A Modified GrabCut Using a Clustering Technique to Reduce ... - MDPI

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A Modified GrabCut Using a Clustering Technique to Reduce Image Noise GangSeong Lee 1 , SangHun Lee 1, *, GaOn Kim 2, *, JongHun Park 2 and YoungSoo Park 1 1 2

*

Ingenium college of liberal arts, Kwangwoon university, Seoul 01897, Korea; [email protected] (G.L.); [email protected] (Y.P.) Department of plasmadiodisplay, Kwangwoon university, Seoul 01897, Korea; [email protected] Correspondence: [email protected] (S.L.); [email protected] (G.K.); Tel.: +82-2-940-5287 (S.L.)

Academic Editor: Angel Garrido Received: 31 March 2016; Accepted: 29 June 2016; Published: 14 July 2016

Abstract: In this paper, a modified GrabCut algorithm is proposed using a clustering technique to reduce image noise. GrabCut is an image segmentation method based on GraphCut starting with a user-specified bounding box around the object to be segmented. In the modified version, the original image is filtered using the median filter to reduce noise and then the quantized image using K-means algorithm is used for the normal GrabCut method for object segmentation. This new process showed that it improved the object segmentation performance a lot and the extract segmentation result compared to the standard method. Keywords: median filter; K-means, image clustering; GraphCut; GrabCut; object segmentation

1. Introduction Digital image processing deals with a wide variety of applications ranging from biology, military, medical, space science, art, games and movie industries. The object segmentation is an important step in image processing and analysis [1]. In computer vision, segmentation divides the input image into background and objects. The purpose of the segmentation is to simplify and make it easy to interpret or convert to more meaningful representation of an image. Segmentation is one of the most difficult subjects in an digital image processing, and many studies on this subject have been done to get more accurate results. GrabCut method is based on object segmentation algorithm called GraphCut [2,3]. While GraphCut algorithm segments an image without user intervention, GrabCut accepts an interest area defined by a user and extracts objects using the clues given to get better results. Many studies have been done to improve performance of GrabCut detecting objects in unknown regions [4,5]. In the proposed method, the image is smoothed using median filter and the quantized using k-means clustering technique. Then, GrabCut extracts objects from the quantized image [6]. In this way, we got improved performance. 2. Related Work In general, object segmentation is one of the most fundamental tasks in image processing. Image segmentation is to divide an image into a number of pixel sets on the basis of shape or area. In this work, we following image filters and a clustering technique is applied for an efficient object segmentation. 2.1. Image Filter Filtering is one of the main tasks of signal processing. Filtering is used to remove noise in the image, to extract visual characteristics of interest, and to resample the image. Representative filters are Gaussian filter, Mean, etc. Symmetry 2016, 8, 64; doi:10.3390/sym8070064

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Filtering is one of the main tasks of signal processing. Filtering is used to remove noise in the 2 of 9 image, to extract visual characteristics of interest, and to resample the image. Representative filters are Gaussian filter, Mean, etc. Gaussian filter filter is is used used to to remove remove the the noise noise using using the the following following equations: equations: Gaussian


„  x 2  1 G( x )  1 exp  ´x2 Gpxq “ σ? 2π exp  2σ  2σ σ 2π „  x 22 y 2 2  ` y q 11 exp  ´px G ( x , y )  2 Gpx, yq “ 2πσ22exp 2σ  2πσ 2σ2  

(1) (1)

(2) (2)

where the standard deviation. where σσis is the standard deviation. Mean filter is the representative Mean filter is the representative noise noise removing removing filter filter and and is is defined defined as as follows: follows:

O( x,yq y)“  Opx,

MM 11 ř I x  i, y  j I px ` i, y ` jq Mˆ M M Mi,ji , j





(3) (3)

M MPW W M M“ 2N 2N `  11 where Ipx a neighbor pixel and a mask size +ˆ 1)p2N × (2𝑁 + 1). I ( x`i,iy, y`jqjis ) aisneighbor p2N(2𝑁 ` 1q ` 1q. where pixel and WW is aismask of of size

2.2. Image Segmentation Segmentation is the process of dividing the digital image into a set of multiple pixels to simplify the image representation. Typical methods of image clustering are Mean Shift (MS), Fuzzy C-Means (FCM), etc. [7]. [7]. Mean shift (MS) is a procedure for locating the maxima of a given window area by selecting a pixel (mode) most close to the averaged color, then moving the center of the window to the mode to find local it is [8,9]. TheThe result of MS good in lowinfrequency areas, localmaxima maximarepeatedly repeatedlyuntil until it converged is converged [8,9]. result of is MS is good low frequency but it has to grouptohigh frequency areas. The following Figure 1 show the areas, butsome it hasdifficulties some difficulties group high frequency areas. The following Figure 1 example. show the example.

(a)

(b)

Figure 1. 1. MS MS clustering. clustering. (a) image; (b) (b) Result Result image. image. Figure (a) Original Original image;

FCM is to overcome the difficulty of MS by considering belonging or membership degree into FCM is to overcome the difficulty of MS by considering belonging or membership degree into the the distance. Data-points close to a cluster center have a high belonging degree [10,11]. distance. Data-points close to a cluster center have a high belonging degree [10,11]. p Let X  x1, , xN  R p a data set to be clustered, where p is feature dimension, R is a real vector Let X “ x1 , ¨ ¨ ¨ , x N Ď R p a data set to be clustered, where p is feature dimension, R p is a real space, and N is the number of pixels. Each pixel of color image is expressed as feature vectors like vector space, and N is the number of pixels. Each pixel of color image is expressed as feature vectors xk xkxk“1, xk1,,x¨kp¨ ¨ ,and center of cluster is VisV v“ p is feature dimension and and C is Cthe v,C¨¨,¨ where like xkp and center of cluster , vC q, where p is feature dimension is 1 , pv, 1 . the number of clusters. FCM calculates matrix U minimizing target function J pU, V|Xq number of clusters. FCM calculates matrix U minimizing the the target function . FCM J (U , V | X ) FCM

m

m C Cÿ NN ÿ |X q “ pu q JFCM pU, V uikik ||xxkk ´ vvii |2|2 J FCM (U , V X ) 



i“1i k1“k11

(4) (4)

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CC ř C u “ 1, and u is membership degree that data k belongs to cluster i. V is the center of where uik  1 , and uik is membership degree that data k belongs to cluster i. V j is the center of where where i“1 uikik  1 , and uikik is membership degree that data k belongs to cluster i. V jj is the center of i  1 cluster i,i defined using Equation (5). 1 cluster i, defined using Equation (5). cluster i, defined using Equation (5). m N m 1 ÿ N 1 N puik q m x k , my1 (5) vi “ N1 uuik  xxk ,, mm11 vvi  ř N k “ 1 (5) u i ik k N ik k 1 (5) k 1 k “1 u

 

 u k 1 k 1

 

ik ik

where uik is the mean value of xk using fuzzy constant m. One disadvantage of FCM is that the number uuik should where is the mean value ofinxadvance. constant Onemembership disadvantagemap of FCM is that the k using fuzzy of clusters be provided Figure 2 is them. class applying FCM where ik is the mean value of xk using fuzzy constant m. One disadvantage of FCM is that the number ofand clusters should be provided advance. Figure 2 is the class membership map applying algorithm Figure 3 is result of FCM in clustering. number of clusters should be provided in advance. Figure 2 is the class membership map applying FCM algorithm and Figure 3 is result of FCM clustering. FCM algorithm and Figure 3 is result of FCM clustering.

(a) (a)

(b) (b)

(c) (c)

Figure 2. FCM class membership map. (a) Class 1; (b) Class 2; (c) Class 3. Figure Figure 2. 2. FCM FCM class class membership membership map. map. (a) (a) Class Class 1; 1; (b) (b) Class Class 2; 2; (c) (c) Class Class 3. 3.

(a) (a)

(b) (b)

Figure 3. FCM clustering. (a) Original image; (b) Result image. Figure3.3.FCM FCMclustering. clustering.(a) (a)Original Originalimage; image;(b) (b)Result Resultimage. image. Figure

Image segmentation can be accomplished also by using GraphCut. Boykov proposed GraphCut Image segmentation can be accomplished also by using GraphCut. Boykov proposed GraphCut segmentation canimage be accomplished also by using GraphCut. Boykov proposed GraphCut to getImage optimized interactive segmentation: to get optimized interactive image segmentation: to get optimized interactive image segmentation: E α   U α   V α  (6) E α   U α   V α  (6) E pαq “ U pαq ` V pαq (6) where α is a vector of either 0 or 1. 0 means background and 1 means object. U (α) is continuity where α is a vector of either 0 or 1. 0 means background and 1 means object. U (α) is continuity between pixels and V0 (or representing muchobject. the data belongs to object α ) is a data term where α adjacent is a vector of either background andhow 1 means Upαq is continuity between adjacent pixels and V (α )1.is0ameans data term representing how much the data belongs to object or background. Data term requires information about object and background, and provided between adjacent pixels and Vpαq isprior a data term representing how much the data belongs to object or background. Data term requires prior information about object and background, and provided probability density function, data term calculated usingabout Equation (7).and background, and provided or background. Data term requires prior information object probability density function, data term calculated using Equation (7). probability density function, data term calculated using Equation (7).



 





log p I H if α  0 $ ř   log p` I I pp|HHbb˘ ifi f αPPα  “ 0 0  ppPP´logp ’ p P b & V  α   pPP V “α   ř V pαq   log p(pI |HHo q) otherwise ’ otherwise %  ´logppI p o pP PP  log p ( I p H o ) otherwise   p pP

(7) (7) (7)

andH are are histograms of background object, is a pixel is aset pixel setimage. of an where HHb band histograms of background and and object, p is appixel and Pand is a P pixel of an where H b and oH Hoo are histograms of background and object, p is a pixel and P is a pixel set of an Iimage. of pixel P. Figure 4 is result of GraphCut algorithm that is another typical method of p is the Iintensity is the intensity of pixel P. Figure 4 is result of GraphCut algorithm that is another typical image.segmentation. I pp is the intensity of pixel P. Figure 4 is result of GraphCut algorithm that is another typical image method of image segmentation. method of image segmentation.


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(a) (a)

(b) (b)

Figure 4. GraphCut algorithm. (a) Original image; (b) Result image. Figure 4. GraphCut algorithm. (a) Original image; (b) Result image.

3. The 3. Theproposed proposedMethod Method 3. The proposed Method The flow flow of of proposed proposed method method is is show show in in Figure Figure 5. 5. The The flow of proposed method is show in Figure 5.

Figure 5. A flowchart of the proposed method. Figure 5. 5. A A flowchart flowchart of of the the proposed proposed method. method. Figure

3.1. Clustering to Reduce Noise 3.1. Clustering to Reduce Noise Digital image can be contaminated during data transmission. Digital image can be contaminatedN during data transmission. transmission. N

 

 

N Xmed    N Y  Xi (8) N N ÿ i 1 Xmed    ÿ i 1 Y  Xi (8) |Xmed ´ E| ď i 1 |Y ´ Xi| (8) i 1 where N is the size of data set. K-means clustering method is applied to the output of the filter. Ki “1 i “1 where is the size data K-means clustering method is applied thethe output ofof the filter. Kmeans N classifies the of data setset. to the predefined number of classes. Let μto center i-th cluster i be where N is the size of data set. K-means clustering method is applied to the output of the filter. means data set to the predefined of classes. center ofasi-th cluster μ i besetthe and 𝑆𝑖 classifies beclassifies the setthe of pixels cluster i.number The variance of allLet the is defined Equation K-means the data belongs set to thetopredefined number of classes. Letdata µi be the center of i-th cluster and bethe theset setofofpixels pixelsbelongs belongs cluster i. The variance data is defined as Equation (9). S𝑆i𝑖 be and toto cluster i. The variance of of allall thethe data setset is defined as Equation (9). (9). 2 k k ÿˇ V ÿ x  μ ˇ22 k (9) V “ i 1 jS ˇx jj ´ µiiˇ (9) V i x j  μi (9)

  i“1 jPS i 1 jSii

The goal is to find 𝑆𝑖 minimizing V. K-means starts with arbitrary initial values μ𝑖 . Allocating The goal is isμ to to find findrecalculating S𝑆i minimizing K-means starts arbitrary The goal V.repeated K-meansuntil startsitwith with arbitrary initial initial values values µμi𝑖.. Allocating Allocating pixels to close μ𝑖 V. is is converged. 𝑖 minimizing 𝑖 and pixels repeated until it it is is converged. pixels to to close close µμi𝑖 and andrecalculating recalculatingµiμis is repeated until converged. 𝑖 2 K

KK ř x  μ 2 J MSE ř   i ´μµi |2 J MSE i 1 x ωi |x J MSE“i“ x  i x « ω 1 i (10) (10) i 1 x ω ř where µi “ n1 i 1 x (10) where μ i x«1ω x i  ωi x where μ i  n x n x  ωi Equation (10) is the simplest clustering method minimizing J MSE repeatedly. Figure 6 shows

Equation (10) isfilter the in simplest applied the median image. clustering method minimizing 𝐽𝑀𝑆𝐸 repeatedly. Figure 6 shows Equation (10) isfilter the in simplest applied the median image. clustering method minimizing 𝐽𝑀𝑆𝐸 repeatedly. Figure 6 shows applied the median filter in image.

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(a) (a)

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Figure Figure 6. 6. An An image image applied applied the the median median filter filter image. image. (a) (a) Original Original image; image; (b) (b) Result Result image. image. Figure 6. An image applied the median filter image. (a) Original image; (b) Result image.

3.2. Object Segmentation Using Improved GrabCut 3.2. Object Segmentation Using Improved GrabCut 3.2. Object Segmentation Using Improved GrabCut GrabCut accepts an interest area defined by a user and extracts objects using the clue given. GrabCut accepts an interest area defined by a user and extracts objects using the clue given. GrabCut areaofdefined byalgorithm. a user and extracts objects using the clue given. Figure 7 showsaccepts trimapan of interest foreground GrabCut Figure 7 shows trimap of foreground of GrabCut algorithm. Figure 7 shows trimap of foreground of GrabCut algorithm.

Figure 7. Composition of trimap; shows trimap of foreground (𝑇𝐹 ), background (𝑇𝐵 ) and unknown Figure 7.𝑈Composition of background (𝑇(T unknown Composition oftrimap; trimap;shows showstrimap trimapofofforeground foreground(𝑇(T background ) and unknown region (𝑇 ). 𝐹 ), 𝐵 )Band F ), (T𝑈U).). region (𝑇

Object and background is mixed in unknown region. Background 𝑇𝐵 is defined as Equation and background backgroundisismixed mixedininunknown unknown region. Background is defined as Equation (11). Object Object and region. Background TB 𝑇 is𝐵 defined as Equation (11). (11). T  T  T    z    S  (11) TBB“ TFF X rpTUU Y Γ pzqq ‘ Ss (11) TB  TF  TU    z    S  (11) ˇ #   + where   z    z ˇˇ řg  p   t  is the area greater than gradient. Symbol ⊕ is a dilation operator   n   where Γ pzq “  zn pˇN  zi  ∇ g ppqy ist the is area the area greater than gradient. Symbol dilationoperator operator where greater than gradient. Symbol ⊕‘isisaadilation    z   zn ˇ pP N p zigq  p   t   zi     pNelement  and element for it. it. and S S is is aa structure structure for and SA is a structure element for it. Gaussian mixture model is A Gaussian mixture model is aa probabilistic probabilistic model model that that assumes assumes all all the the data data points points are are generated generated A Gaussian mixture model is a probabilistic model that assumes all the data points are from a mixture of a finite number of Gaussian distributions with unknown parameters is given from a mixture of a finite number of Gaussian distributions with unknown parameters andand isgenerated given by: from by: a mixture of a finite number of Gaussian distributions with unknown parameters and is given N ÿ by: N (12) p pxp |θ q “ p px |ωi , θi qP pωi q  x θ  i“ (12) N p  x ωi ,θi P  ωi  1 i 1 p x ω ,θ P ω p  x θ    i i  i (12) i 1 where i-th vector component is characterized by normal distributions with weights α and a pair of Where i-th vector by normal distributions with weights α𝑖i θθi 𝑖. .ωωi 𝑖represents relative importance. αiαis𝑖 defined as as follows: Where i-thcovariance vector component is characterized by normal distributions with weights α𝑖 and a pair of mean and represents relative importance. is defined follows: mean and covariance θ𝑖 . ω𝑖 represents relative importance. α is defined as follows: 𝑖 M M ÿ 0  α  1 and α  1 (13) M i 1 and 0 ď αi ď αi i “ 1 (13) 0  αi  1 and ii“1 1αi  1 (13)

  i1

Parameters for GMM (Gaussian Mixture Model) of M components is expressed as Equation (14): Parameters for GMM (Gaussian Mixture Model) of M components is expressed as Equation (14):


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Parameters for GMM (Gaussian Mixture Model) of M components is expressed as Equation (14):

θ (μpµ , , θ2 2 , 2θ2 , 1, μ 2 , , . . ,. , μ θ“ µM 1, µ 2 M , . . . , θ1 1, θ2 , 2 22 . . . ,,θθ , α, 1α, α , . . . , α M, qα M ) MM 1 ,2 α 2 ,

(14) (14)

TU “ TF ´ TB

(15) (15)

𝑇T𝑈U is defined as follows:

TU  TF  TB

Figure 8 shows a result of the improved GrabCut algorithm. Figure 8 shows a result of the improved GrabCut algorithm.

(a)

(b)

Figure Figure 8. Improved Improved GrabCut GrabCut algorithm. (a) (a) Original Original image; (b) Result image.

4. 4. Experiment Experimentand andDiscussion Discussion The photos such such as as figures, figures, plants, plants, food, food, etc. etc. The experiments experiments were were performed performed using using about about 400 400 photos Performance ofGraphCut, GraphCut,standard standard GrabCut proposed method is compared. 9 Performance of GrabCut andand proposed method is compared. FigureFigure 9 shows shows some results. GrabCut is better than GraphCut and, the proposed method shows better results some results. GrabCut is better than GraphCut and, the proposed method shows better results than than GrabCut in most by detecting background in unknown area [12,13]. GrabCut in most casescases by detecting background in unknown area [12,13]. Evaluation Evaluation is is performed performed using using precision precision and and recall. recall. Precision Precision is is the the fraction fraction of of retrieved retrieved instances instances that are relevant, while recall (also known as sensitivity) is the fraction of relevant instances that are relevant, while recall (also known as sensitivity) is the fraction of relevant instances that that are are retrieved: retrieved: N pObjEX X ObjGT q (16) precision “ N ObjEX  Obj  precision  N pObjEX qGT (16)   N ObjEX N pObjEX X ObjGT q recall “ (17) N pObj GT qGT  N Obj EX  Obj recall  (17)  ObjGT is ground truth objects. Figure N ObjGT where N p¨ q is the number of pixels, ObjEX is the object and 10 shows the precision and recall of three methods. The proposed method gives the best result. where 𝑁(∙) is the number of pixels, 𝑂𝑏𝑗𝐸𝑋 is the object and 𝑂𝑏𝑗𝐺𝑇 is ground truth objects. Figure 10 Experiments are performed using PSNR (Peak Signal to Noise Ratio). PSNR is the ratio between shows the precision and recall of three methods. The proposed method gives the best result. the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of Experiments are performed using PSNR (Peak Signal to Noise Ratio). PSNR is the ratio between its representation. ¯ the maximum possible power of a signal and the power´ofMAX corrupting noise that affects the fidelity of 2 PSNR “ 10 ¨ log10 MSE its representation. ´ ¯ (18) MAX I “ 20 ¨ log10 ? 2  MAXMSE   PSNR  10  log 10  MSE (Mean Squared Error) is the difference between the estimator and what is estimated. Where MSE  MSE  (18) is defined as follows:  MAX I  mÿ ´ 1 n ´ 1  log 10   1  20ÿ  MSE  jq||2 MSE “ ||Ipi, jq ´ Kpi, (19) mn i “0 j “0 MSE (Mean Squared Error) is the difference between the estimator and what is estimated. Where MSE is defined as follows: MSE 

1 m1 n1  I (i, j)  K (i, j ) mn i 0 j 0

2

(19)

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(a) (a)

(b) (b)

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(d) (d)

(e) (e)

(f) (f)

Figure 9. (a) Original image; (b) GraphCut Algorithm; (c) GrabCut Algorithm; (d) Ref. [12]; (e) Ref. Figure9.9.(a) (a)Original Originalimage; image; (b) GraphCut Algorithm; (c) GrabCut Algorithm; (d) Ref. [12]; (e) Ref. Figure [13]; (f) Proposed Method. (b) GraphCut Algorithm; (c) GrabCut Algorithm; (d) Ref. [12]; (e) Ref. [13]; [13]; (f) Proposed Method. (f) Proposed Method. 1 1 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0

Precision Precision Recall Recall

GraphCut GrabCut Ref.[2] Ref. [13] Proposed GraphCut GrabCut Ref.[2] Ref. [13] Proposed

Figure 10. Precision-recall result. Figure 10. Precision-recall result. Figure 10. Precision-recall result.

Table 1 shows the quantitative comparison of result experiments. Table 1 shows the quantitative comparison of result experiments. Table 1 shows the quantitative comparison of result experiments.


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Table 1. Result of experiment.as quantitative comparison. Comparision Method

Ref. [2]

Ref. [13]

Proposed Method

MSE PSNR

2748.65 29.39 dB

2374.43 34.17 dB

1308.17 38.94 dB

5. Conclusions In this paper, a modified GrabCut method is proposed using median filter and k-means clustering technique to reduce image noise and to extract objects better. An image is preprocessed and then used for the input of standard GrabCut. This method showed better performance than GraphCut or standard GrabCut from the various and complex pictures like medical images, traffic images and people images. This research should be extended further to detect objects in video, and this can be used in many industrial applications. Acknowledgments: The work reported in this paper was conducted during the sabbatical year of Kwangwoon University in 2013. Author Contributions: GangSeong Lee provided guidance for this paper; SangHun Lee was the research and academic advisor of editing; GaOn Kim developed and solved the proposed model, carried out this analysis and wrote the manuscript; JongHun Park contributed to the revisions and performed experiments; YoungSoo Park contributed to the revisions and advisor of editing. Conflicts of Interest: The authors declare no conflict of interest.

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