an improved image segmentation algorithm base on normalized cut

8/8/2019 An Improved Image Segmentation Algorithm Base on Normalized Cut

http://slidepdf.com/reader/full/an-improved-image-segmentation-algorithm-base-on-normalized-cut 1/4

An Improved Image Segmentation Algorithm Base on Normalized Cut

Qiu-Bo Xi

School of Automation Engineering

University of Electronic Science and Technology of China

Chengdu, 611731, P.R.China

e-mail:[email protected]

Abstract— A novel approach for segmentation of images has

been proposed by incorporating the advantages of the mean

shift segmentation and the normalized cut partitioning

methods. The proposed method preprocesses an image by

using the mean shift algorithm to form segmented regions,

region nodes are applied to form the weight matrix W instead

of these regions, the Ncut method is then introduced for region

nodes clustering. Since the number of the segmented region

nodes is much smaller than that of the image pixels. The

proposed algorithm allows a low-dimensional image clustering

with significant reduction of the computational complexity

comparing to conventional Ncut method based on direct image

pixels. The experimental results also verify that the proposed

algorithm behaves an improved performance comparing to themean shift and the Ncut algorithm.

Keywords-Mean shift; Normalized cut (Ncut); Image

segmentation

I. INTRODUCTION

Mean shift [1] concept was first proposed in a estimatesof probability density gradient function by Fukunaga et al in1975. Until 1995, another important document with respectto the Mean-shift was published by Cheng Yizong [2], he hasmade a lot of promotion work for the basic Mean-shiftalgorithm, and pointed out the possible areas application of

the Mean-shift. In recent years, Mean-shift algorithm hasbeen widely used in computer vision areas, such as tracking,image segmentation, image smoothing, filtering, image edgeextraction, information fusion, motion estimation, featurespace analysis, video data analysis and so on. It’s apt to over-segmentation phenomenon, which is the common failing of this algorithm.

The image segmentation technique based on graph theoryis a new research highlight in the international imagesegmentation area, the technique considered pixel as nodesand essentially transformed image segmentation issue tooptimization problem, undirected weighted graph is alwaysused in image segmentation based on graph theory, A graphis always partitioned into multiple components , which can

minimize some cost function of the vertices in thecomponents and the boundaries between those components.Up to now, a lot of graph cut-based methods have been putforward for image segmentations. For instance, a generalimage segmentation approach based on normalized cut(Ncut) by solving an eigensystem, which was proposed byShi and Malik [3] .In recent years, Ncut algorithm is widelyused for image processing and related fields, such as the

motion picture [5], medical imaging [6], vector field [7] of the segmentation. However, this approach is NP-hardproblem, the more pixels in the image, the larger thegenerated graph of nodes is, which bring difficulties to solvethe algorithm.

Considering the above issues come from the twoalgorithms, this paper designed a combination of bothmethods, the specific algorithm can be find in the followingpart.

II. THE MEAN SHIFT ALGORITHM AND THE NCUT

A. The Mean Shift AlgorithmConsidering radially symmetric kernels satisfying

2( ) (|| || )

d K x c k x= , where 0

d c > ,which is chosen such

that2

0 0( ) (|| || ) 1

d K x dx c k x dx

∞ ∞

= =∫ ∫ [note that ( )k x

is defined only for 0 x ≥ ]. ( )k x is a monotonically

decreasing function , which is referred to the profile of the

kernel. Given the function ( ) ( )g x k x′= − as profile, the

kernel ( )G x is defined as2

,( ) (|| || )g d G x c g x= . For

n data points i x , i =1,…, n in the d -dimensional space Rd,

the mean shift vector is defined as

2

1,

2

1

(|| || )

( )

(|| || )

ni

i

ih G n

i

i

x x x g

hm x x

x xg

h

=

=

−

= −−

∑

∑(1)

where x is the center of the kernel, and h is a bandwidthparameter. Based on the above analysis, we present a brief review of the image segmentation method based on the meanshift procedure. Form the reference [4], we know that themean shift algorithm includes mean shift filtering and meanshift segmentation. The segmentation is actually a mergingprocess performed on a region that is produced by the meanshift filtering. The use of the mean shift segmentationalgorithm requires the selection of the bandwidth parameterh=(hr,hs). By controlling the size of the kernel, the bandwidthparameter can determines the resolution of the modedetection.

V7-293978-1-4244-6349-7/10/$26.00 c2010 IEEE



B. The Ncut Algorithm

The set of points in an arbitrary feature space can bedescribed as a weighted undirected graph G= (V, E), wherethe nodes of the graph are the points in the feature space, andan edge is formed between every pair of nodes. The weighton each edge,W(i,j), is a function of the similarity betweennodes i and j. A graph G= (V, E) can be partitioned into two

disjoint sets, A , B , A B V =U , A B = ∅I ,we expected

that the intragroup similarity is high and the intergroupsimilarity is low. In graph theoretic language, a mathematicalformulation of a cut is [3]

,

( , ) ( , )u A v B

cut A B w u v∈ ∈

= ∑

(2)

In this paper, we will use this normalized cut (Ncut) as the

partition criterion. The Ncut is

( , ) ( , )( , )

( , ) ( , )

cut A B cut A B Ncut A B

assoc A V assoc B V = +

(3)

where,

( , ) ( , )u A v V

assoc A V w u v∈ ∈

= ∑ is the total connection

from nodes in A to all nodes in the graph and

,

( , ) ( , )u B v V

assoc B V w u v∈ ∈

= ∑ is similarly define. When we

obtain the least value of Ncut, that is the best imagesegmentation.

III. THE IMPROVED IMAGE SEGMENTATION ALGORITHM

Normalized cut is proved to be NP-hard problem, whenthe nodes of graph increases, the solution of the problembecomes extremely complex, and the calculation of theproblem becomes large. Therefore, by incorporating the

advantages of the mean shift segmentation and thenormalized cut (Ncut) partitioning methods, the proposedmethod preprocesses an image by using the mean shiftalgorithm to form segmented regions, we use region nodesinstead of these regions, then use the Ncut method for regionnodes clustering. In many literatures, the Ncut method isapplied directly to image pixels. So for some large images,the weight matrix W is large, which brings hugecomputational complexity. However, the proposed methodoffers a considerable reduction of computational complexity,because the number of image region nodes is much smallerthan that of the pixels, the size of the weight matrix W issignificantly reduced. Moreover, the mean shift algorithmnot only removes noise, which limits the accuracy of graph

partitioning in the Ncut method, but also achieves improvedsegmentation performance. Nonetheless, it will produce thephenomenon of over-segmentation. The Ncut algorithm is aglobal clustering method, it can compensate for thephenomenon of over-segmentation, but it is very dependenton the selection of classification parameter K. however,mean shift is a non-supervised clustering segmentation

method, it is a good solution for solving the drawback of theNuct. This shows that the combination of the two methods isalso feasible. The proposed method consists of the followingsteps:

1) An image is preprocessed into multiple separatedregions using the mean shift algorithm.

2) These regions are much smaller than the image pixels,so we extracted each region, and use one region node insteadof one region. The information of the region nodes includes

features vector information and spatial location.3) According to the step 2, these region nodes are

represented as a weighted undirected graph, the graph as theNcut algorithm input, and use these region nodes to constructthe weight matrix W, and then use the Ncut method forregion nodes clustering.

IV. EXPERIMENTAL RESULTS AND ANALYSIS

In this paper, we demonstrate the superiority of theproposed method by comparing the performance of theproposed approach to existing methods using two images.The weight W(i, j) between regions i and j is defined as

22( ) ( ) 2( ) ( ) 2

22

|| |||| ||

i and j are adjacent

otherwise

*

0

i ji j

X I

X X F F

ij

if eW e

σ σ

− −− −

= ⎧⎪⎨⎪⎩

(4)

where F(i)={ R(i) ,G(i) ,B(i)} is the color vector of region i, if the image is the gray-level image, then F (i) is the gray value.and X(i) is the spatial location of region node i. in this paper,we defined the F(i) is the average gray of the region i, andthe X(i) is the center of the region i. in this case, the select of F(i) and X(i) are more representative.

In order to compare other method to the proposedalgorithm, we use the example of two image, as depicted inFig. 1 and Fig. 2. Fig. 1 image size is 277×384. Fig. 1(a)

shows the original image, and Fig. 1(b) depicts the resultantimage after applying the mean shift algorithm, with the whitecontours depicting the boundaries between the regions. Weset h=(hr,hs)=(8,8) and M=2000. As a result, the mean shiftalgorithm produces 8 regions. This eight regions of R(i) in F(i)

is 34,51,54,75,78,82,84,and 193 respectively (from small tolarge). The G(i) and B(i) are not list. Therefore, theconstructing the weight matrix W of the graph based onregion nodes using the Ncut algorithm is easier and smallerthan that based on pixels. Fig. 1(c) shows the partitioningresults by directly applying the Ncut algorithm to the imagepixels. With the partitioning parameter K=2 and table Idepicts the weight matrix W of the region nodes. Fig. 1(d) is

the grayscale display results of the proposed algorithmpartitioning. With the partitioning parameter K=2. Fig. 1(e)shows the results of the proposed algorithm partitioning.

The Fig. 1 image includes the bird in the foreground andthe bulrush in the background. Therefore, an effectionsegmentation algorithm should distinguish the bird from thebulrush background. In Fig. 1(b), many separated regions aresegmented by mean shift algorithm, it is not a good segment

V7-294 2010 2nd International Conference on Computer Engineering and Technology [Volume 7]



result. In Fig. 1(c), the Ncut algorithm is directly applied tothe image pixels, the image is partitioned into two parts.from Fig. 1(d) and Fig. 1(e). the segment result distinguishthe bird from the bulrush background. So the proposedmethod provides an improved performance compared to themean shift and the Ncut algorithm.

(a) (b)

(c) (d)

(e)

Fig. 1. (a) Original image. (b) The resultant image after applying the meanshift algorithm. (c)The partitioning results by directly applying the Ncutalgorithm to the image pixels. (d)The results of the proposed algorithmpartitioning grayscale display. (e) The results of the proposed algorithmpartitioning.

The Fig. 2(a) size is 240×160. Set h=(h r,hs)=(6,4) andM=10. With the partitioning parameter K=4. the analysis of the segment result is the same as the Fig. 1.

Finally, we consider the computational cost of theproposed algorithm and compare it with that of the Ncut

method. A PC with a 2.8-GHz Pentium CPU and 1Gmemory is applied to carry out the computation of theproposed method which consists of two sections. The firstsection is to segment the original image using the mean shiftmethod. The second section is to partition the region nodesby the mean shift method using the Ncut. The Ncut method[3] requires 40-50 s to process the image of 277×384 pixels.

When use the Ncut method, an image has to be decimatedinto a size of 120×120, the required time is only 8-10 s.Table II compares the computational cost between theproposed algorithm and the Ncut method for the imagesdepicted in Fig. 1 and Fig. 2.

(a) (b)

(c) (d)

(e)Fig. 2. (a) Original image. (b) The resultant image after applying the meanshift algorithm. (c) The partitioning results by directly applying the Ncutalgorithm to the image pixels. (d) The results of the proposed algorithmpartitioning grayscale display. (e) The results of the proposed algorithmpartitioning.

V. CONCLUSION

In this paper, a novel image segmentation algorithm has

been proposed and designed based on the conventional meanshift algorithm and Ncut algorithm. The effectiveness androbustness of the proposed algorithm have verified by someexperimental results to express an improved performancecompared to the Ncut algorithm. Also, the significantreduction to the computational cost of the proposed algorithm

in the experiments is favorable for practical applications.

[Volume 7] 2010 2nd International Conference on Computer Engineering and Technology V7-295



REFERENCES

[1] K. Fukunaga and L. D. Hostetler, “The estimation of the gradient of adensity funtion, with application in pattern recognition,” IEEE Trans.on Information Theory, vol. 21, no. 1, pp. 32-40, 1975.

[2] Y. Cheng, “Mean shift, mode seeking, and clustering,” IEEE Trans.on Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 790-799, 1995.

[3] J. Shi and J. Malik, “Normalized cuts and image segmentation,” IEEETrans. on PAMI, vol. 22, no. 8, pp. 888-905, 2000.

[4] D. Comariciu and P. Meer, “Mean shift: a robust approach towardfeature space analysis,” IEEE Trans. on PAMI, vol. 24, no. 5, pp.603-619, 2002.

[5] J. Shi and J. Malik, “Motion segmentation and tracking usingnormalized cuts,” Proceedings of the Sixth International Conferenceon Computer Vision (ICCV), Bombay, India, pp. 1154-1160, 1998.

[6] J. Carballido-Gamio, S. J. Belongie, and S. Majumdar, “Normalizedcuts in 3-D for spinal MRI segmentation,” IEEE Trans. on MedicalImaging, vol. 23, no. 1, pp. 36-44, 2004.

[7] H. Y. Li, W. B. Chen, and I. F. Shen, “Segmentation of discrete

vector fields,” IEEE Trans. on Visualization and Computer Graphics,vol. 12, no. 3, pp. 289-301, 2006.

TABLE I. WEIGHT MATRIX W OF ALL REGION NODES

1 2 3 4 5 6 7 8

1 1 0.2257 0.4804 0 0 0 0 0

2 0.2257 1 0.2210 0.6888 0.2738 0 0 0

3 0.4804 0.2210 1 0 0.6706 0.0135 0.4260 0

4 0 0.6888 0 1 0.3291 0.1376 0 3.6470e-04

5 0 0.2738 0.6706 0.3291 1 0 0.7491 5.7401e-04

6 0 0 0.0135 0.1376 0 1 0.1418 0.0014

7 0 0 0.4260 0 0.7491 0.1418 1 5.4429e-04

8 0 0 0 3.6470e-04 5.7401e-04 0.0014 5.4429e-04 1

TABLE II. COMPARED COMPUTATIONALCOST BETWEEN THE PROPOSED METHOD AND THE NCUT METHOD

Region num. of

mean shift

The value of

the K

Time of mean

shift (s)

Time of Ncut

Merging (s)

Time of the

proposedmethod (s)

Time of Ncut

algorithm (s) [3]

Fig.1 8 2 3.51 0.83 4.34 9.47

Fig.2 24 4 0.54 0.36 0.9 3.76

V7-296 2010 2nd International Conference on Computer Engineering and Technology [Volume 7]

an improved image segmentation algorithm base on normalized cut

Documents