) ≥ k(r, i)]   



k(r, I) ≥ k(r, i)



= B



n(r), k(r, i) , p



 B(n, k, p)       :

B(n, k, p) =

∑

j=k





(1 − p)

n−j



T number of tests N

test

           

   . N     oriented,       

     :       line segment  . T, 

   A   B          B   A.

T              . I  N × M

   NM × NM  . A,

√

NM     

  . S  5.

NM width values

N x M options

F 5: E     .

T      

(NM )

5/2



T precision p       τ π;          

  ;       2.9. W   γ    p 

 . E    p     . T,   number of tes ts



(NM )

5/2

γ

F,    N  F A (NFA)     r    i



NFA(r, i) = (N M )

5/2

γ · B



n(r), k(r, i) , p





LSD: a Line Segment Detector

T              aligned

points      r  H

. W  NFA       , 

         a contrario , ..,      

. O   ,   NFA   ,        

. A  ε        NFA(r, i) ≤ ε    ε-meaningful

rectangle    .

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

T        ε-meaningful rectangles   a con trario

 H

   ε. T,          ε    

    . I  ,    LSD   H .

T              [1].

Proof W 

k(r) 

k(r) = 

{

κ  N, P



k(r, I) ≥ κ



≤

(NM )

5/2

}



T, NFA(r, i) ≤ ε    k(r, i) ≥

k(r). N,



∑

r ∈R

NFA(r,I)≤ε



∑

r ∈R



NFA(r, I) ≤ ε



∑

r∈R

[

k(r, I) ≥

k(r)

]



B,   

k(r)   

[

k(r, I) ≥

k(r)

]

≤

(NM )

5/2



   #R = (N M )

5/2

γ  



∑

r ∈R

NFA(r,I)≤ε



≤

∑

r ∈R

(NM )

5/2

= ε

   . 

F D, M,  M [3, 4],   ε = 1   . T  

          a contrario ,   .

A,           ε. I,    (  

          ε-meaningful rectangle)  

√

− ε.

S ε         .

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