**4. Ovarian classification**

image of the ovary and the resultant images at different steps of fuzzy based method are shown in Figure 7(b)-(e). Many undesired spurious regions are also obtained (e.g., regions inside the endometrium). These spurious regions must be removed as much as possible. Therefore, the regions having an area less than T are removed (Figure 7(f)). The Figure 7 (g) depicts the segmented follicles (outlined in white) superimposed on the original image. The Figure 7 (h) depicts the recognized follicles after applying classification rules and Figure 7 (i) shows the

The Figure 8 depicts comparison of the fuzzy logic based classification with the 3σ intervals based classification [section 3(i)]. In the Figure 8 (a) and (d) are two original images, (b) and (e) are their corresponding resultant images by the 3σ intervals based method. and, (c) and (f) are resultant images of fuzzy based method. It is observed that the regions which are misclas‐ sified as follicles, by the method in [section 3(i)] (Figure 8 (b) and (e)), are correctly classified by the fuzzy logic based method (Figure 8 (c) and (f)). Hence, the classification accuracy of the fuzzy logic based method is improved as compared to the method in [section 3(i)]. The Table 6 presents number of follicles detected in the results of the fuzzy based method and the method

**Number of follicles detected**

**3(i)]**

**Manual (by medical expert)**

follicles annotated manually by the medical expert.

184 Advancements and Breakthroughs in Ultrasound Imaging

classification based method for original images in the Figure 8.

Input original image

in [section 3(i)] corresponding to the original images in the Figure 8.

**Method fuzzy based method 3σ intervals based method [section**

Total Correct False Total Correct False

Figure 8(a) 3 3 - 5 3 2 3

Figure 8(d) 1 1 - 3 1 2 1

**Table 6.** Comparison of experimental results of proposed fuzzy logic based classification and 3σ interval based

as compared to that in the 3σ intervals based method [section 3(i)] for classification.

The Table 7 shows the comparison of classification results of fuzzy based method and the method in [section 3(i)] after ten-fold experiments for both the data sets. The average detection rates for the fuzzy based method with D1 and D2 sets are 98.18% and 97.61%, false acceptance rates (FAR) are 4.52% and 9.05%, and false rejection rates (FRR) are 1.76% and 2.37%, respec‐ tively. The average detection rates for the method in the Section 3(i) with D1 and D2 sets are 92.3% and 96.66%, false acceptance rates (FAR) 13.6% and 15.04%, and false rejection rates (FRR) are 7.62% and 3.33%, respectively. It is observed that the false acceptance rate (FAR) is reduced and the classification accuracy is improved in case of the fuzzy logic based method

The ovaries are classified into three types based on the number and size of the follicles. Ovary is scanned, follicles are identified by using the method described the section 3, and the size of the follicles are measured and the number of follicles are counted.

There are three categories :

**•** The ovary containing 1-2 follicles with size measuring greater than 28mm in size, is a cystic ovary.

n1 - number of follicles of normal ovary

n2 - number of follicles of cystic ovary

which is shown in the Table 8.

Type I error (FAR)

Type II error (FRR)

ten-fold experiments.

sz2- size of the follicles in the cystic ovary

n3 - number of follicles of polycystic ovary

Methods Fuzzy logic method

sz3 - size of the follicles in the polycystic ovary

The number of follicles and size of follicles of these three classes are stored as knowledge base

3σ interval based method

Classification rate 98.18 % 92.3 % 97.61% 96.66%

**Table 7.** Comparison of classification results of fuzzy based classification method with 3σ intervals based method after

The construction of the membership functions for the output variables is done in the similar manner. Since this is Sugeno-type inference (precisely, zero-order Sugeno), constant type of output variable fits the best to the given set of outputs (0 for normal ovary and 0.5 for cystic ovary and 1 for polycystic ovary). Based on the descriptions of the inputs (the number of the follicles NN and size of the follicles S) and output variables (normal ovary, cystic ovary, polycystic ovary). The fuzzy rules for classification procedure in verbose format are as follows:

**i.** IF (n1 is input to mfn1) AND (sz1 is input to mfs1) THEN (class is normal ovary)

**ii.** IF (n2 is input to mfn2) AND (sz2 is input to mfs2) THEN (class is cystic ovary)

**iii.** IF (n2 is input to mfn3) AND (sz3 is input to mfs3) THEN (class is polycystic ovary)

At this point, the fuzzy inference system has been completely defined, in that the variables, membership functions and the rules necessary to determine the output classes are in place.

**Data set D1 set D2 set**

**Classification results**

Follicle Detection and Ovarian Classification in Digital Ultrasound Images of Ovaries

[section 3(i)] Fuzzy logic method

4.52 % 13.6 % 9.05% 15.04%

1.76 % 7.62 % 2.37 % 3.33 %

3σ interval based method [section 3(i)] Based Method

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187

sz1 - size of the follicles in the normal ovary

**Figure 8.** Comparison of resultant images of the fuzzy based method with the 3σ intervals based classification for two different original images. (a) and (d) original images, (b) and (e) resultant images of 3σ intervals based, (c) and (f) re‐ sultant images of fuzzy based method.


The two ovarian classification methods are discussed below [Hiremath and Tegnoor, 2012]:

#### **i.** Fuzzy ovarian classification

*Training phase:* The fuzzy inference system (FIS) of sugeno type is employed using the fuzzy input variables the number of follicles NN and the size of the follicle S and output variables: normal, cystic and polycystic ovarian classes. The Trapezoidal membership function is used for each of the fuzzy input variables with minimum and maximum value of the corresponding variables. Let mfn1 and mfs1, mfn2 and mfs2, and mfn3 and mfs3, be the trapezoidal mem‐ bership functions of the fuzzy input variables NN and S respectively, belonging to the normal ovarian class, cystic ovarian class, polycystic ovarian class.

During the training phase, the parameters, namely, NN and S, are computed for the ovarian images known to be healthy, cystic and polycystic ovary in the training images in consultation with the medical expert, which are used to set the rules for classification of ovarian images.

We denote,


**•** The ovary containing 12 or more follicles with size measuring less than 10mm, is a polycystic

**Figure 8.** Comparison of resultant images of the fuzzy based method with the 3σ intervals based classification for two different original images. (a) and (d) original images, (b) and (e) resultant images of 3σ intervals based, (c) and (f) re‐

**•** The ovary containing 1-10 follicles with size measuring 2-10mm, are antral follicles and with the 10-28mm size, are dominant follicles, is a normal ovary with m number of antral follicles

The two ovarian classification methods are discussed below [Hiremath and Tegnoor, 2012]:

*Training phase:* The fuzzy inference system (FIS) of sugeno type is employed using the fuzzy input variables the number of follicles NN and the size of the follicle S and output variables: normal, cystic and polycystic ovarian classes. The Trapezoidal membership function is used for each of the fuzzy input variables with minimum and maximum value of the corresponding variables. Let mfn1 and mfs1, mfn2 and mfs2, and mfn3 and mfs3, be the trapezoidal mem‐ bership functions of the fuzzy input variables NN and S respectively, belonging to the normal

During the training phase, the parameters, namely, NN and S, are computed for the ovarian images known to be healthy, cystic and polycystic ovary in the training images in consultation with the medical expert, which are used to set the rules for classification of ovarian images.

ovary.

We denote,

and n number of dominant follicles.

186 Advancements and Breakthroughs in Ultrasound Imaging

ovarian class, cystic ovarian class, polycystic ovarian class.

**i.** Fuzzy ovarian classification

sultant images of fuzzy based method.


The number of follicles and size of follicles of these three classes are stored as knowledge base which is shown in the Table 8.


**Table 7.** Comparison of classification results of fuzzy based classification method with 3σ intervals based method after ten-fold experiments.

The construction of the membership functions for the output variables is done in the similar manner. Since this is Sugeno-type inference (precisely, zero-order Sugeno), constant type of output variable fits the best to the given set of outputs (0 for normal ovary and 0.5 for cystic ovary and 1 for polycystic ovary). Based on the descriptions of the inputs (the number of the follicles NN and size of the follicles S) and output variables (normal ovary, cystic ovary, polycystic ovary). The fuzzy rules for classification procedure in verbose format are as follows:

**i.** IF (n1 is input to mfn1) AND (sz1 is input to mfs1) THEN (class is normal ovary)

**ii.** IF (n2 is input to mfn2) AND (sz2 is input to mfs2) THEN (class is cystic ovary)

**iii.** IF (n2 is input to mfn3) AND (sz3 is input to mfs3) THEN (class is polycystic ovary)

At this point, the fuzzy inference system has been completely defined, in that the variables, membership functions and the rules necessary to determine the output classes are in place.


**Ovarian class**

**Number of images**

**Table 10.** Experimental results for classification accuracy for all the three classes

**Figure 9.** Sample results for proposed ovarian classification method

**ii.** Ovarian classification by using SVM

**Number of correctly classified images**

Normal ovary 15 15 15 - -

Cystic ovary 10 10 10 - -

Polycystic ovary 10 10 10 - -

Original image Detected follicle Manual detection Ovary

Normal ovary

The aim of support vector machine (SVM) is to devise a computationally efficient way of learning separating hyper planes in a high dimensional feature space [49]. The SVMs have been shown to be an efficient method for many real-world problems because of its high generalization performance without the need to add a priori knowledge. Thus, SVMs have much attention as a successful tool for classification [50,51], image recognition [52,53] and

**Manual detection**

Follicle Detection and Ovarian Classification in Digital Ultrasound Images of Ovaries

**Type I error**

http://dx.doi.org/10.5772/56518

**Type II error**

189

classification

Polycystic ovary

Cystic ovary

with 2 antral follicles and 1 dominant follicle.

**Table 8.** The knowledge base of number of follicles and size of follicles of all the three classes

*Testing phase:* During the testing phase, we compute the number of follicles NN, and the size of each follicle S, for an ovary with the detected follicles and apply the above classification rules to determine whether an ovary is normal, cystic, and polycystic.

*Experimental results*: The experimentation is done using image data set D3. The D3 set consists of 70 sample ultrasound ovarian images of size 512x512, out of which 35 images are used for training and 35 for testing. In the first step, the ten-fold experiments for the follicle detection are done and then the average follicle detection rate is computed. Further, in the second step, for the ovary classification, 70 sample images of the detected follicles are used, of which 35 are used for training and 35 are used for testing. The ten-fold experiments for the ovarian classi‐ fication are done and the average classification rate for the ovarian type is computed. The Figure 9 shows the sample results for the ovarian classification method. detection method after performing ten-fold experiments for the image data set. The Table 9 shows the average classification results of follicle detection method after performing ten-fold experiments for the image data set. The follicle detection method (Section 3(ii)) yields the average detection rate for the fuzzy based method 98.47%, false acceptance rate (FAR) 2.61% and false rejection rate (FRR) 1.47%.


**Table 9.** Average classification results after ten-fold experiments

The Table 10 shows the ten-fold experimental results of the ovarian classification based on fuzzy inference rules. It is observed that the average normal ovary cyst ovary and polycystic ovary is 100%, with zero false acceptance rate is (FAR) and false rejection rate (FRR). Although, the proposed ovarian classification method yields 100% classification results, it is to be noted that these results are with reference to the limited data set used for experimentation. However, in case of different data sets, with varying image resolution, image sizes and numbers, the classification accuracy may be less than 100%.


**Table 10.** Experimental results for classification accuracy for all the three classes

*Testing phase:* During the testing phase, we compute the number of follicles NN, and the size of each follicle S, for an ovary with the detected follicles and apply the above classification

Normal ovary 1-10 15-10000

Cystic ovary 1-2 4300-75000

Polycystic ovary 12-20 15-9000

**Number of follicles Size of the follicle**

*Experimental results*: The experimentation is done using image data set D3. The D3 set consists of 70 sample ultrasound ovarian images of size 512x512, out of which 35 images are used for training and 35 for testing. In the first step, the ten-fold experiments for the follicle detection are done and then the average follicle detection rate is computed. Further, in the second step, for the ovary classification, 70 sample images of the detected follicles are used, of which 35 are used for training and 35 are used for testing. The ten-fold experiments for the ovarian classi‐ fication are done and the average classification rate for the ovarian type is computed. The Figure 9 shows the sample results for the ovarian classification method. detection method after performing ten-fold experiments for the image data set. The Table 9 shows the average classification results of follicle detection method after performing ten-fold experiments for the image data set. The follicle detection method (Section 3(ii)) yields the average detection rate for the fuzzy based method 98.47%, false acceptance rate (FAR) 2.61% and false rejection rate

**Classification rate Type I error (FAR) Type II error (FRR)** 98.47% 2.61% 1.47%

The Table 10 shows the ten-fold experimental results of the ovarian classification based on fuzzy inference rules. It is observed that the average normal ovary cyst ovary and polycystic ovary is 100%, with zero false acceptance rate is (FAR) and false rejection rate (FRR). Although, the proposed ovarian classification method yields 100% classification results, it is to be noted that these results are with reference to the limited data set used for experimentation. However, in case of different data sets, with varying image resolution, image sizes and numbers, the

**Table 9.** Average classification results after ten-fold experiments

classification accuracy may be less than 100%.

rules to determine whether an ovary is normal, cystic, and polycystic.

**Table 8.** The knowledge base of number of follicles and size of follicles of all the three classes

**Image type**

188 Advancements and Breakthroughs in Ultrasound Imaging

(FRR) 1.47%.

**Figure 9.** Sample results for proposed ovarian classification method

#### **ii.** Ovarian classification by using SVM

The aim of support vector machine (SVM) is to devise a computationally efficient way of learning separating hyper planes in a high dimensional feature space [49]. The SVMs have been shown to be an efficient method for many real-world problems because of its high generalization performance without the need to add a priori knowledge. Thus, SVMs have much attention as a successful tool for classification [50,51], image recognition [52,53] and bioinformatics [54]. The SVM model can map the input vectors into a high-dimensional feature space through some non-linear mapping, chosen a priori. In this space, an optimal separating hyperplane is constructed. SVM is the implementation of the structural risk minimization principle whose object is to minimize the upper bound on the generalization error. Given a set of training vectors (l in total) belonging to separate classes, (x1, y1), (x2, y2), (x3, y3),..., (xl, yl), where *xi* <sup>∈</sup>*<sup>R</sup> <sup>n</sup>*denotes the ith input vector and *yi* <sup>∈</sup>{ <sup>+</sup> 1, <sup>−</sup>1} is the corresponding desired output. The maximal margin classifier aims to find a hyperplane w: wx + b = 0 to separate the training data. In the possible hyperplanes, only one maximizes the margin and the nearest data point of each class. The Figure 10 shows the optimal separating hyperplane with the largest margin. The support vectors denote the points lying on the margin border. The solution to the classification is given by the decision function in the equation 13.

$$f(\mathbf{x}) = \operatorname{sign}\left(\sum\_{i=1}^{N\_{SV}} \alpha\_i y\_i k(s\_{i,\succ} \mathbf{x}) + b\right) \tag{13}$$

where *α<sup>i</sup>* is the positive Lagrange multiplier, *si* is the support vector (NSV in total) and k(si , x) is the function for convolution of the kernel of the decision function. The radial kernels perform best in our experimental comparison, and, hence, are chosen in the proposed diagnosis system. The radial kernels are defined as (equation 14).

$$k(\mathbf{x}, y) = \exp\left(-\gamma \left(\mathbf{x} - y\right)^2\right) \tag{14}$$

**Classification accuracy (%) of follicle detection**

Follicle Detection and Ovarian Classification in Digital Ultrasound Images of Ovaries

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191

1.61 % 2.61%

1.10 % 1.47%

**Method SVM based method Fuzzy based method [4(i)]**

**Table 11.** Comparison of classification results of SVM based method and fuzzy based method [section 4(i)] for follicle

The Table 12 shows the ten-fold experimental results of the ovarian classification based on SVM. It is observed that the average classification rates for normal ovary, cystic ovary and polycystic ovary are 100%, with zero false acceptance rate (FAR) and zero false rejection rate (FRR). It is observed that both the proposed SVM based method and the fuzzy based method [section 4(i)] yield 100% accuracy in ovarian classification, although the SVM outperforms the

The Table 13 shows the comparison of all the follicle detection and ovarian classification methods developed in the present study and the other follicle detection methods available in

Classification rate 98.89 % 98.47%

Type I error (FAR)

Type II error (FRR)

detection after ten-fold experiments

the literature.

fuzzy method [section 4(i)] in follicle detection.

**Figure 10.** Optimal hyperplane for support vector machine

By using the SVM method, firstly, follicles are detected and secondly, the ovarian classification is performed [55]. During the training phase, the parameters, namely, the number of follicles NN and the size of the follicle S, are determined for the ovarian images known to be normal, cystic and polycystic ovary in the training images in consultation with the medical expert. The quadratic kernel is used for training the three-class SVM classifier; normal, cystic and poly‐ cystic ovary being the three classes.

During the testing phase, the parameters, namely, the number of follicles NN and the size of follicles S, are determined, and then, the SVM classifier is used to determine whether an ovary is normal, cystic, or polycystic.

*Experimental results*: The Table 11 shows the comparison of classification results of SVM based method and the fuzzy based method in [section 4(i)] after ten-fold experiments. The average follicle detection rate for the SVM method is 98.89%, false acceptance rate (FAR) is 1.61 % and false rejection rate (FRR) is 1.10%. The average detection rate for the method in [section 4(i)] is 98.47%, false acceptance rate (FAR) is 2.61% and false rejection rate (FRR) is 1.47%. It is observed that the classification accuracy is improved in the SVM based method as compared to the fuzzy based method [section 4(i)].

**Figure 10.** Optimal hyperplane for support vector machine

bioinformatics [54]. The SVM model can map the input vectors into a high-dimensional feature space through some non-linear mapping, chosen a priori. In this space, an optimal separating hyperplane is constructed. SVM is the implementation of the structural risk minimization principle whose object is to minimize the upper bound on the generalization error. Given a set of training vectors (l in total) belonging to separate classes, (x1, y1), (x2, y2), (x3, y3),..., (xl, yl), where *xi* <sup>∈</sup>*<sup>R</sup> <sup>n</sup>*denotes the ith input vector and *yi* <sup>∈</sup>{ <sup>+</sup> 1, <sup>−</sup>1} is the corresponding desired output. The maximal margin classifier aims to find a hyperplane w: wx + b = 0 to separate the training data. In the possible hyperplanes, only one maximizes the margin and the nearest data point of each class. The Figure 10 shows the optimal separating hyperplane with the largest margin. The support vectors denote the points lying on the margin border. The solution to the

,

å (13)

( ( ) ) <sup>2</sup> *kxy x y* ( , ) exp = -g - (14)

, x) is

*ii i*

is the positive Lagrange multiplier, *si* is the support vector (NSV in total) and k(si

the function for convolution of the kernel of the decision function. The radial kernels perform best in our experimental comparison, and, hence, are chosen in the proposed diagnosis system.

By using the SVM method, firstly, follicles are detected and secondly, the ovarian classification is performed [55]. During the training phase, the parameters, namely, the number of follicles NN and the size of the follicle S, are determined for the ovarian images known to be normal, cystic and polycystic ovary in the training images in consultation with the medical expert. The quadratic kernel is used for training the three-class SVM classifier; normal, cystic and poly‐

During the testing phase, the parameters, namely, the number of follicles NN and the size of follicles S, are determined, and then, the SVM classifier is used to determine whether an ovary

*Experimental results*: The Table 11 shows the comparison of classification results of SVM based method and the fuzzy based method in [section 4(i)] after ten-fold experiments. The average follicle detection rate for the SVM method is 98.89%, false acceptance rate (FAR) is 1.61 % and false rejection rate (FRR) is 1.10%. The average detection rate for the method in [section 4(i)] is 98.47%, false acceptance rate (FAR) is 2.61% and false rejection rate (FRR) is 1.47%. It is observed that the classification accuracy is improved in the SVM based method as compared

æ ö = a+ ç ÷ è ø

1 ( ) ( ) *NSV*

*i f x sign y k s x b* =

classification is given by the decision function in the equation 13.

The radial kernels are defined as (equation 14).

190 Advancements and Breakthroughs in Ultrasound Imaging

cystic ovary being the three classes.

to the fuzzy based method [section 4(i)].

is normal, cystic, or polycystic.

where *α<sup>i</sup>*


**Table 11.** Comparison of classification results of SVM based method and fuzzy based method [section 4(i)] for follicle detection after ten-fold experiments

The Table 12 shows the ten-fold experimental results of the ovarian classification based on SVM. It is observed that the average classification rates for normal ovary, cystic ovary and polycystic ovary are 100%, with zero false acceptance rate (FAR) and zero false rejection rate (FRR). It is observed that both the proposed SVM based method and the fuzzy based method [section 4(i)] yield 100% accuracy in ovarian classification, although the SVM outperforms the fuzzy method [section 4(i)] in follicle detection.

The Table 13 shows the comparison of all the follicle detection and ovarian classification methods developed in the present study and the other follicle detection methods available in the literature.


**Method Data set used**

2007] (70) 83.25%

[Potocnik and Zazula, 2000] (50) 78%

[Cigale and Zazula, 2000] (50) 60%

[Potocnick et al., 2002] (50) 61%

[Potocnick and Zazula, 2002] (50) 78%

**Table 13.** Comparison of the proposed method with all the other methods proposed in the present study and also

The main significant research contributions that fulfill the objectives set in the present chapter

**i.** Automatic detection of follicles using better segmentation and classification methods.

**ii.** Automatic ovarian classification into three categories, namely: normal ovary, cystic

The performance comparison of the various methods proposed in the present study and other

**i.** the proposed method using contourlet transform based despeckling, active contour

**ii.** the proposed method for ovarian classification using fuzzy or SVM has yielded better

SVM based classifier, has yielded better follicle detection results; and,

without edges based segmentation, geometric feature extraction and fuzzy logic or

methods in the literature is summarized in the Table 13. It is observed that :

Active contour with fuzzy classification

Active contour with SVM classification

Region growing method

Cellular neural network

Edge based method

Prediction based method

**5. Conclusion**

are :

Note : D1, D2 and D3 are image data sets.

with the other methods in the literature.

ovary and polycystic ovary.

classification results.

Modified region growing and LD classifier [ Maryruth et al.,

of ovary

of ovary

**Classification accuracy**

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193

D2 97.61%

Follicle Detection and Ovarian Classification in Digital Ultrasound Images of Ovaries

D3 98.47%

D3 98.47%

\* Type I Error: Regions are not follicles, but they are recognized as follicles.

\*\*Type II Error: Regions are follicles, but they are not recognized as follicles.

**Table 12.** Experimental results for classification accuracy of the SVM based method for the three classes of ovaries in comparison with the fuzzy based method [section 4(i)]



**Table 13.** Comparison of the proposed method with all the other methods proposed in the present study and also with the other methods in the literature.
