**3. Active contour method for follicle detection**

Now, set T4 = *mi*

Now, set T6 = *mj*

and T5 = *σ<sup>i</sup>*

image *f* of the size *MxN* . The sample mean *mj*

subimage are given by the equations 11 and 12:

and T7 = *σ<sup>j</sup>*

mean (standard deviation) thresholded image fvm ( fvsd ).

deviation) thresholded image fhm (fhsd).

178 Advancements and Breakthroughs in Ultrasound Imaging

. Then multiply T4 and T5 by positive scale factors K1 and K2

and standard deviation *σ<sup>j</sup>* of the jth column

<sup>=</sup> å (11)

s = å - (12)

. Then multiply T6 and T7 by positive scale factors K3 and K4

**Classification results for ten-fold experiments**

(empirically fixed). Binarize ith row subimage using the thresholds K1T4 and K2T5 separately. This procedure is carried out for the rows i=1,...,M and obtain the horizontal mean (standard

*Vertical Scanline Thresholding (VST)*: The VST method is described as follows; Consider the input

1 <sup>1</sup> (,) *M*

<sup>1</sup> ( (,) )

( empirically fixed), respectively. Binarize jth column subimage using thresholds K3T6 and K4T7 separately. This procedure is carried out for the columns j=1,...,N and obtain the vertical

*Image Fusion*: The resultant images fhm and fvm are combined, to yield the image fhvm. Any region touching the borders are removed. The resultant images fhsd and fvsd are combined, to yield the image fhvsd. Any region touching the borders are removed. Finally, the resultant images fhvm and fhvsd are combined, to yield the segmented image fseg, which contains segmented regions in it. The regions in fseg having smaller area than the threshold T8 are removed. The regions are labeled (identified) and possible holes inside them are filled.

The geometric features are extracted and then 3σ-intervals around the mean are used for classification. The Table 2 shows the classification results of the HVST based method after tenfold experiments for both the data sets D1 and D2. The average detection rates for the proposed Method I with D1 and D2 sets are 90.10% and 92.76%, false acceptance rates (FAR) are 11.71%

> Data set D1 set D2 set Classification rate 90.10% 92.76% Type I error (FAR) 11.71% 21.55% Type II error(FRR) 9.89% 7.23%

and 9.89%, and false rejection rates (FRR) are 21.55% and 7.23%, respectively.

**Table 2.** Classification results of proposed method after ten-fold experiments.

*fij m <sup>M</sup>* <sup>=</sup>

2

*i m fij <sup>M</sup>* <sup>=</sup>

1

*M j j i*

*j*

The active contour method is used for segmentation of ultrasound image to increase the follicle detection accuracy. Either 3σ intervals based classifier or fuzzy classifier may be employed for follicle detection.

**i.** Active contour method with 3σ intervals based classification

The follicle detection in ultrasound images of ovaries using active contour method uses the contourlet transform based method for preprocessing, active contour method for segmentation and 3σ-intervals around the mean for classification [37]. Initially, the input image is despekled by using the contourlet transform method. Next, histogram equalization is applied to enhance the contrast of the despeckled image. Further, the negative transformation is applied on the histogram equalized image [38], as the proposed segmentation method works on high intensity valued objects. In the segmentation stage, the active contour without edges method is used [39]. The resulting image after applying active contour method contains segmented regions with it. The geometric features are extracted and then 3σ-intervals around the mean is used for classification.

The Figure 5 (a) depicts sample original ultrasound image of the ovary. The resultant images obtained at different steps of the proposed method are shown in the Figure 5 (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 (empirical value) are removed (Figure 5(f)). The Figure 5(g) depicts the segmented follicles (outlined in white) superimposed on the original image. The Figure 5(h) depicts the recognized follicles after applying the classification rules and the Figure 5(i) shows the follicles annotated manually by the medical expert.

The Figure 6 depicts comparison of the active contour method with the HVST based segmen‐ tation method. In the Figure 6, (a) and (e) are two original images, while (b) and (f) are their corresponding segmented images by HVST method. Similarly, (c) and (g) are segmented images of active contour method. It is observed that the follicles, which were not detected by HVST based segmentation method (Figure 6 (b) and (f)), are correctly identified by the active contour method (Figure 6 (c) and (g)). The Figure 6 (d) and (h) show the manual segmentation rendered by the medical expert. Hence, the classification accuracy is improved in the active

**Figure 5.** Original ultrasound image of the ovary and resultant images at different steps of proposed method. a) Origi‐ nal image, b) Contourlet transformed image (despeckling), c) Histogram equalized image, d) Image after applying negative transformation, e) Image after applying active contour without edges method, f) Segmented image after clearing the border, filling the holes and removing the small regions, g) Image showing recognized follicles(outlined in white) super imposed on the original image, h) Output image after classification, i) Manual segmentation of follicles by medical expert.

contour method as compared to HVST based segmentation method. The Table 3 presents the comparison of the experimental results of active contour method and HVST based method obtained for the original images in Figure 6. It is observed that the HVST based method leads to higher false acceptance rate (FAR) and false rejection rate (FRR). Further, the active contour method is found to yield more accurate results.

are 7.62% and 3.33%, respectively. The average detection rates for the HVST based method using D1 and D2 sets are 90.29% and 92.76%, false acceptance rates (FAR) are 14.10% and 21.55%, and false rejection rates (FRR) are 9.60% and 7.23%, respectively. Clearly, the method

**Table 3.** Comparison of experimental results of active contour method and HVST based method for original images in

based on active contours outperforms the HVST based method.

Original images Resultant images

**Original Image**

Figure 6.

by HVST method

(a) (b) (c) (d)

(e) (f) (g) (h)

**Figure 6.** Comparison of resultant images of the active contour method with the HVST based method for two differ‐ ent original images. (a) and (e) original image, (b) and (f) resultant images of HVST method, (c) and (g) resultant im‐

Total Correct False Total Correct False

Figure 6 (a) 6 6 - 6 5 1 7

Figure 6 (e) 6 4 2 2 2 - 4

**Number of follicles detected**

**Active contour method HVST based method Manual (by medical**

ages of the active contour method, (d) and (h) manual segmentation by medical expert.

Resultant images by active contour method

Follicle Detection and Ovarian Classification in Digital Ultrasound Images of Ovaries

Manual segmentation 181

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

**expert)**

The Table 4 shows the comparison of classification results of the active contour method and the HVST based method after performing ten-fold experiments for both the data sets D1 and D2. The average detection rates for the active contour method using D1 and D2 sets are 92.3% and 96.66%, false acceptance rates (FAR) are 13.90% and 15.04%, and false rejection rates (FRR)

**Figure 6.** Comparison of resultant images of the active contour method with the HVST based method for two differ‐ ent original images. (a) and (e) original image, (b) and (f) resultant images of HVST method, (c) and (g) resultant im‐ ages of the active contour method, (d) and (h) manual segmentation by medical expert.


**Table 3.** Comparison of experimental results of active contour method and HVST based method for original images in Figure 6.

contour method as compared to HVST based segmentation method. The Table 3 presents the comparison of the experimental results of active contour method and HVST based method obtained for the original images in Figure 6. It is observed that the HVST based method leads to higher false acceptance rate (FAR) and false rejection rate (FRR). Further, the active contour

**Figure 5.** Original ultrasound image of the ovary and resultant images at different steps of proposed method. a) Origi‐ nal image, b) Contourlet transformed image (despeckling), c) Histogram equalized image, d) Image after applying negative transformation, e) Image after applying active contour without edges method, f) Segmented image after clearing the border, filling the holes and removing the small regions, g) Image showing recognized follicles(outlined in white) super imposed on the original image, h) Output image after classification, i) Manual segmentation of follicles

The Table 4 shows the comparison of classification results of the active contour method and the HVST based method after performing ten-fold experiments for both the data sets D1 and D2. The average detection rates for the active contour method using D1 and D2 sets are 92.3% and 96.66%, false acceptance rates (FAR) are 13.90% and 15.04%, and false rejection rates (FRR)

method is found to yield more accurate results.

180 Advancements and Breakthroughs in Ultrasound Imaging

by medical expert.

are 7.62% and 3.33%, respectively. The average detection rates for the HVST based method using D1 and D2 sets are 90.29% and 92.76%, false acceptance rates (FAR) are 14.10% and 21.55%, and false rejection rates (FRR) are 9.60% and 7.23%, respectively. Clearly, the method based on active contours outperforms the HVST based method.


During the training phase, the geometrical features, namely, R, Cp, Cr, Tr, E and C=(Cx,Cy), are computed for regions known to be follicles in the training images in consultation with the medical expert. Then, the mean and standard deviation of each of the geometric parameters R, Cp, Cr,Tr, E and C=(Cx,Cy), are computed which are used to set the rules for classification of follicles. The mean and standard deviation of these parametric values are stored as knowl‐ edge base which is shown in the Table 5. These values are used as the pattern (parameters) in

> Ratio(R) 1.82 0.58 Compactness (Cp) 37.35 10.16 Circularity (Cr) 0.37 0.09 Tortousity (Tr) 0.27 0.03 Extent (E) 0.51 0.09 Centriod C=(Cx,Cy) (251, 55) (201,70)

**Table 5.** The knowledge base of mean and standard deviation of parametric values of geometric features or the

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 (1 for follicle and 0 to non-follicle classes). Based on the descriptions of the inputs (the ratio R of majoraxislength to minoraxislength, the compactness Cp, the circularity Cr, the tortousity Tr, the extent E and the centriod C=(Cx,Cy)) and output variables (follicle and non follicle). The fuzzy rules for classification procedure in

**i.** IF (R is input to mfr) AND (Cp is input to mfcp) AND (Cr is input to mfcr) AND (Tr

**ii.** IF (R is input to mfr1) AND (Cp is input to mfcp1) AND (Cr is input to mfcr1) AND

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.

*Testing phase:* During the testing phase, the geometric features R, Cp, Cr, Tr, E and C= (Cx, Cy) are computed for each segmented region of the input image and then the above fuzzy classification rules are applied to determine whether the region is a follicle or not a follicle.

*Experimental results:* The ten-fold experiments are performed for the classification and the average follicle detection rate is computed. The Figure 7 (a) depicts an original ultrasound

is input to mftr) AND (E is input to mfe) AND (Cx is input to mfcx) AND (Cy is input

(Tr is input to mftr1) AND (E is input to mfe1) AND (Cx is input to mfcx1) AND (Cy

**Mean value Standard deviation**

Follicle Detection and Ovarian Classification in Digital Ultrasound Images of Ovaries

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183

FIS membership function design.

follicle regions

verbose format are as follows:

to mfcy) THEN (class is follicle)

is input to mfcy1) THEN (class is non-follicle).

**Table 4.** Comparison of average classification results of the active contour method with the HVST based method after performing ten-fold experiments.

#### **ii.** Active contour method with fuzzy classification

To improve the performance of follicle detection in ultrasound images of ovaries, a new algorithm using fuzzy logic is developed. The method employs contourlet transform for despeckling, histogram equalization and negative transformation in the preprocessing step, the active contours without edges method for segmentation and fuzzy logic for classification. The seven geometric features are used as inputs to the fuzzy logic block of the Fuzzy Inference System (FIS). The output of the fuzzy logic block is a follicle class or non follicle class. The fuzzy-knowledge-base consists of a set of physically interpretable if-then rules providing physical insight into the process. The experimentation has been done using sample ultrasound images of ovaries and the results are compared with the inferences drawn by 3σ interval based classifier and also those drawn by the medical expert. The experimental results demonstrate the efficacy of the fuzzy logic based method [40].

Fuzzy set theory has been successfully applied to many fields, such as pattern recognition, control systems, and medical applications [41,42]. It has also been effectively used to develop various techniques in image processing tasks including ultrasound images [43]. The existence of inherent "fuzziness" in the nature of these images in terms of uncertainties associated with definition of edges, boundaries, and contrast makes fuzzy set theory an interesting tool for handling the ultrasound imaging applications [44]. Fuzzy logic was initiated in 1965 by L. A. Zadeh [45-48].

*Training phase:* The fuzzy inference system (FIS) of sugeno type is employed using the fuzzy input variables the ratio R of majoraxislength to minoraxislength, the compactness Cp, the circularity Cr, the tortuousity Tr, the extent E and the centriod C= (Cx, Cy) and output variables: follicle and non follicle classes. The Gaussian membership function is used for each of the fuzzy input variables with mean and standard deviation of the corresponding variables. Let mfr, mfcp, mfcr, mftr, mfe, mfcx and mfcy be the Gaussian membership functions of the fuzzy input variables R, Cp, Cr, Tr, E and C=(Cx,Cy), respectively, belonging to the follicle class. Let mfr1, mfcp1, mfcr1, mftr1, mfe1, mfcx1 and mfcy1 be the Gaussian membership functions of these input variables belonging to the non-follicle class.

During the training phase, the geometrical features, namely, R, Cp, Cr, Tr, E and C=(Cx,Cy), are computed for regions known to be follicles in the training images in consultation with the medical expert. Then, the mean and standard deviation of each of the geometric parameters R, Cp, Cr,Tr, E and C=(Cx,Cy), are computed which are used to set the rules for classification of follicles. The mean and standard deviation of these parametric values are stored as knowl‐ edge base which is shown in the Table 5. These values are used as the pattern (parameters) in FIS membership function design.


**Table 5.** The knowledge base of mean and standard deviation of parametric values of geometric features or the follicle regions

**ii.** Active contour method with fuzzy classification

Active contour method

the efficacy of the fuzzy logic based method [40].

input variables belonging to the non-follicle class.

Zadeh [45-48].

Method

182 Advancements and Breakthroughs in Ultrasound Imaging

performing ten-fold experiments.

To improve the performance of follicle detection in ultrasound images of ovaries, a new algorithm using fuzzy logic is developed. The method employs contourlet transform for despeckling, histogram equalization and negative transformation in the preprocessing step, the active contours without edges method for segmentation and fuzzy logic for classification. The seven geometric features are used as inputs to the fuzzy logic block of the Fuzzy Inference System (FIS). The output of the fuzzy logic block is a follicle class or non follicle class. The fuzzy-knowledge-base consists of a set of physically interpretable if-then rules providing physical insight into the process. The experimentation has been done using sample ultrasound images of ovaries and the results are compared with the inferences drawn by 3σ interval based classifier and also those drawn by the medical expert. The experimental results demonstrate

**Table 4.** Comparison of average classification results of the active contour method with the HVST based method after

**Data set D1 set D2 set**

HVST based method

Classification rate 92.3% 90.29% 96.66% 92.76% Type I error (FAR) 13.90% 14.10% 15.04% 21.55% Type II error (FRR) 7.62% 9.60% 3.33% 7.23%

**Classification results**

Active contour method

HVST based method Based Method

Fuzzy set theory has been successfully applied to many fields, such as pattern recognition, control systems, and medical applications [41,42]. It has also been effectively used to develop various techniques in image processing tasks including ultrasound images [43]. The existence of inherent "fuzziness" in the nature of these images in terms of uncertainties associated with definition of edges, boundaries, and contrast makes fuzzy set theory an interesting tool for handling the ultrasound imaging applications [44]. Fuzzy logic was initiated in 1965 by L. A.

*Training phase:* The fuzzy inference system (FIS) of sugeno type is employed using the fuzzy input variables the ratio R of majoraxislength to minoraxislength, the compactness Cp, the circularity Cr, the tortuousity Tr, the extent E and the centriod C= (Cx, Cy) and output variables: follicle and non follicle classes. The Gaussian membership function is used for each of the fuzzy input variables with mean and standard deviation of the corresponding variables. Let mfr, mfcp, mfcr, mftr, mfe, mfcx and mfcy be the Gaussian membership functions of the fuzzy input variables R, Cp, Cr, Tr, E and C=(Cx,Cy), respectively, belonging to the follicle class. Let mfr1, mfcp1, mfcr1, mftr1, mfe1, mfcx1 and mfcy1 be the Gaussian membership functions of these

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 (1 for follicle and 0 to non-follicle classes). Based on the descriptions of the inputs (the ratio R of majoraxislength to minoraxislength, the compactness Cp, the circularity Cr, the tortousity Tr, the extent E and the centriod C=(Cx,Cy)) and output variables (follicle and non follicle). The fuzzy rules for classification procedure in verbose format are as follows:


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.

*Testing phase:* During the testing phase, the geometric features R, Cp, Cr, Tr, E and C= (Cx, Cy) are computed for each segmented region of the input image and then the above fuzzy classification rules are applied to determine whether the region is a follicle or not a follicle.

*Experimental results:* The ten-fold experiments are performed for the classification and the average follicle detection rate is computed. The Figure 7 (a) depicts an original ultrasound 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 follicles annotated manually by the medical expert.

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


**Table 6.** Comparison of experimental results of proposed fuzzy logic based classification and 3σ interval based classification based method for original images in the Figure 8.

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

**4. Ovarian classification**

licles by medical expert.

There are three categories :

ovary.

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

**Figure 7.** Original ultrasound image of the ovary and resultant images at different steps of fuzzy based method. a) Original image, b) Contourlet transformed image (despeckling), c) Histogram equalized image, d) Image after apply‐ ing negative transformation, e) Image after applying active contour without edges method, f) Segmented image after clearing the border, filling the holes and removing the small regions, g) Image showing recognized follicles(outlined in white) super imposed on the original image, h) Output image after fuzzy classification, i) Manual segmentation of fol‐

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185

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

the follicles are measured and the number of follicles are counted.

Follicle Detection and Ovarian Classification in Digital Ultrasound Images of Ovaries http://dx.doi.org/10.5772/56518 185

**Figure 7.** Original ultrasound image of the ovary and resultant images at different steps of fuzzy based method. a) Original image, b) Contourlet transformed image (despeckling), c) Histogram equalized image, d) Image after apply‐ ing negative transformation, e) Image after applying active contour without edges method, f) Segmented image after clearing the border, filling the holes and removing the small regions, g) Image showing recognized follicles(outlined in white) super imposed on the original image, h) Output image after fuzzy classification, i) Manual segmentation of fol‐ licles by medical expert.
