Uterine Fibroid Segmentation on Multiplan MRI Using FCM, MPFCM and Morphological Operations

Alireza Fallahi, Mohammad Pooyan Biomedical Engineering Department

Shahed University Tehran, Iran

afallahi@shahed.ac.ir, pooyan@shahed.ac.ir

Hassan Khotanlou Computer Engineering Department

Bu-Ali Sina University Hamedan, Iran hkh@basu.ac.ir

Hassan Hashemi, Kavous Firouznia Advanced Diagnostic and Interventional Radiology

Research Center (ADIR), Tehran, Iran

Mohammad Ali Oghabian Research Center for Science and Technology in Medicine,

Tehran University of Medical Science Tehran, Iran

oghabian@sina.tums.ac.ir

Abstract— Uterine fibroid is the most common benign tumor of the female in the world. Uterine volume measurement before and after surgery has an important role in predict and following the result of surgery. Fibroids segmentation in patient with multi fibroids is the challenging task manually. We propose tow step method for robustly segmentation of these cases. The first step results in a uterine segmentation using FCM and some morphological operations in T1-Enhanced and T1 images. In the second step by applying a new method based on FCM, PCM and information of voxels neighborhoods (Modified PFCM_MPFCM) and knowledge based image processing final segmentation created. We compared manually segmented images results with the output of our system and we obtained 79.9% average of similarity index and 68.28% Jaccard index.

Keywords-Uterine; Uterine Fibroid; FCM; MPFCM; Knowledge based Image Processing; Morphological Operations

I. INTRODUCTION

Magnetic Resonance Image (MRI) is widely used in radiology diagnosis especially in soft tissues. Different modalities like T1, T2 and FLAIR and the fusion of information provided by them can be useful in diagnosis. One of the recent applications of MRI is to diagnosis uterine fibroid. As the uterine fibroid is the most common benign tumors of the female pelvis (1), MR imaging can be very useful in follow-up the patient condition, diagnosis and treatment process (2). Uterine fibroid segmentation and volume measurement is one of the important tasks for clinical reasons, e.g., for treatment planning and therapy evaluation. In multi fibroids cases because of various number, size and location and low contrast boundaries of fibroids, segmentation is a challenging task and exactly extracting them is impossible in some cases.

There are several proposed methods in the literature for tumor segmentation and volume estimation. Active contours are popular method that are widely used for segmenting 2D and 3D objects, implicitly in the form of level set function or explicitly as a snake function. Active contours and fast marching level set have been used in (3) to segment the fibroids. In (4) fast marching level set and Laplacian level set have been applied for segmentation. Markov random fields (5), Bayesian framework, Support vector machines are also popular models for many medical image processing tasks such as segmentation. Fuzzy-connectedness is also a useful method that has been adapted for segmentation of medical images (6). In this paper we propose two step methods for segmentation of uterine fibroids in multi fibroid patients. First we segment uterine from T1-Enhanced image and registered T1 image by applying FCM and some morphological operations. In second step by applying new MPFCM algorithm on segmented uterine in registered T2 image and using knowledge based image processing, fibroids have been segmented. The paper is organized as follows. Uterine segmentation as a first step is presented in section 2. In section 3 we proposed a method based on MPFCM algorithm for uterine fibroid segmentation. Section 4 presents the results with their evaluation and some conclusions are presented in Section 5.

II. UTERINE SEGMENTATION

Here, our aim is to propose an automatic method for segmentation of uterine. Uterine is initially segmented using FCM method in T1-enhanced image and some morphological operations are then applied to refine the initial segmentation. Finally redundant parts have been removed by

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masking the segmented region in T1-enhanced image over the registered T1 image.

A. Initial Segmentation With FCM Algorithm and Morphological Operations

Clustering is the partitioning of unlabeled data set X = {x1, x2, ..., xn} ⊂ Rp into 1 < c < n classes, by assigning labels to the vectors in X. A c-partition of X is a set of (cn) values uik that can be represented as a (c × n) matrix U = [uik] (7). The value uik denotes the membership degree of sample xk to class i. One of the most widely used clustering methods is the FCM algorithm (8). The FCM algorithm assigns memberships to xk which are related to the relative distance of xk to the c points prototypes V = {vi} that are class centers in the FCM. The objective function of FCM is written as:

∑∑= =

=c

i

n

k

mikm uXVUJ

1 1

)();,(

(1)

Where m > 1, 0 ≤ uik ≤ 1,∑ ==

c

i iku1

1 , i∀

Because of texture properties in Enhanced-T1 MR image we chose c=3 and m=2. As the uterine is enhanced in T1-enhanced images their pixels appear in third class that has higher intensity value. Ideally, upon FCM clustering, the cluster corresponding to the brightest region would represent the uterus. The representation can be obtained by converting the clustering result into a binary image in which each pixel is labeled as either belonging or not belonging to the desired region, while representing uterus. However, the region so obtained may not be fully connected and may contain other region pixels (such as colon due to the anatomical ambiguities). Morphological operations can also be used to correct certain large miss-clustered regions that are inevitably presented in FCM segmentation results. Two types of morphological operations are applied to the binary images in order to clarify the anatomical ambiguities. In some cases due to the infarct fibroids in uterus some holes will appears after FCM clustering. We first applied filling algorithm to fill the holes. The opening is then applied to the image to eliminate the small isolated regions and disconnect poor connectivity’s that don’t belong to the region. The largest region in each cross section that located in centre of the image is chosen as the candidate region belonging to the uterus “Fig 1”. The anatomical ambiguity caused by the lack of clear boundary between uterus and colons in Enhanced-T1 image would still is present after the initial morphological operations.

Figure 1. (a) Enhanced-T1 image, (b) Result of applying FCM algorithm, (c) Third class result (d) Prior result after applying morphological operations.

The elimination of such ambiguity needs to utilize the registered T1 image that described in the next Section.

B. Segmentation Refinement by T1 Image

The essential of further identification of the region-of-interest (ROI) lies in the fact that problem is still unsolved. Due to the analogous signal intensity, some parts of the colon are classified that connected to the upper part of the uterus. As we have pointed out earlier, such ambiguity cannot be differentiated solely by the intensity. Because of natural liquid in the colons these regions usually have high signal intensity in T1 images and appear brighter than uterus. By applying a threshold in the image we can eliminate such regions. In order to extract segmented region from T1 image we must register T1 image to the Enhanced-T1 image. To register the images, we use MIPAV software package. We chose the affine twelve degree transformation, trilinear interpolation and correlation ratio similarity function. The registration tools of this package use a local- global optimization method (9). After registration, segmented result applied as a mask on T1 image. This new image contains uterus and colons that we can apply a threshold to eliminate the colon (using histogram). As the colon parts are brighter than the uterine pixels we select the start of the last peak as the threshold value. By applying this threshold, another redundant parts are eliminated and uterine can be obtained. After these steps ultimately in some cases redundant parts that have same signal intensity in T1 and Enhanced-T1 images still remain. We eliminate these parts by applying some morphological operations, opening followed by closing with structure element that depend on size of the region. Fig.2 explain refinement segmentation result using T1 image.

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Figure 2. (a) Registered T1 image ;(b) Result of applying segmented region as a mask on T1 image; (c) Histogram of the region; (d) Result of applying threshold and eliminate redundant parts.

III. UTERINE FIBROIDS SEGMENTATION

FCM algorithm has some problems that have limited its application. The main one is that the membership functions are not decreasing with respect to the distance to the class centre. To overcome this problem, a new clustering method named possibilistic c-mean (PCM) was proposed by (10). In this algorithm the objective function is modified and the

normalization constraint ∑ ∀= kuik ,1 is not considered

and each element of k’th column can be any number between 0 and 1 (at least one of them is non zero). The authors named the value uik as typicality (typicality of xk

relative to cluster i). However this algorithm also has some problems. It is very sensitive to initialization and sometimes coincident clusters will occur. In addition it is very sensitive to additional parameters in this model. To address the problems of FCM and PCM a new fuzzy possibilistic c-mean (FPCM) algorithm was proposed in (11) by combining these two algorithms. In data classification, both membership and typicality are mandatory for data structures interpretation and FPCM computes these two factors simultaneously. FPCM solves the noise sensitivity defect of FCM and overcomes the problem of coincident clusters of PCM. The objective function of FPCM is written as:

∑∑= =

+=c

i

n

kikik

mikm DtuXVTUJ

1 1, )();,,( ηη

(2)

Where m > 1, η > 1, 0 ≤ uik ≤ 1, 0 ≤ tik ≤ 1,

∑ ==

c

i iku1

1 ,∑ ==

n

k ikt1

1 , i∀

And 2|||| ikik vxD −= ( ||.|| is any inner product norm).

Here T = [tik] is the typicality matrix. Although FPCM is less prone to the problems of FCM and PCM, in the case of a large data set this algorithm does not work properly (it operates such as FCM), because FPCM normalizes the possibility values, so that the sum of typicality of all data points in each row of U is one. Hence the typicality values are very small in large data sets. (7) proposed a new algorithm for data clustering that is named possibilistic fuzzy c-mean (PFCM). In this algorithm the

constraint of the typicality values ( itn

k ik ∀=∑ =,1

1) has

been relaxed to overcome the problem of FPCM. The objective function of PFCM is written as:

∑ ∑

∑∑

= =

= =

−+

+=

c

i

n

k

niki

c

i

n

kikik

mikm

t

DbtauXVTUJ

1 1

1 1,

)1(

)();,,(

γ

ηη

(3)

Where, kuc

i ik ∀=∑ =,1

1,0 ≤ uik, tik ≤ 1 and a > 0, b > 0, γi >

0, m > 1, η > 1 are user defined constants. The relative importance of fuzzy membership uik (as in FCM) and typicality tik (as in PCM) in the objective function are defined by the constants a and b. If a = 1, b = 0 and γi = 0, i∀ PFCM reduces to FCM and if a = 0 and b = 1, it reduces to PCM. In (10) the following equation is suggested to compute γi:

1,

1

1 >=

∑∑

=

= Ku

DK

n

kmik

n

k ikiγ

(4)

PFCM algorithm overcomes the problems of PCM and FCM and functions properly on large data sets. It can easily be seen from Equation above that the objective function of PFCM does not take into account any spatial information.

A. MPFCM

Recently, approaches have been proposed by modifying the objective function to increase the robustness of FCM to noise (12), (13), (14), (15), (16) and (17). In (12) the distance is weighted by a term based on the difference between the membership values of pixels in the neighbourhood of the pixel. (13) modified the objective function to discourage undesirable configurations according to the neighbourhood of the pixels. In (15), (17) and (14) a term is added to the objective function that allows the labelling of a pixel to be influenced by the labels in its immediate neighbourhood. In the proposed methods the objective function is modified to make the algorithm to be

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indirectly similar to the Markov random field (MRF). (16) proposed a modified FCM based on Markov and Gibbs random field theory. A spatial context constraint based on Gibbs random field is added to the objective function. We already proposed a new algorithm (modified PFCM (MPFCM)) (18) which uses the information of voxels and their neighbourhoods (inspired from Markov Random Fields (MRF)), membership and typicality for classification. We modify Equation (3) by adding a term that allows the labeling of a data point being influenced by its immediate neighbourhood. The added neighbourhood term is similar to the one which is used in modified FCM (MFCM) (15) to incorporate the neighbourhood effects in the classic FCM (similar terms are also used in (14) and (17)):

∑∑

= =

+c

i

n

kikik

mik Sbtau

1 1

)( η

(5)

Here

∑ =

−=wn

w iwik vxS1

2

(6)

Where xw is a neighbour pixel/voxel of xk in a window around xk and nw is the number of neighbours in this window. The sum of Equations (3) and (5) is the objective function of the proposed method:

∑∑∑ ∑

∑∑

= == =

= =

++−

+=

c

i

n

kikik

mik

c

i

n

k

niki

c

i

n

kikik

mikm

Sbtaut

DbtauXVTUJ

1 11 1

1 1,

)()1(

)();,,(

η

ηη

βγ

(7)

The relative importance of the added term (neighbourhood effect) is controlled by β (β can be written

aswn

α).

B. SEGMENTATION

We applied MPFCM algorithm with three classes to segment uterine from registered T2 images. As this algorithm is sensitive to initial clustered centres, using histogram analysis we determined three clusters centres. When uterine is segmented from previous stage and extracted from registered T2 image, a histogram for each slice is generated. However since this histograms are of real data containing noise it is difficult algorithmically determine its peaks. Therefore the histogram is smoothed with a Gaussian filter of =1.5 and its peaks are considered as initial centers. Fig.3 shows result of applying MPFCM algorithm. Due to the similarity signal intensity between fibroids and some parts of uterine we applied knowledge based image processing to eliminate this redundant parts. This system operates under two assumptions: fibroids have a convex and nearly rounded shape and cervix located in left side of the uterine. We computed major axis and minor axis ratio and circle area formulation for each region as criteria

Figure 3. (a) Regisered T2 image,(b) Result of applying segmented region as a mask on T2 image (c) Histogram of the region (d) Result of applying MPFCM method.

for first assumption. We then eliminate each region that located left side and near uterine contour in sagital view that determine cervix. After this step uterine fibroids are completely segmented. Fig.3 shows the final segmentation result.

I. RESULT AND DISCUSSION

The dataset contain the MR images of 5 patients that were acquired at the Imam Khomeini Hospital Medical Imaging Centre. All the patients were imaged on a 1.5T MR scanner using standard clinical imaging protocol to obtain T2-weited, T1-weighted and contrast enhanced T1 (gadolinium enhanced) images. Each MR image has an in-plan resolution of 512×512 and slice thickness of 5 mm with 15-20 slices. Fig. 4 shows the segmentation results. With determine first and last slice that contain uterine, other slices were automatically segmented. To validate the segmentation results, we compare obtained results with manual segmentation performed by a senior radiologist. We used four measures to evaluate the results which are (M denotes the manually segmented area and A automated segmented area):

• Similarity index:

%100*2

AM

Ti NN

NS p

+=

Where pTN the number of true positive voxels and MN is

the cardinality of M and AN is the cardinality of A;

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• Jaccard index:

%100*p

p

TAM

Ti NNN

NJ

++=

• Ratio of correct detection (Sensitivity):

%100*M

Tp N

NT

p=

•Specifity: SE=100-Fp:

%100*A

Fp N

NF

p=

Where

pFN is the number of false positive.

As seen in Table 1 the average value of similarity index is 79.91%. The Jaccard index mean value is 68.28% which shows a good accuracy of segmentation. The average of sensitivity is 76.44% and mean value of the specifity is 85.9%. These results show the reliability of proposed method in these cases that manual segmentation is inapplicable.

Figure 4. (a) Final segmented region (b) Result of proposed method.

TABLE I. EVALUATION OF THE SEGMENTATION RESULTS

Patient Volume metric (%)

SI JI SE SP

1 83.94 72.89 84.62 74.7

2 74.39 65.34 71.91 89.8

3 77.35 63.76 69.9 89.7

4 82.83 70.99 75.92 91.78

5 81.06 68.44 79.88 83.55

Average 79.91 68.28 76.44 85.90

II. CONCLUSION

This paper proposed an automatic method for the segmentation of uterine fibroid in multi fibroid patients MR images. By applying fuzzy C-means algorithm and some morphological operations T1-enhanced images are initially segmented. Resulted image refined by registered T1 image and histogram processing. In second step by applying new MPFCM algorithm and knowledge based image processing fibroids has been segmented from registered T2 image. The quantitative results illustrate the good performance of this method. By uterine fibroid segmentation, in the future

works we can analyze fibroid properties like infarct regions and calcified regions. This task has critical features in diagnosis and treatment of uterine fibroids.

ACKNOWLEDGMENT

The authors would like to thank Dr A.Jalali and Dr M.Shakiba of the Diagnostic and Interventional Radiology Research Center (ADIR) for supplying all patient images.

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