Efficient edge-preserving algorithm for color contrast enhancement with
application to color image segmentation
Kuo-Liang Chung
a,*,1, Wei-Jen Yang
b, Wen-Ming Yan
ba
Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, No. 43, Section 4, Keelung Road, Taipei, 10672 Taiwan, ROC bDepartment of Computer Science and Information Engineering, National Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei, 10617 Taiwan, ROC
a r t i c l e
i n f o
Article history: Received 17 July 2006 Accepted 22 February 2008 Available online 13 March 2008 Keywords:
CIE color model
Color contrast enhancement Color edge detection Color histogram moment Color image segmentation Color saturation and desaturation Edge-preservation effect
Seed-based region growing approach
a b s t r a c t
In this paper, a new and efficient edge-preserving algorithm is presented for color contrast enhancement in CIE Lu0v0color space. The proposed algorithm not only can enhance the color contrast as the previous
algorithm does, but also has an edge-preservation effect. In addition, the spurious edge points occurred due to the color contrast enhancement can be well reduced using the proposed algorithm. This is the first edge-preserving algorithm for color contrast enhancement in color space. Furthermore, a novel color image segmentation algorithm is presented to justify the edge-preservation benefit of the proposed color contrast enhancement algorithm. Based on some real images, experimental results demonstrate the advantages of color contrast enhancement, edge-preservation effect, and segmentation result in our pro-posed algorithm.
Ó 2008 Elsevier Inc. All rights reserved.
1. Introduction
The purpose of color contrast enhancement is to enhance a col-or image such that the enhanced colcol-or image is mcol-ore colcol-orful than the original color image from the viewpoint of human visual sys-tem[8,21,22]. Previously, many efficient algorithms for color con-trast enhancement have been successfully developed. Based on reducing color ordering approach[2], Zaharescu et al. [31] pre-sented a color contrast enhancement algorithm. Based on the curv-elet transform approach [4,26], Starck et al. [25] presented an efficient algorithm for color contrast enhancement. Recently, a two-step approach, namely the saturation step and the desatura-tion step, was proposed for color contrast enhancement[13,20]. In Lucchese et al.’s algorithm[13], they considered the chromatic-ity diagram[11,14]. In Pei et al.’s algorithm[20], the considered color domain is the modified chromaticity diagram, i.e. the CIE Lu0v0color space[11]. In[20], Pei et al. also developed some
effi-cient methods to the restoration of Chinese paintings.
Among these previously published color contrast enhancement algorithms, although the enhanced color image has good color con-trast enhancement effect, some degree of edge-loss may happen. Due to the edge-loss side effect, some further color image processing
tasks, such as color image segmentation and object recognition, may be degraded. The main motivations of this research are twofold: (1) presenting a new algorithm to come to a compromise between the edge-preservation effect and the color contrast enhancement effect and (2) presenting a novel color image segmentation algorithm to justify the edge-preservation benefit in some application.
In this paper, a new edge-preserving algorithm for color con-trast enhancement is presented. Our proposed algorithm has both advantages of edge-preservation effect and color contrast enhance-ment. Our proposed algorithm consists of three steps: in the first step, a saturation operation is performed to maximize the color contrast effect. In order to speed up the first step, a new history-aid strategy is presented to determine the most possible side of the color gamut triangle in the CIE Lu0v0color space. In the second
step, a desaturation operation is performed to enrich the colorful degree. The above two steps are similar to the previous color con-trast enhancement algorithms in[13,20]. In the third step, an edge-preservation operation is performed to preserve the edge informa-tion while keeping the color contrast enhancement effect as much as possible. In addition, the spurious edge points occurred due to the color contrast enhancement can be well reduced using the pro-posed algorithm. Some experiments are carried out to demonstrate that our proposed algorithm has a good compromise between the edge-preservation effect and the color contrast enhancement. This is the first edge-preserving algorithm for color contrast enhance-ment in color space. Finally, a novel color image segenhance-mentation algorithm is presented to justify the application of edge-preserva-tion effect. In our proposed color image segmentaedge-preserva-tion algorithm,
1047-3203/$ - see front matter Ó 2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jvcir.2008.02.002
* Corresponding author. Fax: +886 2 27301081.
E-mail address:[email protected](K.-L. Chung).
1 Supported by the National Science Council of ROC under Contracts NSC96-2221-E-011-102-MY3, NSC96-2221-E-011-026, and NSC96-2219-E-001-001.
Contents lists available atScienceDirect
J. Vis. Commun. Image R.
we have better segmentation results on our obtained enhanced im-age when compared to those on the previous obtained enhanced image without edge-preservation.
The remainder of this paper is organized as follows: in Section
2, first the notion of CIE Lu0v0 color space is introduced and then
the previous color edge detector, which will be used in our pro-posed color contrast enhancement algorithm, is described. In Sec-tion3, our proposed edge-preserving algorithm for color contrast enhancement and the relevant speedup strategy are presented. In Section 4, a novel color image segmentation algorithm is pre-sented. In Section5, some experimental results are carried out to demonstrate advantages of color contrast enhancement, edge-preservation effect, and segmentation result in our proposed algo-rithm. Finally, some conclusions are addressed in Section6.
2. Preliminaries
Before presenting our proposed color contrast enhancement algorithm, this section introduces two backgrounds, namely the notion of CIE Lu0v0 color space[11]and the previously published
color edge detector by Trahanias and Venetsanopoulos [29]. The two backgrounds will be used in Section3.
2.1. The CIE Lu0v0color space
Suppose the input color image is an RGB color image. First, the transformation from the RGB color space to the CIE Lu0v0 color
space is described. The relevant transformation can be expressed by X Y Z 2 6 4 3 7 5 ¼ 0:49000 0:31000 0:20000 0:17697 0:81240 0:01063 0:00000 0:01000 0:99000 2 6 4 3 7 5 R G B 2 6 4 3 7 5 ð1Þ
In Eq.(1), the component Y is the L component in the CIE Lu0v0color
space. Therefore, the CIE Lu0v0color space can be called the CIE Yu0v0
color space. Based on the values of X, Y, and Z, the two components u0and v0can be obtained by the following equation:
u0¼ 4X
X þ 15Y þ 3Z; v
0¼ 9Y
X þ 15Y þ 3Z ð2Þ By Eqs.(1) and (2), the RGB color space can be transformed into the CIE Lu0v0color space.
Considering only the two components u0and v0,Fig. 1depicts the
so called spectral locus of the u0v0chromatic diagram and the spectral
locus is depicted by the exterior curve. Within the spectral locus, the triangle area denotes the color space which can be displayed by the CRT monitor. This triangle area is commonly called the color gamut
triangle. The three corners of the color gamut triangle are denoted by the three points R0, G0,and B0 which are corresponding to ðu0
R0;v0R0Þ
¼ ð0:4507; 0:5229Þ, ðu0
G0;v0G0Þ ¼ ð0:1250; 0:5625Þ, and ðu0B0;v0B0Þ ¼
ð0:1754; 0:1579Þ. The interior point W ¼ ðu0
W;v0WÞ ¼ ð0:1978;
0:4683Þ is defined as the white point[11]. Since the colors lain around the white point W are regarded as achromatic colors, it is infeasible to enhance these colors which are very near to the point W.
2.2. Color edge detector
In this subsection, the color edge detector by Trahanias and Venetsanopoulos[29]is described and it will be used in our pro-posed edge-preserving algorithm for color contrast enhancement although some other color edge detectors[23,28,32]can also be considered.
Suppose the window mask used in the color edge detector is of size w w and the w2color pixels covered by the window mask
are denoted by the set P ¼ fP1;P2; . . . ;Pw2g. Usually, w is selected
to 3 or 5. The color contrast or difference expressed in the CIE Lu0v0 color space is more fruitful than that in the RGB color space [11]. Thus, instead of measuring the color difference in RGB color space, we estimate the color difference in the CIE Lu0v0color space.
The three color components of each color pixel are denoted by Pi¼ ðu0i;v0i;YiÞ.
Based on the vector order statistic and the R-ordering concept
[3], the color edge detector[29] consists of the following three steps:
Step 1: Sum up the color distances between each color pixel Pi
and the other color pixels covered by the window mask. For color pixel Pi, 1 6 i 6 w2, the resulting distance is
given by di¼Pw
2
k¼1kPi Pkk; i ¼ 1; 2; . . . ; w2, where k k
represents an appropriate vector norm. Step 2: Sort these w2distances d
1;d2; . . . ;and dw2. Suppose these
sorted w2ascending distances are d
ið1Þ;dið2Þ; . . . ;and diðw2Þ
for 1 6 ið1Þ; ið2Þ; . . . ; iðw2Þ 6 w2. Among these w2indices,
Pið1Þ is the color pixel with the minimal distance dið1Þ;
Piðw2Þ sometimes can be viewed as the outlier pixel in
the w2color pixels.
Step 3: Based on the robustness consideration, compute the min-imum vector dispersion (MVD) which is given by
MVD ¼ min j Pi wð 2jþ1Þ Xn m¼1 PiðmÞ n ( ) ; j ¼ 1; 2; . . . ; k; k; n < w2:
In[29], k and n are selected to 3 or 4 empirically. When the value of MVD is greater than the specified threshold, the central pixel of the concerned w w subimage is determined to be an edge pixel; otherwise, it is determined to be a non-edge pixel.
3. The proposed edge-preserving algorithm for color contrast enhancement
This section presents our proposed novel algorithm which can come to a compromise between the edge-preservation (including spurious edge-reduction) consideration and the color contrast enhancement. In what follows, we first describe the main concepts used in our proposed algorithm, and then a speedup strategy is gi-ven to improve the proposed algorithm.
3.1. The main concept
As mentioned above, our proposed edge-preservation algorithm for color contrast enhancement has two considerations, namely: (1) keeping the edge information after enhancing the color image
in the CIE Lu0v0color space and (2) reducing the created spurious
edges due to the side effect of the color contrast enhancement. For simplifying the exposition, in what follows, we only focus on the presentation of keeping the edge information after enhancing the color image in the CIE Lu0v0color space. In what follows, we will
point out how to reduce the created spurious edges due to the side effect of the color contrast enhancement.
In order to keep the edge information in the original RGB color image as the edge-preservation reference, given an RGB color im-age I, the edge map is first obtained by using the previous edge detector which has been introduced in Section3.2. For exposition, the obtained edge map is expressed by IE where IEðx; yÞ ¼ 1ð¼ 0Þ
means the color pixel Iðx; yÞ is an edge (non-edge) pixel. Our pro-posed color contrast enhancement algorithm mainly consists of three steps, namely: the saturation step, the desaturation step, and the edge-preservation step.
3.1.1. The saturation and desaturation steps
Here, the saturation step and the desaturation step are described. The two steps are adopted from the previous algorithms
[13,20].
Given an input color pixel C = ðu0
C;v0C;YÞ as shown inFig. 2(a), in
the saturation step, the color pixel C moves forward along the line WC
!. When the color pixel C intersects the line segment B0R0, the
intersection point is called the maximally saturated color Cs.
Be-cause the saturation step affects only chromatic components u0
and v0, C and C
sare associated with the same brightness
compo-nent Y where Csis represented by ðu0Cs;v
0 Cs;YÞ.
When all color pixels of a color image have been maximally sat-urated, the image appears rather unnatural because the displayed colors are only confined at the boundary of the gamut triangle. Therefore, the desaturation step is proceeded to overcome the chromatic information reduction problem in the saturation step.
Fig. 2(b) illustrates the concept of desaturation step in order to en-rich the colorful degree of the color image. Instead of maximizing the color contrast by using the color point Cs, the modified color
point Cds is used according to the Center of Gravity Law of Color
Mixture[11]. The three components of the modified color point Cds¼ ðu0Cds;v 0 Cds;YCdsÞ are determined by u0 Cds¼ u0 W YW v0 Wþ u 0 Cs Y v0 Cs YW v0 Wþ Y v0 Cs ; v0 Cds¼ YWþ Y YW v0 Wþ Y v0 Cs YCds¼ Y þ YW
where YW¼ kY; Y is the mean luminance of the color image and k is
a factor to control the luminance.
Since the determined modified color point Cds may generate
some degree of edge-loss or add spurious edge points, in next step, an efficient strategy is presented to solve the edge-loss problem occurred in the previous color contrast enhancement method
although the proposed strategy can be slightly modified to solve the edge-addition problem. The proposed strategy can keep a good compromise between the color contrast enhancement and the edge-preservation consideration.
3.1.2. The edge-preservation step
When IEðx; yÞ ¼ 1, i.e. the original color pixel Iðx; yÞ is an edge
pixel, it is necessary to examine whether the edge information of the original color pixel has been lost after performing the satura-tion and desaturasatura-tion steps. When IEðx; yÞ ¼ 0, it is necessary to
examine whether the mapped color pixel becomes a spurious edge pixel after performing the saturation and desaturation steps.
Fig. 3is used to depict the concept of our proposed edge-pres-ervation step. After performing the saturation and desaturation steps, instead of enhancing the color contrast by using Cds which
may lose the edge information, conceptually the edge-preserving color point Ces¼ ðu0Ces;v
0
Ces;YCesÞ is determined to come to a
com-promise between the edge-preservation and the color contrast enhancement. Here the determined color point Cesis the final
en-hanced color point not only preserving the edge information in the RGB color space inherited from the corresponding pixel, but also enhancing the color contrast as maximal as possible. How to determine the enhanced color point Ces from the modified color
point Cdswill be described in the following paragraphs.
Suppose the window mask used in the adopted color edge detec-tor is of size 3 3. According to row-major scanning order, the sub-image covered by the window mask is illustrated inFig. 4where the symbol P denotes the enhanced color pixel which has been pro-cessed by using our proposed edge-preserving algorithm for color contrast enhancement; the symbol C denotes the current color pixel being processed and the symbol U denotes the color pixel to be pro-cessed. The previous color edge detector is applied to the subimage as shown inFig. 4to determine whether the current color pixel is an edge pixel or not. For convenience, let ‘‘EðCÞ ¼ 1” denote that the cur-rent color pixel is an edge pixel; otherwise, let ‘‘EðCÞ ¼ 0” denote that the current color pixel is a non-edge pixel.
For the current color pixel, if the condition EðCÞ ¼ 1 holds, the previous color edge detector is used to determine whether the cur-rent color pixel Cdsis an edge pixel or not. If the current color pixel
Cdsis an edge pixel, Cdsis the final enhanced color and we perform
the assignment Ces¼ Cds; otherwise, the enhanced color point Ces
should be determined further by the help of the modified color point Cds.
Suppose the modified color point Cdsis not an edge pixel.Fig. 5
depicts the binary alternative search direction in our proposed edge-preservation step to determine the enhanced color point Ces, where d denotes the first movement distance and is set to kCsCdsk
5 , empirically. By running the previous color edge detector, if
the current color pixel Ctð1Þis an edge pixel, where kCtð1ÞCdsk ¼ d,
we move it to the next color pixel Ctð2Þwhich is the near point of
Fig. 2. The first two steps in our proposed algorithm. (a) The saturation step. (b) The
Cdsand examine whether the color pixel Ctð2Þis an edge pixel or
not, where kCtð1ÞCtð2Þk ¼2d. If Ctð2Þis an edge pixel, we move it to
the pixel Ctð3Þ; otherwise, we move it to the pixel C0tð3Þ. The binary
alternative search in the edge-preservation step is repeated until finding an edge pixel which near the point Cdsas close as possible
or the number of testing color pixels along the binary alternative search path is over the specified bound.
According to the above way, the color edge pixel is found at the right side of Cds. Finally, we select the minimum one from the two
found edge pixels at both side of Cdsas the enhanced color point
Ces. Consequently, it comes to a compromise between the color
contrast effect and the edge-preservation effect. For finding the en-hanced color point Ces, our proposed binary alternative search
scheme has 40% execution–time improvement ratio ¼TLASTBAS
TLAS
, where TLASdenotes the time required in linear alternative search
and TBAS denotes the time required in binary alternative search,
when compared to the linear alternative search scheme.
For the current color pixel, if the condition EðcÞ ¼ 0 holds, after running the previous color edge detection, on the mapping color point Cds, we further test whether the mapped color point becomes
a spurious edge point or not. If yes, the binary alternative search is repeated until finding the non-edge pixel which is nearest to Cds; if
no, the mapped point is set to Cds.
If we do not take the edge-preservation into consideration, ide-ally the modified color point Cdsis the good choice for the purpose
of color contrast enhancement. In order to make the distance be-tween the enhanced color point Cesand the modified color point
Cds as small as possible, the search direction of our approach is
not always toward the white point.
After performing the previous edge-preservation step for all col-or pixels within the gamut triangle, given a colcol-or pixel ðu0;v0;YÞ
within the gamut triangle, the mapped color pixel ðr; g; bÞ in the RGB color domain can be obtained by first solving the following equation: X ¼ xðX þ Y þ ZÞ Y ¼ Y Z ¼ zðX þ Y þ ZÞ ð3Þ where x ¼ 9u0 6u016v0þ12, y ¼ 4v 0 6u016v0þ12, z ¼ 1 x y, and X þ Y þ Z ¼Yy.
Next, by solving the inverse of Eq.(1), the obtained values of X, Y, and Z in Eq.(3)can be transferred into the values of r, g, and b.
Based on the original Peppers image (see Fig. 6(a)),Fig. 6(b) illustrates the enhanced color image obtained by using the
previ-ous color contrast enhancement algorithm. Fig. 6(c) illustrates the enhanced color image obtained by using our proposed color contrast enhancement algorithm. It is observed that both enhanced color images, Fig. 6(b) and (c), have the same color contrast enhancement effect and they looks more colorful than that in
Fig. 6(a). Besides the color contrast enhancement effect, our pro-posed algorithm has a good compromise between the edge-preser-vation effect and the color contrast enhancement effect. This good compromise will be demonstrated and evaluated in Section 5. Especially, the enhanced color image obtained by using our pro-posed edge-preserving algorithm plays a good input role for some applications, such as the color image segmentation.
3.2. The speedup strategy
In this subsection, a speedup strategy is presented to improve the computational effort in the saturation step of our proposed col-or contrast enhancement algcol-orithm.
In order to quickly obtain the maximally saturated color Cs
when giving the input color pixel C, an Oð1Þ-time intersection point determination strategy is presented. Considering only the two chromatic components u0and v0, first assume the intersection point
between line WC!and the gamut triangle is on the segment B0R0
(seeFig. 2(a)) where the two end points B0and R0have the
chro-matic values ðu0
B0;v0B0Þ and ðu0R0;v0R0Þ, respectively. It is known that
W ¼ ðu0
W;v0WÞ is the white point. According to this assumption,
we have the following two equalities: u0
Wþ sðu0C u0WÞ ¼ u0R0þ kðu0B0 u0R0Þ
v0
Wþ sðv0C v0WÞ ¼ v0R0þ kðv0B0 v0R0Þ:
ð4Þ
Eq.(4)can be rewritten by su0 C u0W k u0 B0 u0R0 ¼ u0 R0 u0W sv0 C v0W k v0 B0 v0R0 ¼ v0 R0 v0W: ð5Þ
After solving Eq. (5), if the values of s and k satisfy s P 1 and 0 6 k 6 1, the above assumption, i.e. the intersection point between
Fig. 6. The color contrast enhancement results for Peppers image. (a) Original im-age. (b) The enhanced image by using the previous algorithm. (c) The enhanced image by using our proposed algorithm.
Fig. 4. One 3 3 subimage covered by the window mask.
line WC!and the gamut triangle, is true. If so, the chromatic compo-nents u0
Csand v
0
Cs of the maximally saturated color Cscan be
com-puted by the following equation: u0 Cs¼ u0Wþ s u0C u0W v0 Cs¼ v0Wþ s v0C v0W :
Otherwise, if the values of s and k violate the conditions, s P 1 and 0 6 k 6 1, we try to examine next assumption: assume the intersec-tion point between line WC!and the gamut triangle is on the seg-ment B0G0, and so on.
Besides the above strategy to speedup the determination of point Csin saturation step, now our proposed history-aid strategy
is presented to predict the most possible side of the gamut triangle such that the intersection point of WC!and the gamut triangle is on that side. In general, the intersection point between WC and the gamut triangle may be on the side R0B0, B0G0, or G0R0. Heuristically,
each side of the gamut triangle must be examined one-by-one to test whether the intersection point is on that side or not. However, due to the color locality property, especially in smooth regions, moving the point C forward along the line WC!will usually intersect the same side which has been determined in the iteration. If the proposed history-aid strategy does not work, the other two sides of gamut triangle are further checked. Experimental results show that the proposed Oð1Þ-time intersection point determination strategy and the history-aid strategy have a good computation-saving effect and in average 20%¼ðold timenew timeÞold time 100% execu-tion-time improvement ratio is obtained when compared to the heuristic approach for determining the side of gamut triangle. Be-sides the u0v0 chromatic domain in the gamut triangle, luminance
ðYÞ channel may be considered in our proposed history-aid strategy.
Based on the four testing images, the Pepper image, F14 image, Table Tennis image, and Akyio image (see Section5), in average, the total execution-time required in the previous color contrast enhancement algorithm to map the RGB color domain into the CIE Lu0v0 domain is 0.149 s. Based on the same testing images, in
average, the total execution-time required in our proposed edge-preserving algorithm without considering the binary alternative search strategy and the history-aid strategy is 0.788 s. Employing the two speedup strategies in our proposed edge-preserving algo-rithm is 0.347 s. In summary, the time required in any one of the above three concerned algorithms is much less than 1 s. Once the previous enhanced color images and our obtained enhanced color images have been obtained, they can be reused in any color image operations such as edge detection, segmentation, etc. Based on the same testing images, experimental results demonstrate that in average, the execution-time required in color image segmentation (see next section) is more then 3 s. Therefore, the time required in color contrast enhancement could be ignored when compared to the ones in color image operations.
4. Color image segmentation application
In this section, our proposed novel color image segmentation algorithm, which uses the enhanced color image obtained in Sec-tion3to be the input image, is presented. In Section5, some exper-iments will be carried out to demonstrate the edge-preserving benefit in our proposed color image segmentation algorithm.
Our proposed color image segmentation algorithm consists of two major phases, namely the seed-based region growing phase and the merging phase. Maybe some other color segmentation algorithms[30,12,6]also have better segmentation results on our obtained enhanced color image when compared to those on the previous obtained enhanced color image without edge-preservation.
4.1. The seed-based region growing phase
Our proposed seed-based region growing phase is modified from the previous ones in[1,7,16,24]. In what follows, two major stages of the seed-based region growing phase, namely the seed determination stage and the region growing stage, are presented. 4.1.1. The seed determination stage
The seeds used in the seed-based region growing phase are the homogeneous pixels of the input color image and are selected when their homogeneity levels are greater than the threshold. The homogeneity level of one pixel in the image is determined by its standard deviation and discontinuity of the subimage cov-ered by the w w window mask. Let Cijdenote the color
informa-tion of pixel Pijat location ði; jÞ in the image and the window mask
be centered at ði; jÞ. The standard deviation of each component of Pijcan be obtained by rCij¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 w2 Xiþðw1Þ 2 m¼iðw1Þ 2 Xjþðw1Þ 2 n¼jðw1Þ 2 Cmn lij 2 r
where Cij2 fY; u0;v0g and
lij¼ X iþðw1Þ2 m¼iðw1Þ2 X jþðw1Þ2 n¼jðw1Þ2 Cmn:
The discontinuity of pixel Pijis measured by its neighboring edge
information. By Eq.(3), the calculated value of MVD is assigned to tTij, i.e. tTij¼ MVD: Let rPij¼ rTij rmax tPij¼ tTij tmax
where rTij¼ rYþ ru0þ rv0, rmax¼ MaxfrTijg, and tmax¼ MaxftTijg. It
is easy to check that the values of rPij and tPij are within the range
[0, 1]. When rPij and tPij are large, the pixel Pijcould be defined to
be a non-homogenous pixel. Therefore, the homogeneity level of pixel Pijis defined as
HPij¼ 1 ðrPij tPijÞ:
When the value of HPijfor pixel Pijat location ði; jÞ is greater than the
specified threshold TH, the pixel Pijis selected to a seed which will
be used in the second stage of this phase. Let TH¼ 0:99, the blue
color pixels shown inFig. 7are the determined seeds in the en-hanced color Peppers image as shown inFig. 6(b).
Fig. 7. The determined seeds as shown in blue colors of the enhanced Peppers image.
4.1.2. The region growing stage
After determining the seeds from the enhanced color image, the region growing stage is followed to gather the relevant pixels for each region. The region growing stage consists of the following four steps:
Step 1: Connect the adjacent seeds and assign the same region number to them. That is, adjacent seeds are treated as a large seed of the image.
Step 2: Examine the connected neighbors of the seeds and mark the pixels which are not seeds. Then, compute the color contrast between each marked pixel and its adjacent regions, each region only consisting of seeds. The color contrast level between the marked pixel Pmand its
adja-cent region Riis measured by
C Pð m;RiÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi YPm YRi 2 þ u0 Pm u 0 Ri 2 þ v0 Pm v 0 Ri 2 r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Y2 Pmþ u 02 Pmþ v 02 Pm q where YRi, u 0 Ri, and v 0
Riare the mean values of the three CIE
components of region Ri.
Step 3: Select the minimum one among these calculated color contrast levels and its associated Pm and Ri. Then, put
the associated marked pixel Pm into the region Ri and
remark the connected neighbors of Pm.
Step 4: According to the color contrast level measure defined in Step 1, update the color contrast level between the updated region Ri and its adjacent marked pixels. Then,
repeat Step 3 until all pixels in the image have found their regions.
The above seed-based region growing phase may over-segment the enhanced color image. After performing the above seed-based region growing phase on the enhanced Peppers image as shown in
Fig. 6(b),Fig. 8illustrates the related over-segmented result. Due to this over-segmentation problem, it is necessary to merge the sim-ilar regions in the over-segmented image further. In next subsec-tion, our proposed merging phase is presented to alleviate this over-segmentation problem. In our proposed merging phase, the fruitful edge information preserved in the enhanced color image, which has been obtained by using our proposed edge-preserving algorithm for color contrast enhancement, can result in a more desirable segmentation result.
4.2. The merging phase
This subsection presents our proposed novel merging phase. Let Riand Rjbe two adjacent regions. For measuring the difference
be-tween the two adjacent regions Riand Rj, we first compute the
dif-ference between the centroid and the geometric center of Rk
ð¼ Ri[ RjÞ, the color moment difference between Ri and Rj, and
the boundary edge information between Ri and Rj. Since the
en-hanced color image obtained by our proposed edge-preserving algorithm for color contrast enhancement has more true edge information, we believe that our proposed merging phase used in color image segmentation does inherit the edge-preserving benefit and it will lead to better color image segmentation result.
The centroid of Rkð¼ Ri[ RjÞ[8]is given by
CRk;x;CRk;y ¼ m10 m00 ;m01 m00
where m10¼P Pðx;yÞ2Rkxf ðx; yÞ, m01¼
P P
ðx;yÞ2Rkyf ðx; yÞ, and m00
¼P Pðx;yÞ2R
kf ðx; yÞ; f ðx; yÞ denotes the relevant three components
of the enhanced color image. The geometric center of Rkis given by
GCRk;x;GCRk;y ¼ m GC 10 mGC 00 ;m GC 01 mGC 00 where mGC 10 = P P ðx;yÞ2Rkxf 0 ðx; yÞ, mGC 01 ¼ P P ðx;yÞ2Rkyf 0 ðx; yÞ, and mGC 00¼ P P ðx;yÞ2Rkf
0ðx; yÞ. From the above defined centroid and
geo-metric center, the difference between the centroid and geogeo-metric center of Rkis measured by DCGC Ri;Rj ¼ k GCRk;x;GCRk;y CRk;x;CRk;y k: ð6Þ
The larger the difference between the centroid and geometric cen-ter of Rkis, the more improper the merge of Riand Rjis.
Besides the difference between the centroid and geometric cen-ter of Rk, the color difference between Riand Rjis also employed to
be a factor in the proposed merging phase. Based on the color do-main histogram moments[15,18,27], our proposed color domain difference between Riand Rjis given by
CD Ri;Rj ¼ kCCRi CCRjk ð7Þ where CCR¼ CCð R;u0;CCR;v0Þ ¼ M R 10 MR 00 ;MR01 MR 00 , MRpq¼ P P ðu0;v0Þ2Ru0pv0q DR Hðu0;v0Þ, and D R
Hðu0;v0Þ denotes the number of pixels in the RGB
col-or image where these related pixels are mapped to the same region R in ðu0;v0Þ–domain. In Eq.(7), CC
R¼ ðCCR;u0;CCR;v0Þ denotes the color
domain centroid of region R; MR
pqdenotes the color histogram
mo-ment of region R; DR
Hðu0;v0Þ denotes the relevant two-dimension
histogram.
Besides Eqs. (6) and (7), the boundary edge information be-tween Riand Rj [17]is definitely used to measure the difference
of two adjacent regions in the proposed merging phase. It has been defined that the edge map obtained from the enhanced color image I is denoted by IE where IEðx; yÞ ¼ 1 (¼ 0) means the color pixel
Iðx; yÞ is an edge (non-edge) pixel. Let BR
i;Rj
ð Þ be the set of pixel loca-tions which constitute the posiloca-tions of boundary between two re-gions Riand Rj. The ratio of the edge information occupied on the
boundary can be expressed by
cE Ri;Rj ¼ P ðx;yÞ2B Ri;Rj ð Þ IEðx;yÞ jBR i;Rj ð Þj ð8Þ where jBR i;Rj
ð Þj denotes the number of pixels on the boundary BðRi;RjÞ.
By Eqs. (6)–(8), when the values of DC
GCðRi;RjÞ, CD R i;Rj and
cE Ri;Rj
are larger, the two adjacent regions Riand Rjare more
dif-ferent from each other. Integrating the above three difference mea-sures, the difference between two adjacent regions Riand Rjcan be
defined by DTðRi;RjÞ ¼ w1 DC GCRi;Rj DC GCðmaxÞ þ w2 CD R i;Rj CD ðmaxÞþ w3 cE Ri;Rj ð9Þ
Fig. 8. The over-segmented result after performing the seed-based region growing phase on the enhanced Peppers image inFig. 6(b).
where DC
GCðmaxÞ¼ Maxi6¼jfDCGCRi;Rjg and CDðmaxÞ¼ Maxi6¼jfCD R i;Rjg; DC GCðRi;RjÞ DC GCðmaxÞ , CD Ri;Rj ð Þ CDðmaxÞ, and cE Ri;Rj
are within the range ½0;1; empirically, the three weights are set to w1¼ 1, w2¼ 1:8, and w3¼ 2:5.
Based on the above description, in summary, our proposed merging phase consists of the following three steps:
Step 1: For each region Ri, consider its all adjacent regions Rj0s
and compute all the differences DTRi;Rjs by Eq.(9).
Step 2: Select the minimum difference DT Ri;Rj
among these cal-culated DT Ri;Rj
s obtained from Step 1. When the selected minimal DTRi;Rj is greater than the specified
threshold or the current segmented image only contains a region, output the segmentation result and stop this phase. Otherwise, go to Step 3.
Step 3: Merge Riand Rjinto a region. After merging Riand Rj, by
Eq.(9), update all the related differences DTðRi;RkÞs and
DT Rj;Rk
s for all the concerned two adjacent region-pairs (Ri,Rk) and (Rj,Rk). Go to Step 2.
After presenting two phases of our proposed color segmenta-tion algorithm, next secsegmenta-tion will illustrate the segmentasegmenta-tion result by running our proposed color segmentation algorithm on our ob-tained enhanced color image and compare it with the segmenta-tion result by running our proposed color segmentation algorithm on the enhanced color image obtained by the previous color contrast enhancement algorithm.
5. Experimental results
In this section, some experimental results are demonstrated to show that our proposed algorithm has a good compromise between the edge-preservation effect and the color contrast enhancement effect when compared to the previous algorithm
[13,20]. Besides, some experiments are carried out to demonstrate the edge-preservation benefit of our proposed color image segmentation algorithm when running it on the enhanced color image obtained by the proposed color contrast enhancement algorithm. For convenience, the enhanced color image obtained by the previous color contrast enhancement algorithm is called the previous obtained enhanced color image; the enhanced color image obtained by our proposed color contrast enhancement algorithm is called our obtained enhanced color image.
Fig. 9(a) illustrates the edge map of the original Peppers image shown inFig. 6(a). The edge map of the previous obtained en-hanced color Peppers image is illustrated inFig. 9(b). The edge map of our obtained enhanced color Peppers image is illustrated inFig. 9(c) and it is observed that our obtained edge map of each pepper is quite similar to that in the original edge map (see
Fig. 9(a)). However, the edge map inFig. 9(b) is some different from the original edge map. Quantitative demonstrations (seeFigs. 11, 12, and Tables 1 and 2) will be given later to explain why
Fig. 9(c) is better thanFig. 9(b). Besides the color contrast enhance-ment effect existed in the previous color contrast enhanceenhance-ment algorithm and our proposed one (seeFig. 6(b) and (c)), the edge– preservation effect of our proposed color contrast enhancement algorithm is better than that of the previous enhancement algorithm.
After demonstrating the color contrast enhancement benefit of both algorithms and the edge-preservation benefit of our proposed algorithm over the previous algorithm, let us take F14 color image (seeFig. 10(a)) as the second testing image.Fig. 10(b)–(f) demon-strate the edge map of the original color F14 image after running the previous color edge detector, the previous obtained enhanced color image, the edge map of the previous obtained enhanced
image, our obtained enhanced color image, and the edge map of our obtained enhanced image, respectively. Similar to the perfor-mance evaluation for color Peppers image, experimental results for color F14 image also reveal that the previous and our proposed color contrast enhancement algorithms make the original F14 im-age more colorful. In addition, our proposed enhancement algo-rithm has better edge-preservation effect when compared to the previous enhancement algorithm.
Next, we adopt the set of edge–losing pixels and the set of edge–adding pixels to demonstrate the edge–preservation effect of our proposed color contrast enhancement algorithm. It has been defined that the edge map of the original image is expressed by IE
and IEðx; yÞ ¼ 1 ð¼ 0Þ denotes that the color pixel Iðx; yÞ is an edge
(non–edge) pixel. Let IEEdenote the edge map when running the
previous color edge detector on the related enhanced color image.
Fig. 9. The edge maps of color Peppers images. (a) The edge map of original image. (b) The edge map of the previous obtained enhanced image. (c) The edge map of our obtained enhanced image.
Table 1
Edge-loss ratios for the concerned two color contrast enhancement algorithms Previous algorithm Our proposed algorithm
Peppers (%) 31.17 9.34 F14 (%) 31.69 12.92 Table Tennis (%) 23.93 4.75 Akiyo (%) 18.72 5.10 Average (%) 24.78 7.59 Improvement ratio (%) 69.37 Table 2
Edge-add ratios for the concerned two color contrast enhancement algorithms Previous algorithm Our proposed algorithm
Peppers (%) 10.18 8.92 F14 (%) 7.08 5.15 Table Tennis (%) 11.77 11.63 Akiyo (%) 15.30 14.27 Average (%) 11.08 9.99 Improvement ratio (%) 9.84
The set of edge-losing pixels in the resulting edge map is denoted by Nel. Each pixel in the set of edge–losing pixels must satisfy
IEðx; yÞ ¼ 1 and IEEðx; yÞ ¼ 0. On the other hand, one pixel is called
the edge-losing pixel when the pixel is an edge pixel in the original color image, but the pixel at the same position in the enhanced im-age is a non-edge imim-age pixel. Alternatively, the set of edge-adding pixels in the resulting edge map is denoted by Nea, and each pixel
in the set of edge–adding pixels must satisfy IEðx; yÞ ¼ 0 and
IEEðx; yÞ ¼ 1.Fig. 11(a) and (b) illustrate the set of edge–losing
pix-els Nelfor the edge map of the previous obtained enhanced color
Peppers image (seeFig. 9(b)) and the edge map of our obtained en-hanced color Peppers image (seeFig. 9(c)), respectively.Fig. 12(a) and (b) illustrate the set of edge–adding pixels Nea for the edge
map of the previous obtained enhanced color Peppers image and the edge map of our obtained enhanced color Peppers image, respectively. ByFigs. 11 and 12, our obtained enhanced color im-age has less edge–losing pixels and edge–adding pixels when com-pared to the previous obtained enhanced color image. Then, the set of edge–losing pixels Nelfor the edge map of the previous obtained
enhanced color F14 image (seeFig. 10(d)) and the edge map of our obtained enhanced color F14 image (seeFig. 10(f)) are illustrated inFig. 13(a) and (b), respectively; the set of edge–adding pixels
Nea for the edge map of the previous obtained enhanced color
F14 image and the edge map of our obtained enhanced color F14 image are illustrated inFig. 14(a) and (b), respectively. From the above demonstrations, our proposed color contrast enhancement
Fig. 10. The enhancement demonstration for color F14 images. (a) Original color F14 image. (b) The edge map of image (a). (c) The previous obtained enhanced image. (d) The edge map of image (c). (e) Our obtained enhanced image. (f) The edge map of image (e).
Fig. 11. The set of edge-losing pixels Nelfor color Peppers image. (a) Nelfor the previous obtained enhanced color Peppers image. (b) Nelfor our obtained enhanced color Peppers image.
algorithm has better edge-preservation effect when compared to the previous color contrast enhancement algorithm.
In order to quantify the edge-preservation effect of our proposed color contrast enhancement algorithm, the edge-loss ratio and edge-addition ratio are defined. The edge-loss ratio Rel
is defined as Rel¼ Nel j j IEðx; yÞ ¼ 1 j j
where jNelj denotes the number of edge-losing pixels in the
resulting edge map; jIEðx; yÞ ¼ 1j denotes the number of edge pixels
in the original image. Contrary to the defined edge-loss ratio, the edge-addition ratio Reais defined as
Rea¼
Nea
j j IEðx; yÞ ¼ 1
j j
where jNeaj denotes the number of edge-adding pixels in the
result-ing edge map. To compare the edge-loss ratios between the con-cerned two algorithms, four testing images are used. Besides the color Peppers image and the color F14 image, the other two testing images, the color Table Tennis image and the color Akiyo image as shown inFig. 15(a) and (b), respectively, are used. Based on the four testing images,Table 1 demonstrates the edge-loss ratios for the concerned two algorithms. For both enhancement algorithms, in average, our proposed enhancement algorithm only has 7.59% edge-loss ratio, but the edge-loss ratio of the previous enhancement algorithm is 24.78%. The edge-loss improvement ratio of our pro-posed color contrast enhancement algorithm over the previous enhancement algorithm is 69.37%.Table 2demonstrates the edge-addition ratios for the concerned two algorithms. Based on four testing images, the average edge-addition ratio of our proposed enhancement is 9.99% and that of the previous enhancement algo-rithm is 11.08%. The edge-addition improvement ratio of our pro-posed color contrast enhancement algorithm over the previous enhancement algorithm is 9.84%
Further, we take the color Peppers image to depict the visual edge-preserving effect.Fig. 16(a) illustrates the segmentation re-sult when running our proposed segmentation algorithm on the original image. Fig. 16(b) illustrates the magnified subimage cut from the left portion of one red pepper inFig. 16(a) and the edge map ofFig. 16(b) is illustrated inFig. 16(c).Fig. 16(d) and (e) illus-trate the segmentation results when running our proposed seg-mentation algorithm on the previous obtained enhanced color image and running the same proposed segmentation algorithm on our obtained enhanced color image which has the edge-pre-serving effect, respectively.Fig. 16(f) illustrates the magnified sub-image cut from the left portion of one red pepper inFig. 16(d) and the edge map ofFig. 16(f) is illustrated inFig. 16(g). The magnified subimage cut from the same portion of the same red pepper in
Fig. 12. The set of edge-adding pixels Neafor color Peppers image. (a) Neafor the previous obtained enhanced color Peppers image. (b) Neafor our obtained enhanced color Peppers image.
Fig. 13. The set of edge-losing pixels Nelfor color F14 image. (a) Nelfor the previous obtained enhanced color F14 image. (b) Nelfor our obtained enhanced color F14 image.
Fig. 16(e) is illustrated inFig. 16(h) and (i) depicts the edge map of
Fig. 16(h). After comparing the three edge maps of magnified sub-images (seeFig. 16(c), (g), and (i)), it is observed that the edge map
Fig. 16(i) is quite similar toFig. 16(c), butFig. 16(g) is some
differ-ent fromFig. 16(c). In addition, the density and the distribution of edge pixels ofFig. 16(i) are rather close to those inFig. 16(c), but the density of edge pixels ofFig. 16(g) is some sparse and is much less than that inFig. 16(c).Tables 1 and 2reveal that for the color Peppers image, the edge-loss improvement ratio and edge-addition improvement ratio of our proposed color contrast enhancement algorithm over the previous enhancement algorithm are 70.04%
¼0:31170:0934 0:3117 100% and 12.38% ¼0:10180:0892 0:1018 100% , respec-tively, and it justifies the edge-preserving effect of our proposed color contrast enhancement algorithm. After comparing
Fig. 16(h) with Fig. 16(b) and comparing Fig. 16(f) with
Fig. 16(b), it is observed that our segmentation result when run-ning the proposed segmentation algorithm on our obtained en-hanced color image (see Fig. 16(h)) is better than the segmentation result (seeFig. 16(f)) when running the proposed segmentation algorithm on the previous obtained enhanced color image. Especially, the segmented boundary of the right pepper in
Fig. 16(h) is more clear than that inFig. 16(f) because our color contrast enhancement improves the segmentation quality.
Further, the color F14 image is used to be the second testing image for segmentation comparison when running the proposed segmentation algorithm on the original F14 image and two kinds of enhanced F14 images. From the cockpit part ofFig. 17, it is observed that the number of preserved edge pixels and the distri-bution of edge pixels inFig. 17(i) are quite similar toFig. 17(c). However, the number of preserved edge pixels in Fig. 17(i) is greater than the one in Fig. 17(g). Tables 1 and 2 provide the qualitative evidences. After examiningFig. 17(a), (d), and (e), it is observed that the segmentation result inFig. 17(e) is quite sim-ilar toFig. 17(a) and is better than that inFig. 17(d). This confirms that the edge-preserving effect of our proposed color contrast enhancement improves the segmentation quality. For color Table Tennis image and color Akiyo image, we have the same segmentation quality improvement due to our proposed color contrast enhancement. Finally, Fig. 18(a) and (b) demonstrate the good segmentation results when running our proposed color segmentation algorithm on our obtained enhanced color Table Tennis image and color Akiyo image, respectively. For saving space, we ignore the elaborated comparison.
6. Conclusions
In this paper, a novel and efficient edge-preserving algorithm has been presented for color contrast enhancement in the CIE Lu0v0 color space although our proposed algorithm can be applied
to the other color spaces, such as the CIE xyY color space. In order to improve the computational effort of the proposed algorithm, a speedup strategy has also been given. To the best of our knowl-edge, this is the first edge-preserving algorithm for color contrast enhancement in color space.
Fig. 15. The other two testing images. (a) The color Table Tennis image. (b) The color Akiyo image.
Fig. 16. The segmentation comparison for original Peppers image and two kinds of enhanced Peppers images. (a) The segmentation result when running the proposed segmentation algorithm on original image. (b) One magnified subimage extracted from (a). (c) The edge map of (b). (d) The segmentation result when running the proposed segmentation algorithm on the previous obtained enhanced color image. (e) The segmentation result when running the proposed segmentation algorithm on our obtained enhanced color image. (f) One magnified subimage extracted from (d). (g) The edge map of (f). (h) The magnified subimage extracted from (e). (i) The edge map of (h).
Further, a new color image segmentation has been presented to justify the edge-preservation effect. Some experimental results have been carried out to demonstrate that our proposed color con-trast enhancement algorithm has a good compromise between the edge-preservation effect and the color contrast enhancement effect when compared to the previous algorithm. Besides, experimental results also confirms that the edge-preserving effect of our pro-posed color contrast enhancement improves the segmentation quality.
It is an interesting research topic to apply the results of this paper to the field of color image retrieval issue[5,9,10,19]when the relevant retrieval techniques include the consideration of edge information.
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Fig. 17. The segmentation comparison for original F14 image and two kinds of enhanced F14 images. (a) The segmentation result when running the proposed segmentation algorithm on original image. (b) One magnified subimage extracted from (a). (c) The edge map of (b). (d) The segmentation result when running the proposed segmentation algorithm on the previous obtained enhanced color image. (e) The segmentation result when running the proposed segmentation algorithm on our obtained enhanced color image. (f) One magnified subimage extracted from (d). (g) The edge map of (f). (h) The magnified subimage extracted from (e). (i) The edge map of (g).
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