Proceedings of the International Conference on Applied Mathematics and Theoretical Computer Science - 2013
183
A Robust Thresholding Technique for Image Segmentation from Gray Images T. Kalaiselvi and P. Nagaraja Abstract--- This work aimed to find a robust thresholding technique to segment the gray images. Thresholding is a simple method that plays a vital role in image segmentation. This paper compares three popular conventional thresholding techniques such as Ridler and Calvard’s, Kittler and Illingworth’s (MET) and Otsu’s thresholding. Gray image processing finds applications on the medical imaging, remote sensing images, SAR images, scanning electron microscope and transmission electron microscopy images and document images. Experiments were done using the mixture of gray images chosen form popularly available image databases. The performance analysis was carried out by using the region nonuniformity parameter. The study reveals that the three techniques considered have their own feasibility depending on the input images taken. Otsu’s thresholding finds to produce better quality of results when compared to other methods while considering MRI head scan images. A Kittler and Illingworth’s thresholding technique provides better feasibility for general gray images. This work provides a best framework to decide about the thresholding technique to be used while considering the input images as either medical scans or general gray images. Keywords--- Gray Images, Image Segmentation, Kittler and Illingworth, Medical Scans, Otsu, Ridler and Calvard, Thresholding
different shades of gray. Where the size of the gray image is smaller then the color images. It is easily to manipulate the image processing operations such as segmentation, restoration, image pre-processing etc., these images are effectively used for many tasks and more complicated, harder to process than color images. Gray image processing finds applications on the medical imaging, remote sensing images, SAR images, scanning and transmission of electron microscopy images and document images. Thresholding techniques are classified into two categories: global and local threshold. The global threshold is single threshold value, which is used in the whole image. The local threshold is threshold value assigned a each pixel by finding its belongs to background or foreground of pixel using the information in the region of pixel. Several popular techniques were developed for thresholding [3]. This paper presents the most popularly used three thresholding methods namely Otsu’s method, Ridler and Calvard’s method and Kittler and Illingworth’s method. Experiments were done using some MRI of human head scans and general gray images selected from popular imaging pools. The comparison is done by using the region non-uniformity parameter, a unique parameter the does not require any ground truth for the comparison. The methods are explained in section 2. The results and discussion is given in section 3 and the conclusion is given in section 4. II. METHODS
I. INTRODUCTION
I
MAGE segmentation is an important study of digital image processing. The image segmentation processed through several methods. Segmentation algorithms are categorized into two properties, discontinuity and similarity. The first category is based on the abrupt changes on the gray level of image. The second category is based on the partioning image is to similar pixels within the regions. Thresholding method is a simplest method of image segmentation and it is based on the second category. Thresholding converts any higher scale images into binary images where it’s assigned into two levels of pixels that are above or below that specified parameter, is called threshold value [1] [2]. The monochromatic image which is the range of measured values of monochromatic light from black to white is called gray image. The gray image posses the intensity values of T. Kalaiselvi, Assistant Professor, Image Processing Lab, Department of Computer Science and Applications, Gandhigram Rural Institute - Deemed University, Dindigul, India. E-mail:
[email protected] P. Nagaraja, Research Scholar, Image Processing Lab, Department of Computer Science and Applications, Gandhigram Rural Institute - Deemed University, Dindigul, India. E-mail:
[email protected]
2.1 Ridler and Calvard’s Method This method is called as an iterative approach method [4]. First compute the initial threshold value of given image. Initial threshold (T0) is the mean of the intensity values of pixels. It separates image into foreground and background classes respectively. The mean of the foreground classes as μ f and background as μb. Then mean values of two classes are threshold value for foreground T fg and threshold value for background Tbg. The improved threshold value is T1:
T1
(Tbg
T fg )
(1)
2
The new threshold value T1 is taken as T0 and this process continues iteratively until T1 ≈ T0. Finally T1 and T0 close to each other then T1 is taken as threshold value T. the algorithmic steps are defined here: 1. 2.
Step 1: To assume the histogram of the image h(x) where x is the gray level. Step 2: Select the initial threshold T0 is equal to the average of the gray level of given image.
ISBN 978-93-82338-35-2 | © 2013 Bonfring
Proceedings of the International Conference on Applied Mathematics and Theoretical Computer Science - 2013
3.
Step 3: At step T0, compute the μbg and μfg of mean of the background and foreground pixels. Step 4: μfg is mean of below T0 and μbg is mean of above T0. T1 is computed as: fg
T1 1.
(T0 )
bg
(T0 )
pi – is the probability of occurring of pixel value xi. The mean of foreground and background pixels is,
Step 5: If T1=T0 stop the process otherwise go to step 3.
2.2 Kittler and Illingworth’s Method This method is called as minimum error thresholding (MET) method. The algorithm is based on Bayesian classification rule [5]. In this method, first compute the bimodel histogram of the gray level image h (g) is normally distributed. Then estimate the priori probability (Pi) of gray level of histogram h(g) and find the mean of total probability. It is the initial threshold (T) of given image and separate the image into foreground and background classes (i=1, 2…). Compute the mean of their normal distributions as μi and standard deviations σi. Find the parameters are following:
F
2 bg
2 fg
h( g ) g
1 Pi (T )
i (T )
2
a
a
(4) 2 i
0
(5)
(T )) h( g )
i 1
T
i 1
n
i 2
b
and T 1
(6)
i 2
The criterion function is, J (T )
1
2[ P1 (T ) log
2 bg
(T )
2[ P1 (T ) log P1 (T )
1 WB (T )
(T )
1 W F (T )
(T )
2 fg
P2 (T ) log
(T )]
P2 (T ) log P2 (T )]
T 1 i 0
p (i )
(i
B
(T )) 2 P(i )
i 1
(12)
T
(i
F
(T )) 2 P(i )
i 1
(13)
(T ) -variance of the pixels in the background.
2 fg
(T ) -variance of the pixels in the foreground.
This performance criterion carried out by using some general gray images and MRI human head scans. General gray images were selected from segmentation evaluation data base maintained by Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Israel. The MRI head scans were selected from the “The Whole Brain Atlas” website maintained by Harvard Medical School, USA. The segmented images are evaluated using the performance measure Region Non-Uniformity (NU). Ground truth information is not require for this measure. The measure is defined as,
2 bg
(T ) WF (T )
2 fg
(T )
F fg
NU where 2 fg
2
F fg
W F (T )
N 1 i T
p (i )
Bbg
2 fg 2
(14)
is represent the variance of whole image and
is represent the variance of foreground. A well segmented
image will have non uniformity close to 0. In worst case NU=1. The worst case corresponds to an image for which background and foreground and is indistinguishable up to second order moments.
(8)
Where,
W B (T )
(11)
T
(7)
2.3 Otsu’s Method This method is called as optimum threshold method [6]. Otsu’s thresholding involves all possible threshold values and calculate the pixel levels in each side of the threshold. This threshold value separates the foreground or background of pixels. This algorithm compute the image to be threshold contains the two classes of pixels. We can use the within class variance, it is the weighted sum of the variances of each foreground and background.
(T ) WB (T )
iP(i ) i 1
2 bg
This minimum error threshold is compute the minimizes criterion of J (T).
2 within
(10)
T
III. RESULTS AND DISCUSSION
h( g ) g
iP(i ) i 1
(3)
a
Where
(T )
b
1 b (g Pi (T ) g a
(T )
1 WF (T )
T
The variance of foreground and background pixels is,
b
Pi (T )
1 W B (T )
B (T )
(2)
2
184
(9)
ISBN 978-93-82338-35-2 | © 2013 Bonfring
Proceedings of the International Conference on Applied Mathematics and Theoretical Computer Science - 2013
185
Figure 1: General Gray Images GI1-GI5 are in column 1.The results of Otsu’s method are in column 2, The results of Ridler and Calvard method are in column 3, The results of Kittler and Illingworth method are in column 4.
ISBN 978-93-82338-35-2 | © 2013 Bonfring
Proceedings of the International Conference on Applied Mathematics and Theoretical Computer Science - 2013
186
Figure 2: MRI Head scans BI1-BI5 are in column1. The results of Otsu’s method are in column 2, the results of Ridler and Calvard method are in column 3, The results of Kittler and Illingworth method are in column 4. Table 1: Region Non-Uniformity of General Gray Images Methods Images GI-1 GI-2 GI-3 GI-4 GI-5
Otsu T
NU
127 140 142 182 103
0.0615 0.0047 0.0524 0.0023 0.0404
Ridler and Calvard T NU 126 139 140 180 102
0.0617 0.0048 0.0546 0.0024 0.0415
ISBN 978-93-82338-35-2 | © 2013 Bonfring
Kittler and Illingworth T NU 113 179 190 225 116
0.0555 0.0041 0.0161 0.0021 0.0352
Proceedings of the International Conference on Applied Mathematics and Theoretical Computer Science - 2013
187
Table 2: Region Non-Uniformity of MRI Head Scans Methods Images BI-1 BI-2 BI-3 BI-4 BI-5
Otsu
Ridler and Calvard
Kittler and Illingworth
T
NU
T
NU
T
NU
62 58 65 65 57
0.3940 0.3635 0.2013 0.2377 0.1795
59 59 63 63 55
0.4070 0.3635 0.2035 0.2390 0.1811
8 8 8 8 8
0.5774 0.6121 0.3333 0.3286 0.2860
The comparisons of these three thresholding methods are done by using the final binary images produced by them. In Fig.1, the general gray images are given in column 1. The results of Otsu method given in column 2, the results of Ridler and Calvard’s method given in column 3 and the results of Kittler and Illingworth’s method given in column 4. The performance measure NU is computed for general gray images and values are shown in Table 1. Non uniformity of well segmented image is close to 0. The values of Otsu’s and Ridler and Calvard’s thresholding provide NU similar to each other. But MET provides well segmented images by having NU more close to 0. In Figure 2. the original MRI head scans are given in column 1. The results of Otsu method are in column 2, the results of Ridler and Calvard’s method are in column 3 and the results of Kittler and Illingworth’s method are in column 4. The performance measure is computed for final binary brain images and the obtained result values are shown in Table 2. NU of Kittler and Illingworth’s method is close to 1 for MRI brain images. Further, it had very low threshold value, nearer to 8 and thus provided under-segmented binary images as shown in column4 of Fig.2. NU of Ridler and Calvard’s thresholding value is similar to the Otsu’s method, but slightly higher than Otsu’s NU value. NU of Otsu’s thresholding is close to 0. This thresholding method given best results for MRI brain images. We observed some distinct by comparing these thresholding methods. Kittler and Illingworth’s thresholding given well segmented images for general gray images. This thresholding is not provide best result for MRI head scans. Otsu’s thresholding is given a well segmented image of MRI brain images. Mean values computed from the input images are targeted with the existing Otsu’s method, Ridler and Calvard’s method and Kittler and Illingworth’s method. In future, the standard deviation of the neighborhood regions would be additionally considered to enrich these methods. Based on this standard deviation upgradation, the performance would be compared for their segmentation time. This work is in progress. IV. CONCLUSION This paper compares three popular thresholding methods to choose a robust technique for gray image segmentation. Experiments were done on both general images and medical images. The outputs generated by the three methods were compared using NU measures. Ridler and Calvard thresholding is an iterative approach method and similar to the
Otsu’s thresholding. A Kittler and Illingworth’s thresholding technique provides better results for general gray images. Otsu’s thresholding finds to produce better quality of results when compared to other methods while considering MRI brain images. REFERENCES R.C. Gonzalez, R.E. Woods, “Digital Image Processing,” Pearson Education, Inc., Publication, 2009. [2] M. Sonka, V. Hlavac and R. Boyal, “Digital Image Processing and Computer Vision,” Cengage Learning, 2008. [3] S.S. Al-amri, N.V. Kalyankar and S.D. Khamitkar, “Image Segmentation using threshold techniques,” Journal of Computing, Vol. 2, 2010. [4] T. Ridler and S. Calvard, “ Picture Thresholding using and Iterative Selection Method,” IEEE Transactions of systems, Man and Cybernetics (SMC), Vol. 8, No.8, 1978. [5] J. Kittler and J. Illingworth, “Minimum Error Thresholding,” Pattern Recognition, Vol. 19, Pp. 41-47, 1979. [6] N. Otsu, “A Threshold Selection from Gray level Histograms,” IEEE Transactions of systems, Man and Cybernetics (SMC), Vol. 9, No.1, Pp. 62-66, 1979. [7] M. Sezgin and B. Sankur, “Survey over image thresholding techniques and quantitative performance evaluation,” Journal of Electronic Imaging, Vol. 13(1), Pp.146-165, 2004. [8] P.K. Sahoo, S. Soltani and A.K.C. Wong, “Survey of Thresholding Techniques,” Computer Vision, Graphics and Image Processing, Vol. 41, Pp. 230-260, 1988. [9] J.H. Xue and Y.J. Zhang “Ridler and Calvard’s, Kittler and Illingwroth’s and Otsu’s methods for image thresholding,” Pattern Recognition Letters, Vol. 33, Pp. 793-797, 2012. [10] A. Drobchenko, J. Vartiainen, et.al, “ Thresholding based Detection of Fine and Sparse Details,” Frointiers of Electrical and Electronic Engineering in China, Vol.6 (2), Pp. 328-338, 2011 [11] N. Nacereddine, L. Hamami, M. Tridi and N. Oucief, “ Non-Parametric Histogram- Based Thresholding Methods for Weld Defect Detedtion in Radiography,” World Academy of Science, Engineering and Technology, Vol. 9, 2007. [1]
T. Kalaiselvi currently working as an Assistant Professor in Department of Computer Science and Applications, Gandhigram Rural Institute - Deemed University, Dindigul, India. She received her Bachelor of Science (BSc) degree in Mathematics and Physics in the year 1994 and Master of Computer Applications (MCA) degree in the year 1997 from Avinashilingem University, Coimbatore. She received her Ph.D (Fulltime) degree from Gandhigram Rural Institute in the year 2010. In the year 2008, she received a project from Department of Science and Technology (DST), Government of India under Scheme for Young Scientists and Professionals (SYSP) by Sceince for Equity, Empowerment and Development (SEED) Division for three years (2008-2011). Her research focuses on Brain Image Processing and brain tumor or lesion detection from MR Head Scans to enrich the Computer Aided Diagnostic process, Telemedicine and Tele radiology services. She is Academic Community Member (ACM) in International Congress for Global Sceince and Technology (ICGST), Life
ISBN 978-93-82338-35-2 | © 2013 Bonfring
Proceedings of the International Conference on Applied Mathematics and Theoretical Computer Science - 2013
Member (LM) in Indian Society for Technical Education (ISTE) and Lifetime Member (LM) in Telemedicine Society of India (TSI). P. Nagaraja currently doing as an Research Scholar (Full-time) in Department of Computer Science and Applications, Gandhigram Rural Institute - Deemed University, Dindigul, India. He received his Bachelor of Science (BSc) degree in Physics in the year 2008 and Master of Computer Applications (MCA) degree in the year 2011 from Gandhigram Rural Institute - Deemed University. His Research focuses on Brain Tissue Segmentation in MRI Head scans.
ISBN 978-93-82338-35-2 | © 2013 Bonfring
188
