A Fuzzy Colour Image Segmentation Applied to ... - Semantic Scholar

A Fuzzy Colour Image Segmentation Applied to Robot Vision J. Chamorro-Martínez, D. Sánchez and B. Prados-Suárez

Department of Computer Science and Articial Intelligence. University of Granada, 18071 Granada, Spain E-mail: {jesus,daniel,belenps}@decsai.ugr.es

Abstract

dition.

The growing region techniques [7] and

the split and merge algorithms [1] are two exIn this paper, a new growing region algorithm to

amples of this group. The last type of segmen-

segment colour images is proposed. A region is

tation methods corresponds to the edge based

dened as a fuzzy subset of connected pixels and

algorithms, where a region is dened as a set of

it is constructed using topographic and colour

pixels bounded by a colour contour [11].

information. To guide the growing region pro-

In real images, the separation between regions

cess, a distance dened in the HSI colour space

is usually imprecise.

is proposed. This distance is used both to select

This is one of the main

problems of the crisp segmentation techniques,

the pixels which will be linked in each step of

where each pixel have to belong to an unique

the algorithm, and to calculate membership de-

region. To solve this problem, some approaches

gree of each point to each region. The proposed

propose the denition of region as a fuzzy subset

technique is applied to vision-guided robot navi-

of pixels, in such a way that every pixel of the

gation with the aim of detecting doors in indoor

image has a membership degree to that region

environments.

[3].

Keyword: Colour image segmentation, fuzzy

In this sense, many algorithms have been

developed to segment grey scale images, but the

segmentation, colour distance, robot vision.

fuzzy segmentation of colour images has been paid less attention.

1

Introduction

Other important aspect to take into account is the colour information processing. The most

The image segmentation, view as the process of

common solutions in the literature are (i) com-

dividing the image into signicant regions, is one

bining the information of each band into a sin-

of the most widely used step in image process-

gle value before processing (for example, the

ing.

gradient),

Usually, this operation allows to arrange

or (ii) analyzing each band sepa-

the image in order to make it more understand-

rately and then combining the results (for ex-

able for higher levels of the analysis (for exam-

ample, histogram analysis of each band and sub-

ple, in image database retrieval [4], motion esti-

sequent combination). Apart from the diculty

mation [10] or robot navigation [2, 8]).

to choose an adequate criterion to pool the data, the main problem of these approaches is the

Many types of segmentation techniques have They can be

application of the same combination rule to the

grouped into three main categories correspond-

whole image, without considering the particu-

ing to three dierent denitions of regions: the

larities that appear in the comparison of two

methods in the rst group, called pixel based

colours.

segmentation methods, dene a region as a set of

methods, like those based on growing region,

pixels satisfying a class membership function. In

where the decision in each step depends on the

this category are included the histogram based

dierence between pixels.

been proposed in the literature.

techniques [5] and the segmentation by cluster-

That problem is most signicant in

In this paper, a new growing region algorithm

ing algorithms [12]. The methods in the second

to segment colour images is proposed.

group, corresponding to the area based segmen-

approach, a region is dened as a fuzzy sub-

tation techniques, consider a region like a set

set of connected pixels and it is constructed us-

of connected pixels satisfying a uniformity con-

ing topographic and colour information, i.e., two

1

In our

pixels will be assigned to the same region if they are connected through a path of similar colours. To process the colour information, a distance dened in the HSI colour space is proposed. This distance is used in the growth of a region both (i) to select the pixels which will be linked in each step of the algorithm, and (ii) to calculate the membership degree of each point to each region. Although the proposed algorithm is a multipurpose segmentation technique, in this paper it has been applied to vision-guided robot navigation in indoor environments. Concretely, it has been used to detect doors with the aim of moving a robot to the exit of the room.

2

Colour space

Figure 1: HSI colour space

Many colour spaces may be used in image processing:

RGB, YIQ, HSI, HSV, etc.

[9].

Although the RGB is the most used model to

2.1

acquire digital images, it is well known that it is

Once the colour space is selected, a distance

not adequate for colour image segmentation. In-

between two colour points

stead, other colour spaces based on human per-

pi = [Hi , Si , Ii ]

pj = [Hj , Sj , Ij ] is dened.

For this purpose, we

ception (HSI, HSV or HLS) seem to be a better

Distance between colours

and

rst dene the dierences between components

choice for this purpose [9]. In these systems, hue

as:

(H) represents the colour tone (for example, red



|Hi − Hj | if |Hi − Hj | ≤ π 2π − |Hi − Hj | otherwise dS = |Si − Sj | dI = |Ii − Ij |

or blue), saturation (S) is the amount of colour

dH =

that is present (for example, bright red or pale red) and the third component (called intensity, value or lightness) is the amount of light (it al-

(2)

lows the distinction between a dark colour and with

a light colour).

dH , dS

dI

and

being the distances be-

In this paper, the HSI colour space will be

tween hue, saturation and intensity respectively.

used. This model separate the colour informa-

Based on the previous distances, the following

tion in ways that correspond to the human vi-

equation will be used to measure the dierence

sual system.

between colours:

Moreover, it oers many advan-

tages in a segmentation process (for example,

dC (pi , pj ) =

the use of hue avoids the shading eects). Geo-

h

2

2

(d1 ) + (d2 )

. i1/2 2

(3)

metrically, this colour space is represented as a

d1

cone, in which the axis of the cone is the grey

where

scale progression from black to white, distance

intensities given by

from the central axis is the saturation, and the

M AXI

direction is the hue (gure 1).

mum level of intensity (usually 255), and

images in RGB coordinates, it is necessary to

  0 dHS d2 (pi , pj ) =  dS

dene a relationship between RGB and HSI systems. In this paper, the following transform is applied [9]:

3(G+B) 2R−G−B

d1 = dI / M AXI

with

being a constant equals to the maxi-

d2

is

dened as

Since we use a digital camera to acquire

√

is the normalized dierence between

if pi or pj are achromatic if pi and pj are chromatic otherwise (4)



H = arctan S = 1 − min {R, G, B}/ I I = (R + G + B)/ 3

with (1)

dHS =

r

2

2

(dS ) + (dH /π)



/2

being a

distance which combines information about hue and saturation. Notice that

2

dC (pi , pj ) ∈ [0, 1].

In the previous equation we introduce the notions of chromaticity/achromacitiy to manage two well known problems of the HSI representation: the imprecision of the hue when the intensity or the saturation are small, and the nonrepresentativity of saturation under low levels of intensity.

An often practical solution to solve

this problem is to perform a partition of the colour space based on the chromaticity degree of each point. In equation (4), we propose to split the HSI space into three regions:

chromatic,

semi-chromatic and achromatic (gure 1). This partition is dened on the basis of two thresholds

TI

and

TS

: the rst one,

TI , correspond to

Figure 2: Example of seed points selection

the level of intensity under which both hue and saturation are imprecise; the second one,

Ts , de-

nes the value of saturation under which the hue

In our approach, we have considered that a

is imprecise (but not the intensity). Therefore,

door have at least one corner point in its frame.

pi = [Hi , Si , Ii ] will be achromatic if Ii ≤ TI (black zone in gure 1), semi-chromatic if Ii > TI and Si ≤ TS (grey zone in gure 1), and chromatic if Ii > TI and Si > TS (white a point

Based on the previous assumption, the seed selection is performed in two steps.

band using the Harris method [6]. Afterwards, a

zone in gure 1). In this paper, the thresholds have been xed empirically to and

In the rst

one, corner points are detected in the intensity couple of seeds are put at a distance

TI = M AXI/5

D from each

corner in the direction of its gradient (one per

Ts = 1/5.

each way). In this paper,

D

has been xed to

7

pixels. Figure 2 shows an example where twelve

3

Segmentation method

seed points have been marked corresponding to six corner points (they are showed with green crosses and red points respectively).

Our approach will segment the colour image in

It would be desirable for each door to contain

two steps:

a single seed, but this is not often the case. In1. Firstly, a set of  seed points , noted as

{s1 , s2 , . . . , sq },

deed, it is usual to nd several seeds into the

Θ=

same door (which implies several regions).

will be calculated.

To

solve this problem, the proposed algorithm will 2. Secondly, a collection of fuzzy sets, noted as

discard seeds during the segmentation process.

n o e = Se1 , Se2 , . . . , Seq , will be dened from Θ Θ. For this purpose, a method to calculate

This point will be explained in detail in section 3.3. Although the previous seed selection method

the membership degree of a given pixel to a fuzzy set

Sek

has

will be proposed based on

been

designed

for

a

particular

case,

a

general one could be considered in order to give

topographic an colour information.

more generality to the technique (for example, In the following sections, the previous stages will

seed regions could be located in the local min-

be analyzed in detail.

ima calculated over the gradient of the image). This will be an object of future research.

3.1

Seed points

In the growing region methods, the selection of

3.2

Fuzzy regions

seeds that hopefully may correspond to structural units is a critical step. Due to this paper

In this section, a method to fuzzify a set of seed

is focused in a particular application, i.e., the

points

localization of doors in indoor environments, a

this purpose, a membership function for fuzzy

seed point selection is proposed for this specic

regions is dened (section 3.2.2) based on a dis-

case.

tance between pixels (section 3.2.1).

3

Θ = {s1 , s2 , . . . , sq }

is proposed.

For

Algorithm 1 Algorithm to calculate

dP

Input:

I

Image

of size

N ×M

sv

Seed point Notation:

Contour(L) : N eighbor(pi )

Pixels in the contour of a region : 8-neighborhood of

L

pi

1.-Initialization

dP (sv , sv ) = 0 L = {sv } Card(L) 6= N × M (pin , pout ) = argmin {dC (pi , pj ) / pi ∈ Contour(L) , pj ∈ N eighbor(pi ) \ L} (pi , pj ) dP (pout , sv ) = max [dP (pin , ss ), dC (pin , pout )] (1) L = L ∪ {pout }

2.- While

3.2.1 Let

Q

pixels

Distance between pixels

distance between

ij be the set of possibles paths linking the pi and pj through pixels of the image I .

Given a path

πij ∈

3.2.2

(5) of

πij ,

pr+1 are dC (pr , ps ) is

and

will be high. That

Membership function for fuzzy regions

cost(πij ) = max {dC (pr , pr+1 ) / pr , pr+1 ∈ πij } and

pj ,

the edge, with a high distance between them.

points on the path:

pr

and

points, in the portion of the path that cross over

Q

ij , its cost is dened as the greatest distance between two consecutive

where

pi

is because of the fact that there are consecutive

The membership degree

two consecutive points

a fuzzy region

dened in equation (3)

fv S

v

of a pixel

pi

to

is dened as

and measures the distance between colours. Let

Q ∗ πij ∈ ij be the optimum path between pi and pj dened as the path that link both points with

µSe (pi )

1 − d∗P (pi , sv ) ∗ k=1 (1 − dP (pi , sk ))

µSe (pi ) = Pq v

(8)

minimum cost:

∗ πij =

argmin {cost(πi,j )} πi,j ∈ Πi,j

sv ∈ Θ is the seed point of d∗P (pi , sv ) is dened as where

(6)

Based on the previous denition, the distance between two pixels

pi

and

pj

is dened as the

cost of the optimum path from

dP (pi , pj ) = Let

us

remark

that

pi

to



(paths linking the pixels) and distances between

fuzzy regions

colours. In addition, it is sensitive to the pres-

set of seed

ence of edges in the following sense: if the op-

pj

v=1

ship degree of every point

sv ∈ Θ.

and

Pq

µSe (pi ) = 1. v

Using

the equation (8) we can calculate the member-

dened

in (7) make use of topographic information

pi

1 if pi ∈ Θ , pi 6= sv dP (pi , sv ) otherwise

Let us remark that

(7)

distance

timum path linking two points

and

pj :

∗ cost(πij ) the

d∗P (pi , sv ) =

fv , S

pi ∈ I

to each seed

That allows n us to obtaino the set of

e = Se1 , Se2 , . . . , Seq from Θ points Θ = {s1 , s2 , . . . , sq }.

the

pass

1 Notice that d (p , s ) has been calculated in a prein v P vious step

through an edge (that is, a point which separate two regions), its cost, and consequently the

4

3.3

Algorithm

Given a set of seed points

Θ = {s1 , s2 , . . . , sq },

a growing region algorithm is applied to each

sv ∈ Θ in order to obtain the set of fuzzy ren o e e e S1 , S2 , . . . , Seq . For each sv ∈ Θ, gions Θ = the membership degree µ (pi ) is obtained for Se v

every point of the image using the equation (8).

For this purpose, it is necessary to calculate the distance

dP (pi , sv )

given by equation (7). The

algorithm 1 calculates that distance for all the

I with respect to a given sv ∈ Θ. Its computational complexity is O(nK), where n = N · M is the number of pixels of the image, and K is dened as K = max {N, M } (notice that the maximum size of a contour is 4(N + M )). Due to the alpoints

pi

of an image

seed point

Figure 3: Mobile robot Nomad 200

gorithm have to be applied for each seed point

of them are closed, in the second one there are

Θ, the overall process has a complexity O(qnK), where q is the number of seeds.

an open door in the foreground and a close one

of

of

behind it. In both cases, our approach obtains

As we mentioned in section 3.1, it is usual to

one fuzzy region for each door (gure 4(K-L)).

nd several seeds into the same region. To over-

On the image 4(E), the algorithm generates four

sv ∈ Θ,

regions: one of them corresponds to the back-

verifying

ground, another one is associated to a label, and

This new

the last two regions correspond to the doors. On

step may be introduced in the algorithm 1 with-

the example 4(F) our technique obtains eight

out increase its complexity.

In this paper, the

fuzzy regions, four of them corresponding to the

0.01.

two doors and its frames (gure 4(L)). The num-

come this problem, given a seed point all the seeds of the subset

dP (sv , su ) < C

constant

C

{su }u=1..K

will be eliminated.

has been xed to

ber of seeds was

4

Results

applied to dierent colour images.

respectively.

the results show that our methodology detect

To acquire

the doors without split them in several regions. That reveals that the use of a distance which

connected to the mobile robot Nomad 200 has

consider both colour and topographic informa-

been used (gure 3). the

30

dierent brightness (see the door in image B),

these images, a SONY EVI-401 colour camera

of

and

degradation in the luminance and zones with

The proposed segmentation method has been

Six

9

Although in all the examples there are a

images

used

for

testing

tion improves the results.

our

methodology are showed in gure 4(A-F). To

5

show the results, the segmentation has been defuzzied allocating each pixel to the region for

Conclusions

which it has the highest membership degree.

A new fuzzy methodology to segment colour im-

The examples 4(A-D) show images with a single

ages has been presented. The technique is based

closed door. In all the cases, the proposed algo-

on the growth of regions which are treated as

rithm generates a fuzzy region corresponding to

fuzzy subsets.

the door (the associated crisp region is showed

tion, a distance between pixels has been dened

in blue colour in gure 4(G-J)). The number of

in the HSI colour space.

regions obtained are

5, 10, 4

3

Using that distance

respectively,

and topographic information, the membership

although the number of seeds detected in each

degree of each point to each region has been

case was

12, 34, 14

and

12

and

To manage the colour informa-

respectively.

That

calculated.

Our experiments suggest the com-

reveals the goodness of the method proposed to

bination of the proposed colour distance and

discard seeds during the segmentation process

the growing region process improve the results obtained with the classical segmentation tech-

The examples 4(E-F) correspond to images

niques.

with two doors. Whereas in the rst case both

5

D B C A A

for interactive robots.

G

Proc. IEEE Inter.

Conf. on Intelligent Robots and Systems, 3:2061  2066, 2000. [3] B.M. Cavalho, C.J. Gau, G.T. Herman, and T.Y. Kong. Algorithms for fuzzy segmentation. Proc. Inter. Conf. on Advances

in Pattern Recognition, pages 15463, 1999.

B

H

[4] J.M. Fuertes, M. Lucena, N. Perez de la Blanca,

and J. Chamorro-Martinez.

scheme

of

databases.

colour

image

retrieval

A from

Pattern Recognition Letters,

22:323337, 2001.

C

[5] A. Gillet, L. Macaire, C. Botte-Lococq, and

I

J.G Postaire. Color image segmentation by fuzzy morphological transformation of the 3d color histogram. Proc. 10th IEEE Inter.

Conf. on Fuzzy Systems, 2:824 824, 2001. [6] C.G. Harris and M. Stephens.

D

A com-

bined corner and edge detection. Proc. 4th

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ALVEY Vision Conference, pages 147151, 1988. [7] A. Moghaddamzadeh and N. Bourbakis. A fuzzy region growing approach for segmentation of color images. Pattern Recognition, 30(6):867881, 1997.

E

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[8] E Natonek.

Fast range image segmenta-

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6