A Review of Hough Transform and Line Segment Detection Approaches

Payam S.Rahmdel

, Richard Comley

, Daming Shi

and Siobhan McElduff

Media and Graphics Interdisciplinary Centre, University of British Columbia, Vancouver, Canada

School of Science and Technology, Middlesex University London, London, U.K.

Keywords:

Hough Transform, Line Detection, Line Segmentation.

Abstract:

In a wide range of image processing and computer vision problems, line segment detection is one of the most

critical challenges. For more than three decades researchers have contributed to build more robust and accurate

algorithms with faster performance. In this paper we review the main approaches and in particular the Hough

transform and its extensions, which are among the most well-known techniques for the detection of straight

lines in a digital image. This paper is based on extensive practical research and is organised into two main

parts. In the ﬁrst part, the HT and its major research directions and limitations are discussed. In the second part

of the paper, state-of-the-art line segmentation techniques are reviewed and categorized into three main groups

with fundamentally distinctive characteristics. Their relative advantages and disadvantages are compared and

summarised in a table.

1 INTRODUCTION

Straight-line detection and segmentation are the tech-

niques that allow a machine to extract linear features

from a digital image or sequence of images. Extracted

features, can later be used either by human or machine

to make decisions. Extensive applications of line de-

tection can be found in object recognition (Olson,

2001), shape detection (Ayala-Ramirez et al., 2006),

power line detection (Zhang et al., 2012), and road or

lane detection (Borkar et al., 2012; S.Rahmdel et al.,

2013a). However, despite the signiﬁcant progress,

there is still a rising demand for methods that are

swift in computation and precise in segment detec-

tion in real-world applications. In fact, there is always

a trade-off between these two parameters, i.e. speed

and accuracy, as they are two sides of the same coin.

The Hough transform (HT) (Hough, 1962; Duda

and Hart, 1972) is indeed one of the most popular

methods for the detection of linear and curvilinear

structures. It has demonstrated a robust behaviour to

variant noise and degraded environment. This paper

consists of two main parts. In the ﬁrst part, the HT

and its major research directions and limitations have

been discussed in Section 2 and 3 respectively. In the

second part, state-of-the-art line segmentation tech-

niques have been reviewed and categorized in three

main groups in Section 4. This provides an unique

insight to the advantages and disadvantages of each

approach. Section 5 concludes the paper.

2 HT RESEARCH DIRECTIONS

In general, the HT maps every pixel in a binary image

from its 2D Cartesian coordinates (x, y) to a new 2D

coordinate space (ρ, θ) using the mapping function

ρ = x cosθ + y sin θ (1)

The new coordinate space is called Hough space,

also known as parameter space, and the process is

called mapping from image or feature space to data

or parameter space. We classify major research di-

rections of the HT into four group as discussed in the

following.

2.1 Determine Optimal ρ −θ Resolution

It is important for both the accuracy and computa-

tional efﬁciency to determine a sufﬁcient resolution

for discretising the Hough space. The higher the

resolution the slower the process. Numerous works

have tackled the problem such as using gradient direc-

tion (van Veen and Groen, 1981), interpolation in the

Hough space (Niblack and Petkovic, 1988), dynami-

cally quantised spaces (O’Rourke, 1981), trial and er-

ror (Niblack and Petkovic, 1988), sensitivity function

(Svalbe, 1989), using information from the discreti-

sation of image space (Zhang, 1996), error propaga-

tion (Ji and Haralick, 2001), weight of accumulation

(Nguyen et al., 2008), and non-uniform discretisation

(Duan et al., 2007).

411

S. Rahmdel P., Comley R., Shi D. and McElduff S..

A Review of Hough Transform and Line Segment Detection Approaches.

DOI: 10.5220/0005268904110418

In Proceedings of the 10th International Conference on Computer Vision Theory and Applications (VISAPP-2015), pages 411-418

ISBN: 978-989-758-089-5

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

2.2 Enhance Computational and

Memory Efﬁciency

A large number of distinct variations of the HT were

introduced to advance its performance, mainly focus-

ing on computational complexity and memory efﬁ-

ciency of the standard Hough transform (Kiryati and

Bruckstein, 1991; Walsh and Raftery, 2002; Shapiro,

2006; Fernandes and Oliveira, 2008). Representa-

tive works that appear in most of the related liter-

ature include Stephens’s probabilistic Hough trans-

form (PHT) (Stephens, 1991), progressive probabilis-

tic Hough transform (PPHT) (Matas et al., 2000), ran-

domized Hough transform (RHT) (Xu et al., 1990;

Xu and Oja, 1993), hierarchical Hough transform

(HHT) (Princen et al., 1990), elliptical Gaussian

kernel-based Hough transform (KHT) (Fernandes and

Oliveira, 2008), and regularized Hough transform

(Aggarwal and Karl, 2006).

2.3 HT Peak Detection

A peak isolation algorithm can simply detect the lo-

cal maxima in an N ×N neighbourhood in the Hough

space (Thrift and Dunn, 1983), given an odd number

for N. But determining the optimal value of N can be

problematic. The larger the value of N the higher the

probability of missing adjacent lines, and the smaller

the value of N the higher the probability of repeti-

tious detection. (Princen et al., 1990) used an iterative

global peak detection approach where the globally

highest peak is detected ﬁrst and its corresponding

feature points get eliminated. A HT is then applied

and the process repeats iteratively until all the peaks

are found. Peak detection using self-organising maps

were suggested to reduce the memory requirement of

the HT (Choy et al., 1995). More recent works fo-

cused on generating solid and distinguishable peaks

and the ways to search and identify the true peaks with

minimal false detection (Aggarwal and Karl, 2006;

Shapiro, 2006; Fernandes and Oliveira, 2008; Chao

et al., 2009). These have major problems, in particu-

lar memory inefﬁciency and computational complex-

ity. Detection accuracy is directly proportional to the

memory capacity.

2.4 HT Butterﬂy Analysis

HT butterﬂy analysis considers the peak and the area

surrounding the peak. The term butterﬂy refers to

the shape of the peak and its associated sinusoidal

curves. The combination of sinusoids that repre-

sent the line segment form a butterﬂy shape around

the peak. In fact, such butterﬂies contain valuable

information about a segment’s length, endpoint and

thickness. Because every single pixel of a line con-

tributes to create its HT butterﬂy in a one to one map-

ping process, the resulting butterﬂy is capable of pro-

viding highly accurate line-segment parameters. Ef-

forts have been made to parameterise the HT but-

terﬂy. Representative works include line segment

descriptors (Atiquzzaman and Akhtar, 1995), multi-

segmentation (Kamat-Sadekar and Ganesan, 1998),

peak enhancement using butterﬂy features (Ji et al.,

2011; Furukawa and Shinagawa, 2003), HT neigh-

bourhood (Du et al., 2010; Du et al., 2011), butterﬂy

self-similarity (Tu et al., 2011), and butterﬂy symme-

try (Du et al., 2012).

3 HOUGH TRANSFORM

LIMITATIONS

In general, there are three main problems associated

with the existing HT-based line detection methods:

1. Computational Complexity. Despite the efforts

to improve the efﬁciency of the HT, its heavy

computational cost is still a major concern in real-

time applications.

2. Edge Detection. The HT is applicable only to

binary images, hence accurate edge detection is

an important prerequisite. In addition to imposing

extra computational burden, edge detection may

increase the false detection error; when the noise-

level is high, some of the true feature points in

an image can be ignored as noisy pixels and also

some false points may be recognised as true fea-

ture points.

3. Segment Detection. The HT is incapable of spec-

ifying the endpoints of a line segment. It can

identify only line that pass through the entire im-

age. Therefore segmentation procedures have to

be adapted in order for the HT to identify the end-

points of a segment.

A number of works addressed the edge detec-

tion problem of the HT using Fourier-based HT tech-

niques (Ho et al., 2000; Shi et al., 2010; Zheng

and Shi, 2011). One of the recent advances of

this approach is line detection through the high-

resolution parameter space of multi-layer fractional

Fourier transform (MLFRFT) that results in higher

accuracy of the HT in comparison with the repre-

sentative techniques (Shi et al., 2010). Multiple in-

stances of fractional Fourier transform of the same

image provide more frequency samples that lead to

higher accuracy and better performance. Higher ac-

curacy can be achieved by extending the method to a

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412

more customizable Fourier spectrum for each x and y

axes using the generalised interpolated Fourier trans-

form (GIFT) (Zheng and Shi, 2011). Although the

GIFT suggests a more ﬂexible frequency grid than

the MLFRFT, it does not increase the number of fre-

quency samples. Furthermore, without an adaptable

parameter tuning method, the GIFT suffers from te-

dious trial and error tuning for parameter adjustment.

As mentioned earlier, the HT and its extension are

powerful tools to detect straight lines but not line seg-

ments. These techniques are incapable of detecting

line segments and their endpoints. They can identify

only the location and orientation of the straight lines

passing through the segments. Therefore, an addi-

tional segmentation procedure needs to be performed

to extract the segments from the detected lines. In

the following section, which forms the second part of

this paper, we classify the existing line segmentation

methods, including non-HT-based methods, through

an extensive survey of various approaches.

4 LINE SEGMENTATION

APPROACHES

Popular line segmentation methods used in practical

applications can be classiﬁed into three major groups,

namely, bottom-up, top-down, and domain-crossing

approaches. The bottom-up approach starts with sin-

gle pixels, which grow to segments; whereas the top-

down approach extracts straight lines followed by

segmentation. Domain-crossing methods take into

account both local features, from a bottom-up, and

global features, from a top-down approach. In the fol-

lowing, different characteristics of these approaches

will be surveyed.

4.1 Bottom-up Approach

A bottom-up approach, also known as local approach,

typically begins from the pixel level and the line

grows pixel by pixel to reach the requirement of a

true line segment deﬁned by the algorithm. These ap-

proaches mainly use gradient information to draw the

line. State-of-the-art methods include line segment

detector (LSD) (von Gioi et al., 2010), Edge Draw-

ing (EDLines) (Akinlar and Topal, 2011), and two-

orthogonal direction image scanning (TODIS) (Yang

et al., 2011). Other works use a small matrix of eigen-

values (Guru et al., 2004; Koeck and Zhang, 2002).

One of the ﬁrst bottom-up frameworks was intro-

duced in (Nevatia and Babu, 1980). The algorithm

starts with a convolution-based edge detection fol-

lowed by a line thinning and threshold. Afterwards,

a linear approximation is used to link the edge points

based on their gradient orientations. Khan et al. ex-

tended the concept using a connected component al-

gorithm (CCA) (Kahn et al., 1990). A CCA groups

together adjacent feature points with similar gradi-

ent orientation into line support regions. The algo-

rithm was simple and fast, and hence later became the

core of some of the well-known bottom-up algorithms

such as (Burns et al., 1986) and (von Gioi et al., 2010).

The LSD utilises iterative region-growing process

(Burns et al., 1986). Using image gradient magni-

tude and angle, each region starts from a pixel by set-

ting the region’s angle to the pixel’s gradient direc-

tion. In the next iteration the algorithm compares the

gradient direction of adjacent pixels (in an eight-pixel

neighbourhood) with the region angle. If any neigh-

bouring pixel shares a similar angle within a certain

tolerance it will be added to the growing region. Pix-

els belonging to a particular region will be labelled

to avoid revisiting. In the second phase of the LSD,

Desolneux et al.’s (Desolneux et al., 2000) approach

was used to validate the result. LSD has proven to be

a breakthrough in line segmentation. However, there

are two major problems involved with the LSD’s per-

formance: 1) it is highly sensitive to noise that mis-

leads the region-growing process in connecting the

true segments; 2) it loses accuracy when facing dense

intersecting straight lines.

The TODIS partially addressed the LSD’s short-

comings but pays the price of computational time.

Unlike the LSD, TODIS works with binary images,

thus edge detection has to be applied in the ﬁrst place.

An image is examined in both horizontal and verti-

cal directions. A multi-scale scanning approach was

taken to label each candidate line segment. There are

some issues due to the multi-scale nature of TODIS.

In smaller scales a long segment will mistakenly ap-

pear as a number of short segments. Similarly, in

larger scales a number of collinear short segments

may appear as one continuous long segment. In ad-

dition, unlike the LSD, in TODIS each pixel may be

visited more than once and that has a negative effect

on the computational time.

The EDLines suggests a faster algorithm for line

segment detection. In terms of segmentation accu-

racy, the results of EDLines are similar to the LSD’s;

however, the EDLines processes the same image ten

times faster than the LSD. That makes the EDLines

a perfect candidate for real-time applications. In their

algorithm Akinlar and Topal used the concept of Edge

Drawing (ED) (Topal and Akinlar, 2012) to produce

an accurate edge map. The underlying idea is to use

image gradient information to connect the edge pix-

els that belong to the same segment. Unlike the other

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413

(a) (b) (c)

(d) (e) (f)

Figure 1: Performance of the bottom-up versus top-down

method. (a) Original image of arrow (512×512). (b) Re-

sult of the EHT where long segments are correctly detected.

ments due to background noise. (d) Original image of truck

(911×850). (e) Result of the EHT when it fails to detect

many of the short segments. (f) The LSD successfully de-

tects segments as small as a few pixels length.

edge detection approaches such as the Canny edge de-

tector that generates a binary edge map consisting of

arbitrary pixels, ED results in a number of related and

joint edge pixels in a shape of edge segments. This

pre-processing step plays a key role in EDLines’ suc-

cess by reducing the error caused by broken segments.

However, for the next step, i.e. line segment extrac-

tion they applied a Least Square Line Fitting approach

that causes inaccuracy in noisy situations and breaks

down the long segments.

In general, bottom-up approaches are computa-

tionally simple and easy to implement. Plus, their

local nature is well-suited for taking short line seg-

ments into account. However, their local characteris-

tic fails to maintain the robustness in challenging sit-

uations such as when line segments intersect or when

there are rather long segments in an image. Due to the

effect of noise and image resolution such long seg-

ments appear as a series of disconnected short seg-

ments. This sensitive behaviour in response to noise

appears to be the main drawback of the bottom-up ap-

proaches. Using global information can help solve

such problems. The top-down approach looks at the

problem from a rather different perspective.

4.2 Top-down Approach

In the top-down approach, also known as the global

approach, the true straight-lines are ﬁrstly extracted

before they are broken down into segments. Most

of the proposed HT-based line segmentation methods

use the parameter space information during and after

the HT voting process. For instance, the connective

HT (CHT) utilises a probabilistic approach to investi-

gate the connectively of the feature points (Yuen et al.,

1993). After applying the HT, a ﬁxation point is se-

lected using the information obtained during the accu-

mulation to vote for two 1D accumulators. The CHT

suggest a faster computation than the SHT. To capture

segment coordinates using the fast Hough transform

(FHT), Guil et al. (Guil et al., 1995) kept aside those

feature points that collaborate during the voting pro-

cess. By arranging the image points belonging to the

same straight-line in a respective order, coordinates of

the segment endpoint can be captured by selecting the

points that are further away from each other. Never-

theless, the method is not perfectly designed for line

segments with a negative slope smaller than one or

line segments that are collinear.

The PPHT outperforms the SHT in terms of speed

but results in lower accuracy and a large number of

missing lines (i.e. false negative). Moreover, it re-

quires a large set of parameter adjustments such as

threshold that have to be delicately tuned. The prob-

lem with the accuracy of the PPHT was addressed

later in (Nguyen et al., 2008) at the expense of a high

computation and memory requirement.

The extended Hough transform (EHT) optimized

the traditional 2D HT with a third parameter (Cha

et al., 2006). In this 3D representation of the HT,

each individual column or row of the image space

is plotted to a unique dual 2D HT. Later in (Chung

et al., 2009), an optimized algorithm was proposed

to reduce the execution time during the voting pro-

cess. However, similar to all other HT-based methods,

it requires prior edge detection to enhance the linear

features that brings additional computational time. In

addition, edge detection may cause inaccuracy in seg-

mentation performance by neglecting true segments

due to inappropriate threshold selection.

Global searching algorithms embedded in the HT-

based approaches showed a better robustness to vari-

ant noise. Furthermore, in the case of long segments,

a global view helps to detect long lines as a single

continuous segment, unlike the local approaches that

break them down. As a more tangible example, this

is similar to looking through a window with scratched

glass from a distance without noticing the blurriness

caused by the scratches. However if you get closer to

the glass, the scratches will become more noticeable.

Let us compare the performance of the bottom-up and

top-down approaches using natural images to better

understand their differences. As a signiﬁcant limi-

tation, due to its global nature, the HT usually fails

to detect short segments. Because short lines gen-

erate smaller clusters in the accumulator array and,

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414

therefore, it is more difﬁcult to distinguish these small

peaks from the surrounding peaks.

Bottom-up Vs. Top-down

Performance of the above two approaches can be bet-

ter explained in Figure 1. The ﬁrst row shows an

example where the global approach outperforms the

local method. The image of an arrow degraded with

Gaussian noise has been tested with the EHT, as a rep-

resentative of the top-down approach, and the LSD,

as a representative of the bottom-up approach in Fig-

ure 1(b) and (c), respectively. Although not ﬂaw-

less, the EHT detects the segments, especially the

long lines, with an acceptable accuracy. In contrast,

due to the background noise the LSD fails to detect

the true long segments despite the simplicity of the

image. Instead, it produces a number of collinear

and disjointed segments. The additive noise stops

the growing region from expansion before reaching

the true endpoint. However, in an image with rather

complex texture, without additive noise, in the second

row, i.e. Figure 1(d), the LSD performs better by de-

tecting most of the segments with a greater detail, see

Figure 1(f). In contrast, the global nature of the HT-

based approach is incapable of detecting many of the

short segments as shown in Figure 1(e). This is when

the LSD outperforms the HT-based approach.

From the machine learning viewpoint, the top-

down method is a model selection technique from pa-

rameter space to data or feature space, whereas the

bottom-up method is a regularisation technique from

data or feature space to parameter space. The optimal

solution can be obtained using a two pathway learning

process, in which both top-down model selection and

bottom-up regularisation are considered. This leads

us to the third category of the methods which is the

domain-crossing approach.

4.3 Domain-crossing Approach

The domain-crossing approach utilises the informa-

tion from both the image and parameter space. It

starts by mapping the feature points from the image

to the parameter domain and again using the image-

domain data combined with the parameter domain

data to capture the line segments.

Song and Lyu speed up the HT voting process us-

ing image gradient prediction (Song and Lyu, 2005).

After peak detection in Hough space, a unique line

veriﬁcation method is used by crossing from Hough

space over to the image space. In this way, line thick-

ness can also be distinguished as well as achieving a

reduction in false detection. Despite its accuracy the

method is computationally expensive.

Bandera et al. suggest a more efﬁcient algorithm

in (Bandera et al., 2006). A random window ran-

domised Hough transform is used in the global phase

to construct the Hough space and capture the line pa-

rameters, i.e. the peaks. A unique mean shift clus-

tering technique is utilised afterwards to highlight the

peaks and ﬁnd the potential straight-lines. Crossing

over to the image space, edge pixels that are aligned

with the detected lines are projected onto the lines to

approximate the true line segments in a local merg-

ing procedure. The idea was further improved in

slice sampling weighted mean shift (SSWMS) anal-

ysis (Nieto et al., 2011). Sequential sampling of the

Hough space was suggested to enhance the random

sampling approach as well as a new likelihood func-

tion for the local clustering. The SSWMS shows a

better accuracy than the PPHT with faster execution

time.

In (Berlemont and Olivo-Marin, 2010), the beam-

let transform has been viewed as a special case of the

Radon transform (RT). The underlying idea is to ap-

ply a feature-adapted RT in a quadtree decomposition

manner to obtain a feature-adapted beamlet transform

(FABT). The term feature-adapted comes from the

convolution of basis ﬁlters (i.e. second- or third-order

edge and ridge detectors) with the corresponding im-

age scale prior to RT computation. This ﬁltering high-

lights linear structures of the image and enhances the

accuracy and performance of the task. However, the

FABT is also computationally expensive because all

of the convolutions must be applied in the time do-

main due to the indeﬁnability of the convolution the-

orem for the pseudo-polar Fourier transform.

Unite-and-divide (UND) approach to the Radon

transform also uses the unique property of Fourier

slice theorem, however, in a more efﬁcient way (Shi

et al., 2013). Unlike the FABT, which uses pseudo-

polar Fourier transform, the UND uses multi-layer

fractional Fourier transform to compute a higher res-

olution Radon sinogram. The peaks of the sinogram

will later be divided into a number of sub-spaces for

segment detection. A unique windowing approach

was suggested in (S.Rahmdel et al., 2013b) to isolate

the target segment and decompose the Radon butterﬂy

of each segment separately. The proposed segmen-

tation approach outperformed the LSD and EHT in

terms of the robustness to noise.

A new deﬁnition of the HT neighbourhood was

introduced in (Du et al., 2010; Du et al., 2011). The

neighbourhood of a line segment in the parameter do-

main is deﬁned in a lozenge-like quadrangle to ap-

proximate the neighbourhood of the segment in the

image domain. Instead of two endpoints, authors used

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Table 1: An overview of the different approaches to line segment detection.

Methods Description Advantages Disadvantages

Bottom-up Region growth from pixel to segment. Representative

works include (Nevatia and Babu, 1980), (Kahn et al.,

1990), (Burns et al., 1986), (von Gioi et al., 2010), (Akin-

lar and Topal, 2011), (Yang et al., 2011)

Fast and simple, appro-

priate for real-time appli-

cations

Sensitive to noise, breaks

down lengthy segments

Top-Down Straight-line detection, followed by segment extraction.

Representative works include Hough transform family,

(Yuen et al., 1993), (Guil et al., 1995), (Matas et al., 2000),

(Nguyen et al., 2008), (Cha et al., 2006), (Chung et al.,

2009)

Robust to noise, suitable

for detecting large ob-

jects

Slow, inaccuracy in ex-

tracting short lines

Domain-Crossing Decomposition of lines through transformed space. Rep-

resentative works include (Song and Lyu, 2005), (Ban-

dera et al., 2006), (Nieto et al., 2011), (Berlemont and

Olivo-Marin, 2010),(Du et al., 2010; Du et al., 2011),

(S.Rahmdel et al., 2014; S.Rahmdel et al., 2013b), (Shi

et al., 2013)

Robust to noise, more ac-

curate for short segments

slow

the centre point of a segment. However, this method

suffers from the traditional problem of the HT-based

techniques, i.e. detecting short line segments, where

we face a trade-off in the neighbourhood radius selec-

tion. That means segments with shorter length have

bigger approximation errors in comparison to those

with longer length. In addition, the neighbourhood

approach can result in wrong segment endpoint when

the number of intersecting lines increase in the im-

age. A noise elimination algorithm was proposed in

(S.Rahmdel et al., 2014) as a vital extension to the

neighbourhood approach to remove the negative ef-

fect of non-collinear segments. First, the algorithm

identiﬁes those segments that have a common inter-

section point within the image space. Second, it

ﬁlters out the pixels that are not collinear with the

target segment to signiﬁcantly increase the detection

accuracy in comparison with the neighbourhood ap-

proach. Nevertheless, due to its computational cost,

this method cannot be seen as an appropriate candi-

date for real-time video processing.

5 CONCLUSION

Table 1 gives an overview of the different approaches

to line segment detection discussed in this paper.

The traditional point-to-segment extraction meth-

ods are computationally efﬁcient and simple to imple-

ment. That makes such methods suitable for real-time

object detection and tracking applications. Neverthe-

less, their focus is on local information such as gra-

dient magnitude and angle at pixel level. That makes

noise an effective parameter in degrading their per-

formance. In addition, failing to consider global in-

formation results in discontinuity in the case of elon-

gated segments.

The traditional line-to-segment extraction meth-

ods work the other way around. Their global nature

reduces the effect of noise and increases their robust-

ness. That is also the reason that global approaches

can detect large objects more accurately. However,

neglecting the local gradient information in an image

causes inaccuracy in extracting short line segments.

In addition to that, the computational burden of the

global methods is considerable and such methods are

more appropriate for off-line image processing.

The domain-crossing approaches beneﬁt from dif-

ferent properties in both image space and transformed

space to identify the line segments. They are more

robust to noise and occlusion due to their global na-

ture as well as having higher accuracy for short line

segmentation because of their image-domain line seg-

mentation algorithms. However, they require a deli-

cate design of algorithm to speed up the line extrac-

tion process, and it is not well-suited for real-time ap-

plications.

In conclusion, It is important that the user thor-

oughly understands the problem in order to make the

best use of the available algorithms. Authors hope

that this research could highlight some of the key fea-

tures of existing detection algorithms and encourage

the continuation of the work in this open research

question.

ACKNOWLEDGEMENTS

Authors would like to acknowledge MITACS for pro-

viding the support needed for this research under the

Elevate Fellowship.

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416

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