A Proposed Adaptive Image Segmentation Method Based on Local Excitatory Global Inhibitory Region Growing
Trong-Thuc Hoang*, Quang-Trung Trant, and Trong-Tu Bui+
*t+Digital Signal Processing and Embedded System Laboratory (DESLab) Faculty of Electronics and Telecommunications (FETEL) The University of Science, Ho Chi Minh City (VNU-HCMUS) * + {htthuc, bttu} @fetel.hcmus.edu.vn t
[email protected] Abstract-Image segmentation is an indispensable first step in many image processing tasks. Many attempts have been made over the time including traditionally approaches (i.e. threshold based, edge-based, and region growing) to modern methods of machine learning and neural networks. However, the final solu tion hasn't be found as yet. Recently, the Local Excitatory Global Inhibitory Oscillator Network (LEGION) has been proposed aimed to solve the problem. The LEGION has been developed for over a decade and has various ways of advancement. The all-digital model, a hybrid of LEGION and region growing, has been done in order to overcome the analog operation of the origin. However, there is an issue still exist in the origin and all of its advancements. It is the fragmentation which results from the incorrect chosen parameters. In this paper, we proposed an adaptive image segmentation method which has dynamic parameters in order to get the best performance. Our approach is based on the digital hybrid of LEGION and region growing, and the parameters are not chosen manually but be computed from the contents of image.
I.
INTRODUCTION
In the field of signal processing, the pattern segmentation problem has been called for over half of a century and brings a multitude of solutions. As yet, it still attracts attention from many researchers over the time because of its critical role. By segmenting an image into coherent regions, it gives a funda mental for many basis image processing tasks which can be served as a preprocessing step for further advanced algorithms. According to Shitai Raut et al. [1], image segmentation me thods can be categorized into six major approaches: threshold based, histogram-based, edge detection, graph partitioning, watershed transformation, and region-based. Recently, the study of neural network has fueled a flurry of research in the field of image processing. Besides six methodologies mentioned above, bio-inspired neural networks have been applied [2], [3]. On that trend of research, the Locally Excitatory and Global Inhibitory Oscillator Networks (LEGION), which is a hybrid of neural networks and region growing, has been quickly adapted and developed in the so ciety. The LEGION is first proposed by Wang and Terman [4], then the completed model is presented [5]. LEGION consists of two layers: first is the lateral-connection oscillator network which has the size equal to that of the input array; second layer has one Global Inhibitor which has connections to each oscillator in the first layer. The mechanism of LEGION can be described as the "synchronization within blocks of oscillators that are stimulated by connected regions and desynchronization between different blocks" [4]. Therefore, the network is best 978-1-4799-5051-5/14/$31.00 ©2014 IEEE 458
suited for segmentation applications. However, the algorithm has a fragmentation issue, which is caused by the incorrect chosen parameters. There are two critical parameters in the algorithm, Wz and Bp, where is the strength of global inhibition and the threshold for forming high potentials [5], respectively. The problem of choosing parameters has been discussed over the time, but it doesn't have the final solution as yet. Since introduced, the original LEGION model has many different ways of advancements in both algorithms and imple mentation. Various applications of the LEGION-based methods have been developed up to now such as sound monitoring [6], road extraction [7], etc. However, almost LEGION-based designs cannot implement into a compact digital hardware due to its analog operation. By acknowledged that disadvantage of analog design, Morimoto et al. proposed a digital ver sion adapted from the original ones first in 2002 [8], and the completed design in 2004 [9]. The Morimoto's model reduced the analog aspect of the origin LEGION, which has many different possible states, into only four allowed pixel states: self-excitable (leader pixel), not excited (not labeled), excited, and inhibited (labeled) [9]. This digital model has been developed for applications recently [10], [11]. Despite the excellent results of the model in segmentation, it is hard to find the correct parameters for the best performance. The Morimoto's model has the same fragmentation problem as same as the origin LEGION network. In the Morimoto's model, there are two important parameters, Bp and Bz, which have the similar meaning and function to the Bp and Wz in the origin LEGION. The leader-pixel threshold Bp affects on the number of leader pixels which can form a region later. The region-growing threshold Bz means the strength of lateral connections which directly affects on the growing ability of a region. Although there are many advices to choose parameters, it is a limited number of patterns that the algorithm can segment with fixed values of Bp and Bz. Because of this, the authors assume that the parameters should not be fixed but be calculated from the contents of the image. In this paper, our motivation is to develop an adaptive model which has a dynamic parameters based on the contents of the image. With dynamic thresholds, the proposed algorithm can overcome the fragmentation problem and performs well in various circumstances of image such as simple or complex details, sharped or blurred, overlapped objects, clear or noisy, etc. Although the proposed method increases the processing time because of the thresholds computations, it has a pipelined aspect which can be applied for segmenting a streaming video.
The remains of this paper are organized as follows. The background algorithm is described in Section II. The effective ness analysis of leader-pixel threshold Bp and region-growing threshold Bz are discussed in Section III. Our adaptive image segmentation model is proposed in Section IV. The experimen tal results are shown in Section V. And finally, the conclusion is given in Section VI. II.
BACK GROUND AL GORITHM
The background algorithm is the model proposed by Morimoto et al. [8], [9], a hybrid design of the origin LEGION algorithm and region growing technique. The algorithm re duces the analog aspect of the origin LEGION, which has many different possible states, into only four allowed pixel states: self-excitable (leader pixel), not excited (not labeled), excited, and inhibited (labeled). The details of the algorithm are illustrated as follows. [Morimoto's image segmentation algorithm] 1. Initialization
a) Set all pixels (cells) i to non-excitation.
Xi(O) =0;Zi(O) =0;Ii = O.
It can be concluded that there are three major steps in the algorithm: initialization, self-excitation, and excitation, and four main variables for each pixel: Xi(t), Zi(t), t i , and Pi. From the beginning, leader pixels are found by comparing the sum of connection weights Wik with the predefined leader-pixel threshold Bp as can be seen in step 1. If the i-th pixel passes the threshold condition, it will be determined as a leader-pixel by asserting its Pi. A leader pixel then plays a role as a seed in region growing process by self-excitation in step 2. In step 2 and step 3, Xi(t) means that the i-th pixel belong to the region, while the Zi(t) shows that it is newly excited. Additionally, if the i-th pixel belong to the region, Zi(t) active only once while Xi(t) remains actively till the end of the process. As a result, the z(t) which is the logical OR of all Zi(t) will decide the continuation of the iterative process in the step 3. During the process, a pixel will join the region whenever the condition is satisfied, which can be seen in step 3 that if the Si(t) is greater than the predefined region-growing threshold Bz. When there are no new pixels to join the region which means Z(t) equals to zero, the region is completed by labeling all of the pixels in the region. Then, the progress returns to step 2 to find the next leader-pixel to form a new region. The segmentation algorithm ends when there are no leader pixel remains.
b) Calculation of the connection-weights. III.
i) For gray-scale image ":"hl' k E N(i) Wik =
l+iI:
A.
PARAMETERS A NALY SIS
Parameter Effectiveness
As mentioned above, the main attribute of this research is the dynamic parameters. Firstly, a briefly review of the parameters effectiveness is needed. The threshold Bp affects on the probability of how a pixel could become a leader-pixel. If the sum of 8 connection-weights of the i-th pixel is larger than Bp, the i-th pixel is a leader-pixel and has Pi = 1, or else Pi = o. The condition of becoming a leader-pixel is shown in Eq. 1.
ii) For color image
W(R)ik = 1+I W(G)ik = 1+I
I���::I(R)kl' I��::I(Ghl' W(B)ik = 1+II��::I(Bhl'
Wik = min{W(R)ik, W(G)ik, W(B)ik}
c) Determination of leader pixels (cells) if eL jEN, Wij > Bp) then Pi = 1; otherwise Pi = O.
where
d) Initialization of global inhibitor: z(O) = O.
(1)
Where, Ni is the collection of 8 adjacent pixels around the i-th pixel. In each pair of i-th and k-th pixels has a connection weight Wik which is computed by Eq. 2 for gray-scale image. Wi is called the weight at i-th pixel which is the sum of all connection-weights in Ni
2. Self-excitation (New segment's leader-pixel
excitation)
if no leader pixel left then stop; Iiterminate else if (Jind_teaderO == i) then Xi(t+1) = 1;z(t+1) = 1; liseIf-excitation go to (3. Excitation) else go to (2. Self-excitation)
Wi k _
IMax l+I Ii- Ikl
(2)
In Eq. 2, IMax is the maximum value of gray-scale pixel in the image. And, Ii and Ik is the pixel values for i-th pixel and k-th pixel, respectively. In case of color image, the same equation is applied for each plane of color, and then the smallest result is chosen. For example, Eq. 3 shows the calculation for connection weight Wik in cased of RGB color image.
3. Excitation (Segment-growing)
Setting of global inhibitor: z(t) = VViZi(t); Illogical OR of Zi(t) if (z(t) ==0) then
xi(t+1) =0;zi(t+1) =0; Pi =0;ti = 1; Ilinhibition (labeled)
go to (2. Self-excitation) else if (Xi(t) ==0 /\ Zi(t) ==0) then
where,
Si(t) = LkEN, (Wik * Xk(t)) Bz) then Xi(t+1) = 1;Zi(t+1) = 1; Ilexcitation else Xi(t+1) =0;Zi(t+1) =0; Iinon-excitation else if (Xi(t) == 1 /\ Zi(t) == 1) then Xi(t+1) = 1;Zi(t+1) =0;
Wik = min{W(R)ik' W(G)ik, W(B)id W(R)ik = 1+I I(Rhl' I(G)Max W(G)ik = 1+II(G),-I(Ghl'
I����
if (Si(t) >
(3)
I(B)Max W(B)ik = 1+II(B),-I(Bhl· A leader-pixel is the seed in region-growing process. Based on the leader-pixel self-excitation, the other pixels will follow
go to (3. Excitation)
459
if they pass the condition to be excited. The condition for a pixel to join the region is shown in the following equation.
Si
where,
Si
=
>
Bz
LkEN, (Wik
*
(4)
Xk(t))
In Eq. 4, Bz is the predefined region-growing threshold. And, Xk(t) gives the information about the excitation of the k-th pixel. For example, Xk(t) 1 when the k-th pixel is excited and Xk(t) 0 when it is not. If the i-th pixel joins the region, Xi(t) will be set to excited (Xi(t) 1), otherwise it remains the zero value. It can be seen in Eq. 4, when any pixel (leader-pixel or not) becomes excited from not-excited, it will increase the excitation probability of its adjacent pixels. In the other words, excited pixels can trigger its surrounding and create a "domino" phenomenon. The process of region growing reaches the end and a region is completed when there are no more new pixels to join the region. It is clear that the region-growing threshold Bz affects on the growing ability the algorithm. =
=
=
Region-growing Threshold Bz The Bz threshold defines how hard that a not-excited pixel becomes excited during the region-growing process. Generally, keeping low Bz is a good idea to get a fine result. The lower the threshold is, the stronger a region can grow. Therefore, small details in the image cannot trigger a new region but to join into a big main region nearby. Example of low Bz gives a better result is shown in Fig. lea). However, the segmentation algorithm needs high Bz in cases of overlapped objects. In the other words, if the boundaries between overlapped objects are thin, then a low Bz is not enough to separate them. Fig. l(b) shows an example when choosing high Bz leads to a better result. These examples in Fig. I are set with the same leader pixel threshold Bp. B.
gz 1 20
b) Fig. 1: Example of choosing low a better result. Leader i-th pixel has active state x;= 1
I I'
Connection-weight Wi/(
�'
-
-
Fig. 2: Example of Sk growing process.
=
Bz (a) and high Bz (b) gives
/1 --
� ,
,
ez 160
=
,
,
In order to put the Bz into an equation, what variables that the threshold relied on must be figured out first. In case of too many leader pixels, low Bz helps the main-and-big regions can grow over the weak-and-small ones which are usually considered as noises or not-important small details. In the other words, if there are too many leader pixels in the image, then Bz should be low to reduce the number of region and keep only main regions grow. However, if there are too few leader pixels, then those few should grow easily which leads to low Bz, too. Altogether, the authors come to a conclusion that Bz should be low in either case of too few or too many leader pixels. In other cases, the Bz is high when the amount of leader pixels is neither too many nor too few. Therefore, Bz value is depended on the number of leader pixels which is directly affected by the leader-pixel threshold Bp. For this reason, the equation of Bz is the function respect to Bp in which way that reaches to zero when Bp reaches zero or its maximum value. In the next sub-section, the maximum value of Bp threshold is proven that equals to WMax , which is the maximum value of weight in the image. Another important figure of the Bz is that it cannot larger or equal to IMax. The reason can be explained by the example in Fig. 2. Fig. 2 shows a common scenario at very first step of the region-growing process when there is only the leader pixel i has the active state (Xi 1). As a result, the k-th pixel in the example has 8 adjacent pixels with one active pixel (the leader i-th pixel) and seven inactive pixels. Then, according to Eq. 4, the Sk of the k-th pixel equals to one connection-weight Wik between two pixels, i-th and k-th pixels. Hence, Sk equals to Wik. By assuming that the k-th pixel belong to the region, the gray value of the k-th pixel, h, must close to the value of the leader pixel, h Therefore, as seen in Eq. 2, when the values of i-th and k-th pixels are the same ( Ii h), Wik reaches its maximum value, IMax. As a consequence, Sk in the example in Fig. 2 equals to IMax based on the assumption that the k-th pixel belong to the region. But when the k-th pixel belong to the region, the condition in Eq. 4 which is Sk larger than the Bz must be satisfied. In a word, the value Bz must smaller than IMax in order to make the k-th pixel possible to be excited. If Bz larger or equal to IMax , k-th pixel cannot be excited, neither do other seven pixels around the leader i-th pixel. Then, the region which is started by the leader i-th pixel cannot grow further than the leader pixel itself. To conclude, if the region growing threshold Bz larger or equal to IMax , it will eliminate the growing ability of the algorithm. =
=
There are three main aspects of Bz that are mentioned above. Firstly, the function of Bz is a function of Bp. Secondly, the function reaches to zero when Bp reaches to zero or WMax. Lastly, the maximum value of Bz must smaller than IMax. Based on those aspects, the equation of Bz is presented in the following equation.
k-th pixel
,
1'-. -
(5)
j -- - l
the others pixels are at inactive state
Wik at very first step of region-
460
C.
Leader Pixel Threshold
Bp
The Bp decides how many leader pixels will be in the image. Obviously, both cases of too many and too few leader pixels are not good choices as can be seen from the examples
in Fig. 3. Examples in Fig. 3 adjust the value of Bp, and Bz is calculated based on Bp by Eq. 5. Appropriate value of Bp depends on the complexity of the image. Owing to each leader pixel could form an independent region later, a complex image with many different objects and details needs more leader pixels than that of a simple one. Thus, low Bp is an appropriate choice in case of a complex image, and high Bp suits for a simple one. The image complexity could results from the histogram of weights Wi as can be seen in Fig. 4. According to the weight-histogram in Fig. 4(a), the majority of pixels in a complex image have a small value of weight, resulting in a gathering of pixels on the left of the chart. On the other hand, the weight-histogram of a simple image in Fig. 4(b) shows that most of the pixels have a large weight value. The weight of a pixel means the connection-strength of that pixel with its adjacent ones. Thus, a simple image with several objects and one-color background obviously has many stronger weights than that of a complex image with many objects and details due to its homogeneous. To summarize, a weight-histogram of a complex image is a left-skew histogram while that of a simple image is a right-skew one. Consequently, the Bp value depends on the properties of weight-histogram of the image. The authors proposed two properties of a weight histogram: the mean of weights J.Lw and the maximum weight WMax. The WMax is the maximum value of weight in the image, and the mean of weights J.Lw is computed by the following equation. Where, Wi is the weight at i-th pixel and N is the amount of pixels in the image. J.Lw
=
1 N 2: Wi N
(6)
i=l
The criterion of becoming leader-pixel is that the weight must larger than the Bp threshold. Because of this, the chosen value of Bp separates the weight-histogram into two pieces: leader pixels on the right of the threshold and not-leader pixels on the left of the threshold, as shown in Fig. 5.
b) Fig. 4: Histogram of weights Wi of a complex image (a) and a simple image (b).
leader pixels
not·leader pixels
o
Fig. 5: Threshold Bp divide weight-histogram into two pieces of leader and not-leader pixels. According to Fig. 5, the reason for the value of Bp cannot larger than WMax is that there won't be any leader-pixel, which means there will be no region to be grown. Although the Bp value must be chosen smaller than WMax , it should be a high value and close to the WMax. The explanation is that the amount of leader pixels is equivalent to the number of regions in the segmented image. And it cannot have too many regions in an image in order to prevent the fragmentation issue. By experiences, the authors come to a conclusion that a good value of Bp is at half-right of the weight-histogram. As mentioned above, Bp threshold depends on the image complexity which can be predicted by the weight-histogram. Furthermore, the mean of weight J.Lw provides an important figure in the histogram. Therefore, the equation of Bp can be formed by the mean of weight J.Lw. Altogether, the authors present the calculation of Bp in the following equation.
Bp IV.
{ WMax
: J.Lw >
J.Lw
-
-
J.Lw
W�ax
: otherwise
(7)
P ROPOSED ADAPTIV E LOCAL EXCITATORY G LOBAL INHIBITORY REGION-GROW ING ALGORITHM
Fig. 3: Example of adjusting the keys (b).
Bp in image of the plane (a) and
461
According to the above analysis, the thresholds of the algorithm should not be chosen as fixed values, but be computed based on contents of the image. Acknowledged the fix-parameter disadvantages of the Morimoto's model, the paper presents an adaptive model of Local Excitatory Global Inhibitory Region-growing (ALEGIR). The details of the proposed method are given as follows.
[Proposed Image Segmentation ALEGIR Algorithm] 1. Initialization
a) For all pixels: Ii 0, Xi 0, Pi 0, Zi For the global inhibitor: L 0, Z O. =
=
=
=
b) Calculation of weights Wi
=
O.
=
=
�kENi Wik·
where, Wik is the connection-weight of i-th and k-th pixels i) For gray-scale image
Wt. k
==
I l+IIrn{J,rl: i-hl·
ii) For color image
W(R)ik W(G)ik
I���::I(Rlkl' I��::I(Ghl' ���:I(Bhl'
=
1+I HI HII
=
W(B)ik Wik min{W(R)ib W(G)ik' W(B)id =
=
where, Ii and Ik are the value of i-th and k-th pixel. IMax is the maximum pixel value in the image. c) Thresholds calculations.
op-
-
{
: J-lw > WA�ax : otherwise
J-lw WMax-J-lw
(*)
where, J-lw is the mean of weight which formed by: J-lw -h �:l Wi (N is the total pixels in the image). WMax is the maximum weight value in the image. =
d) Determination of leader pixels if (Wi> Op) then Pi 1; otherwise Pi =
=
O.
==
=
=
3. Excitation (Segment-growing)
If Z 0 then Find all pixels in the image which has Xj Xj O;Pj 0; =
=
Ij
=
=
1 then
=
L
(**)
//labeled
go to (2. Leader-pixel self-excitation) Else In each j-th pixel that has lj 0 If Xj 1 then If Zj 1 then Zj 0; Z Z-l Else Zj 0; Z Z Else Calculate the Sj � kENj (Wjk If Sj> Oz then Xj 1; Zj 1; Z Z + 1 Else Xj 0; Zj 0; Z Z go to (3. Excitation) =
=
=
=
=
=
=
=
=
=
=
=
*
EXPERIMENTAL RESULTS
Fig. 6 and Fig. 7 give several results using the proposed ALEGIR algorithm. In the examples, the up images are original images, and the down ones are the segmentation results. Tab. I shows the value of thresholds, Op and Oz, in each example which are calculated by the proposed ALEGIR method.
If no leader pixel left then stop; //terminate Else if (find_leaderO i) then Xi 1; Zi 1; L L + 1; Z 1 IIself-excitation go to (3. Excitation) Else go to (2. Leader-pixel self-excitation) =
Another advantage of the adaptive model is that it can be applied for a real-time video segmentation implementation. According to the thresholds equations in ( *) box, the imple mentation needs to know every pixels values in the image to do the computation. Therefore, the idea that uses the previous image's thresholds to segment the current image can make the pipelined implementation. For instance, when the current image is segmenting, the information of the current image are used to compute the thresholds which will be used for the next image in the streaming video. V.
2. Leader-pixel self-excitation
=
There are two improvements in the proposed algorithm compared to the Morimoto's model. They are ( *) and ( ** ) boxes as shown in the above details. The minor improvement of the algorithm is to enumerate the region as shown in ( ** ) box. In the Morimoto's model, the Ii variable shows that the i-the pixel is inhibited or not. But in the proposed model, the Ii variable means which region the i-the pixel is belonged to after the segmentation process. The default value of Ii is zero. Then, any pixel that has the zero value of l i belongs to no region; it could be the boundaries or details in the image. The major improvement, (* ) box, is also the main attribute of this paper, the dynamic thresholds of Op and Oz. A pixel will become leader-pixel when its weight larger than Op value. On the other word, the leader-pixel threshold Op determines the number of leader pixels in the image. Then, a leader-pixel is treated as a seed in segment-growing step. Whenever a not-excited pixel passes the criterion of homogeneity of region-growing threshold Oz, it joins the region. Therefore, Oz stands for the growing ability of the algorithm. With dynamic thresholds, the proposed algorithm can overcome the fragmentation problem and performs well in various image circumstances.
Xk)
=
=
462
It can be seen that the algorithm can perform against noisy image as in Fig. 6a. The result of Fig. 6a gives regions of the tree, the sun, the mountain, and the background with no tiny noisy regions in between. The overlapped-object images in Fig. 6c, Fig. 7b, and Fig. 7d need a high Oz threshold to do the separation. According to Tab. I, the Oz thresholds of those images are high (over 210) and the objects are segmented separately. The blurry-image, Fig. 6b, and scene-image, Fig. 6d and Fig. 7a, also get a good segmented result. It can be seen that in noisy image, Fig. 6a, and complex image, Fig. 7a, the Op threshold is high and the Oz threshold is low. High Op keeps the heavy weight leader pixels only, which strongly represents for a coherent region. And low Oz means strong growing ability; it helps the regions are easily to grow over the noises and small details in the image. Generally, high Op and low 0z are the good thresholds for the cases of noisy and complex images as seen in Fig. 6a and Fig. 7a. To conclude, the proposed ALEGIR algorithm can overcome the problem of fixed thresholds to apply for various kinds of image such as clear or noisy, blurry or sharped, overlapped objects, simple or complex, etc.
V I.
CONCLUSION
In this paper, we have proposed an adaptive model of Local Excitatory - Global Inhibitory Region-growing (ALEGIR) applied for image segmentation. The proposed algorithm shows good perfonnances due to the dynamic thresholds, the main attribute of the paper. It can overcome the fragmentation issue which exists in the original LEGION model and its various advancements. Furthermore, the ALEGIR algorithm can be used to segment various image circumstances such as blurry or sharped, clear or noisy, simple or complex, overlapped objects, etc. Fig. 6: The segmentation results of noisy image (a), balls (b), medals (c), and billards (d).
The ALEGIR algorithm can be implemented for segment ing either static image or streaming video. In addition, the proposed method has a pipelined aspect which can be used as an advantage in applications of video. However, the algorithm has high complexity due to the large amount of calculations. Moreover, there are many iteration loops in the algorithm leads to a hardware-unfriendly approach. In the future, the authors combine the ALEGIR method in this paper with fast scanning algorithm in order to speed up the operation time, and build a hardware-friendly design. REFERENCES [l]
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Fig. 7: The segmentation results of car (a), smart-phone (b), cups (c), and fruits (d).
TABLE I: The thresholds value of Example (Jp (Jz Example (Jp (Jz
Bp and Bz in the examples.
Fig.6(a)
Fig.6(b)
Fig.6(c)
Fig.6(d)
1440.5
1235.3
1270.2
997.3
198.7
217.6
215.3
221.2
Fig.7(a)
Fig.7(b)
Fig.7(c)
Fig.7(d)
1316.5
1192.4
1303.8
1119.8
195.7
219.9
212.8
222.7
According to the details of the Morimoto's model in Section II and the proposed model in Section IV, the number of calculations in the proposed method is equal to that of the Morimoto's model if the thresholds calculations in the ALEGIR algorithm are removed. On the other word, the proposed method has higher complexity than its origin due to two equations of Bp and Bz. However, it can be proven that in a streaming video application, the time-consuming of the ALEGIR method is not increase if the implementation is a pipelined design. The pipelined idea is based on the assumption that two adjacent frames have minor changes. Then, the thresholds of the current image can be applied for the next. For instance, when the current image is being segmented, the information of the current image is used for computing the thresholds which will be used in the next image in the streaming video. As a result, the processing time of the system depends on the leader-pixel selection and region-growing only. Hence, with pipelined implementation, the processing time of the proposed ALEGIR algorithm is equal to that of the Morimoto's model.
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