KR101799680B1 - A method for brain image segmentation using a combination of expectation maximization algorithm and watershed transform - Google Patents

Abstract

The present invention relates to a method for analyzing a brain image, and more particularly, to a method for dividing a brain image for efficient image analysis. According to the present invention, an EM algorithm is combined with a marker-controlled watershed division and the EM algorithm is introduced to divide an image into a cluster. The method comprises the steps of: obtaining an image; obtaining a foreground marker and a background marker; obtaining an initial gradient image; and applying watershed division.

Description

[0001] The present invention relates to a method of maximizing an expectation value and a method of segmenting a brain image using a water-

The present invention relates to a method for analyzing a brain image, and more particularly, to a method for segmenting a brain image for efficient image analysis.

Image segmentation is an essential step in many image analysis tasks (Grau et al., 2004; Weisenfeld et al., 2006; Yahya et al., 2013). The purpose of image segmentation is to partition the image into uniform regions and to accurately assign the contours of the regions. Effective image segmentation is very important in a variety of medical image analysis tasks, and it helps clinicians and researchers in image-guided surgery, radiotherapy and surgery planning (Cates et al., 2005; ., 2005). Magnetic resonance imaging (MRI) is used for medical image segmentation, especially due to high contrast (Pham et al., 1999; Cercignani et al., 2001; Grau et al., 2003). Precise segmentation of brain tissue is not a simple task because there is a large amount of non-uniformity between noise and other effects (Despotovic et al., 2015). WaterShed transformations are based on mathematical morphology and are the first to be proposed by Digabel and Lantuejoul as effective methods for medical image segmentation. The water shed method is a method of dividing an image into two-dimensional terrains, for example, a divided area of a puddle surrounded by one contour when water is filled, assuming that the pixel value of the image is height. In the Watershed method, pixels with high values are represented by peaks or watershed lines, and pixels with low values are represented by valleys or regional minimums. Thus, we consider the topographic surface of the image as a way of considering the set of pixels in the image as a terrain and analyzing the elevation. Water scenes consider three types of points: (a) belonging to a local minimum; (b) reliably falling to a single minimum; (c) falling to the same degree as at least one such minimum. Catchment basins are the results of the points satisfying the condition (b), and those satisfying the condition (c) form ridges dividing other basin basins, which are referred to as the water shed lines. The watershed basin is a section to be obtained in the present invention. The number of objects as a result of the division depends on the local minimum present in the image. Water scenes are simple and intuitive and have been widely used with MRI, CT, and X-Ray because they perform image segmentation in a separate area even if the contrast is poor, For example, do not need to perform outline combining. However, the disadvantage of the WaterShed transformation is excessive, because the image is divided into too many areas or too many objects are compartmentalized. This overdispersion is a common phenomenon because there are too many local minima in the image. Another limitation of water shed splitting is noise sensitivity. Thus, a filtering operation is used to remove noise and undesirable from the MR image. In addition, the concept of morphological reconstruction and marker extraction can be used for the elimination of hyperfine created by applying a watermark transformation on a gradient image. Morphological water shedding is widely described in the prior art (Nallaperumal et al., 2007; Pesaresi et al., 2001; Harris et al., 1998; Mukhopadhyay et al., 2003; ; Hahn et al., 2012; Parvati et al., 2008; Lewis et al., 2012; Gonzalez et al., 2009). MR image segmentation, performed with marker-adjusted water-sheath segmentation solves the problem of over-estimation, but gray matter and cerebrospinal fluid can not be properly displayed in the brain image. Thus, a clustering process has been introduced. Conventional water shed images on gradient images yield severely overdetermined results.

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Grau, R. Kikinis, M. Alcaniz, and S.K. Warfield, Cortical gray matter segmentation using an improved watershed transform, Proceedings of the 25th Annual Int. Conf. In Medicine and Biology Society, 1 (2003), 618-621.  V. Grau, A.U.J. Mewes, A. Alcaniz, R. Kikoinis, and S.K. Warfield, Improved watershed transform for medical image segmentation using prior information, IEEE Transaction on Medical Imaging 23 (2004), 447-458.  G. Hamarneh, and X. Li, Watershed segmentation using prior shape and appearance knowledge, Image and Vision Computing 27 (2009), 59-68.  X. Han, Y. Fu, and H. Zhang, A fast two-step marker-controlled watershed image segmentation method, In Proceedings of the IEEE International Conference on Mechatronics and Automation, Beijing, China, 2012, pp. 1375-1380.  K. Haris, S.N. Efstratiadis, N. Maglaveras, and A.K. Katsaggelos, Hybrid image segmentation using watersheds and fast region merging, IEEE Transactions on Image Processing 7 (1998), 1684-1699.  Z.K. Huang, and K.W. 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Dong, Detection of breast tumor candidates using marker-controlled watershed segmentation and morphological analysis, Proceedings of the IEEE Symposium on Image Analysis and Interpretation, April 2012.  C. Li, C. Kao, J.C. Gore, and Z. Ding, Implicit active contours driven by local binary fitting energy, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR '07), 2007, pp. 1-7.  J. Liu, and L. Guo, Improved K-Means Algorithm for Brain MRI Image Segmentation, 3rd International Conference on Mechatronics, Robotics and Automation,  M.A. Mahjoub, and K. Kalti, Image segmentation by adaptive distance based on EM algorithm, International Journal of Advanced Computer Science and Applications, Special Issue on Image Processing and Analysis, 2011.  S. Mukhopadhyay, and B. Chanda, Multiscale morphological segmentation of gray-scale images, IEEE Transactions on Image Processing 12 (2003), 533-549.  K. Nallaperumal, K. Krishnaveni, J. Varghese, S. Saudia, S. Annam, and P. Kumar, A novel multi-scale morphological watershed segmentation algorithm, International Journal of Imaging Science and Engineering 1 (2007), 60-64 .  H. Ng, S. Ong, K. Foong, P. Goh, and W. Nowinski, Image segmentation using k-means clustering and improved watershed algorithm, in Proc. IEEE < / RTI > Southwest Symp Image Anal Interpretation, 2006, pp. 61-65.  H.T. Nguyen, M. Worring, and R. van den Boomgaard, Watersnakes: Energy-Driven Watershed Segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence 25 (2003), 330-342. . N. Otsu, A threshold selection method from gray-level histograms, IEEE Transactions on Systems, Man and Cybernetics 9 (1979), 62-66.  K. Parvati, B.S.P. Rao, and M.M. Das, Image segmentation using gray-scale morphology and marker-controlled watershed transformation, Discrete Dynamics in Nature and Society, 2008.  M. Pesaresi, and J.A. Benediktsson, A new approach for the morphological segmentation of high-resolution satellite imagery, IEEE Transactions on Geoscience and Remote Sensing 39 (2001), 309-320.  D.L. Pham, C. Xu, and J.L. Prince, A survey of current methods in medical image segmentation, Annual Review of Biomedical Engineering 2 (1999), 315-337.  R. Rodriguez, T.E. Alarcon, and O. Pacheco, A new strategy to obtain robust markers for segmentation by using the watersheds method, Comput. Biol Med 35 (2005), 665-686.  J.B.T.M. Roerdink, and A. Meijster, The watershed transform: definitions, algorithms and parallelization strategies, Fundam Informaticae 41 (2000), 187-228.  J. Sharma, J.K. Rai, and R.P. Tewari, A combined watershed segmentation approach using k-means clustering for mammograms, 2nd International Conference on Signal Processing and Integrated Networks, 2015.  S. Sivasundari, R. Siva Kumar, and M. Karnan, Performance analysis of image filtering algorithms for MRI images, International Journal of Research in Engineering and Technology 3 (2014), 438-440.  H. Tek, and H.C. Aras, Local watershed operators for image segmentation, in Proceedings of the 7th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI, 2004, pp. 127-134.  D. Valencia, and A. Plaza, Efficient implementation of morphological opening and closing by reconstruction on multi-core parallel systems, 2009.  L. Vincent, Morphological grayscale reconstruction in image analysis: applications and efficient algorithms, IEEE Transactions on Image Processing 2 (1993), 176-201.  L. Vincent, and P. Soille, Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations, IEEE Trans Pattern Analysis Machntl 13 (1991), 583-598.  N.I. Weisenfeld, A.U.J. Mewes, and S.K. Warfield, Highly accurate segmentation of brain tissue and subcortical gray matter from newborn MRI, in Proc. of the 9th Int. Conference on Medical Image Computing and Computer-Assisted Intervention, 2006, pp. 199-206.  A.A. Yahya, J. Tan, and M. Hu, A novel model of image segmentation based on watershed algorithm, Advances in Multimedia,

It is an object of the present invention to provide a method for segmenting a brain image.

The present invention also provides an effective method for brain tissue segmentation.

To achieve the above object, the present invention combines the EM algorithm with marker-controlled water-shedding. Where the EM algorithm was introduced to partition the image into clusters. Specifically, the present invention relates to a method for obtaining a brain MR image and Wiener filtering to obtain a filtered image; Applying the filtered brain MR image to an expectation-maximization algorithm (EM algorithm) to obtain a clustered image; Thresholding the clustered image to obtain a binary image and then obtaining an initial gradient image by Sobel filtering; And obtaining a marker-adjusted gradient image from the initial gradient image, and then applying a Watershed segmentation, wherein the EM algorithm and the marker-adjusted water-sheath segmentation are combined to compartmentalize the brain image . The expectation-maximum value (EM) clustering algorithm performs a soft cluster algorithm in a non-mapping manner. Image binarization is performed to perform binarization. EM algorithms and marker-controlled water-sheath splitting provide effective partitioning results that can effectively display gray matter and CSF.

In another embodiment of the present invention, a reconstruction operation is performed with the expectation-maximization algorithm (EM algorithm).

In another embodiment of the present invention, the brightest cluster is selected and converted to a binary image using thresholding. The initial gradient image was obtained by using Sobel filtering on the binarized image while the final gradient image was obtained by introducing a minimum value onto the initial gradient image and foreground and background markers.

In another embodiment of the present invention, for further evaluation, the results of the present invention are compared with Otsu multi-level thresholding and localized binomial fitting models.

In another embodiment of the present invention, the inventors selected three MR brain images to evaluate the algorithm. Conventional watermark algorithms on gradient images lead to severe over-division, and these results are substantially useless. As shown in Figs. 2 (b), 3 (b) and 4 (b), when using conventional algorithms, it was possible to identify hundreds or thousands of overexposed regions. This is due to the noise present in the MR image producing multiple minima. Therefore, in the present invention, a Wiener filter is applied to remove noise artifacts in an image. On the other hand, when applied to images, the marker-adjusted water shed alone can not accurately divide the gray matter and cerebrospinal fluid. In fact, many objects remain unmarked as shown in Figures 2 (c), 3 (c), and 4 (c). Thus, the filtering operation, the EM algorithm, the threshold operation, the reconstruction operation, and the marker extraction are combined to provide an effectively partitioned result.

Brain MR images generally consist of three tissues: gray matter, white matter and cerebrospinal fluid. Accordingly, the EM algorithm uses three clusters together. The clustered images are shown in Figs. 2 (d), 3 (d) and 4 (d). We have found that these are contained within the brightest clusters. Therefore, the average value of the brightest clusters is used as the threshold value. The thresholds used for the MR images shown in Figures 2, 3 and 4 were 71, 60 and 90, respectively. The resulting value is a binary image. An initial gradient magnitude image can be obtained based on this binarized image.

The foreground and background markers can be computed by morphological restoration operations, such as erosion based and expansion based operations, by selecting appropriate structural elements on the filtered image. Thus, the final draft image is obtained using the initial draft image, and the minimum value technique based on the foreground and background markers. Thus, the watermark transformation applied on the final gradient magnitude provides the effective splitting results shown in Figures 2 (e), 3 (e) and 4 (e). As shown in these figures, even though some excess lines are generated in the final result while dividing the brain tissue, this result is much less than the conventional water-seed algorithm results on the gradient image and the simple marker-controlled water- This is a better result. Thus, the present invention can efficiently image brain tissue.

In one embodiment of the invention, the algorithms were tested together to compare Otsu multilevel thresholding (Otsu et al., 1979; Kalavathi et al., 2013). Ots thresholding is the most successful method for image segmentation based on thresholding, which is based on a criterion that minimizes intra-class variance. In one embodiment of the present invention, the gray matter and cerebrospinal fluid were divided, and the threshold values obtained from the Otsu multi-level thresholding on the brain image are shown in FIGS. 2, 3 and 4 as 82, 85 and 98, respectively. These values can be used to obtain a binarized image. The watermark partitioning applied using the algorithm of the present invention resulted in the splitting results shown in Figures 2 (e), 3 (e) and 4 (e). The results shown in Figures 2 (f) and 4 (f) can be compared with the results obtained using the method of the present invention. However, when comparing the results obtained in Fig. 3 (f), the method of the present invention was significantly superior to the results obtained from the combination of the Oats method and the water shed conversion. Comparing the method of the present invention with some results obtained by the Oats method, the Oats method is computationally inefficient. The inefficient formulation of hierarchical dispersion increases the cost of algorithm computation, especially in multi-threshold selection. The computational complexity of the algorithm increases exponentially with the number of thresholds. Similarly, the Oats method first requires the calculation of a gray-level histogram. Similarly, the algorithm of the present invention was tested in a localized binomial fitting model (Li et al., 2007). Figure 5 shows the result of the segmentation of the local binomial fitting model on the MR brain image. Analysis of the results suggests that the two models compete with each other. However, it should be appreciated that the local binarization fitting model is sensitive to accurate tuning of the parameter values. Inappropriate parameter values result in inaccurate partitioning and long computation time. Therefore, the estimation of exact parameter values is very important for accurate partitioning. Thus, the method of the present invention is significantly superior.

According to the method of the present invention, a divided brain image can be generated effectively.

Figure 1 is a flow chart illustrating the method of the present invention.
Fig. 2 (a) is an original image, Fig. 2 (b) is a result of a conventional watermark algorithm, Fig. 2 (c) is a marker-adjusted watermark fragmentation algorithm result, , And Fig. 2F shows the result obtained by combining the Oats method and the water shade fraction.
FIG. 3A shows the result of the conventional watermark algorithm, FIG. 3C shows the marker-adjusted watermark fragmentation algorithm result, FIG. 3D shows the clustered image using the EM algorithm, , And Fig. 3F shows the result of combining the Oats method and the water shade fraction.
Fig. 4A shows the result of the conventional watermark algorithm, Fig. 4C shows the marker-adjusted watermark fragmentation algorithm result, Fig. 4D shows the clustered image using the EM algorithm, Fig. , And FIG. 4F shows the result of combining the Oats method and the water shade fraction.
Fig. 5 shows a fraction using the LBF model. Fig. 5A shows the initial image, Fig. 5B shows the initial contour, and Fig. 5C shows the final result.

In the present invention, a gradient image was obtained by applying a Sobel filter on the input brain MR image. The Sobel filter worked well at the detection end and provided differentiation and smoothing effects. When applied to gradient images, the WaterShad transform produces some excess, because too many local minima are generated. When applied to images, the WaterShad transform generates a lot of local minima, resulting in serious over-division. Noise and artifacts present on the MRI also affect the outcome. Therefore, a filtering process is used as a preprocessing step to remove such noise and artifacts. In addition to the EM algorithm, restoration operations and marker extraction are applied to eliminate redundancy and obtain desired results. A flow chart of the method of the present invention is shown in Fig.

(1) Filtering Operation

We have used brain MRI in one embodiment of the present invention because brain MRI produces detailed information about the internal regions of the human brain. However, MRI is sensitive to a variety of unwanted noise, such as Gaussian, slat and pepper noise, which leads to undesirable results. Therefore, the MRI image should be preprocessed with a filtering operation to remove noise (Sivasundari et al., 2014; Kumar et al., 2015). In this embodiment, the present inventors used a Wienner filter. Wiener filtering performs an optimal trade-off between inverse filtering and noise smoothing. This removes the added noise and reverses the blurring. Wiener filtering is optimal at a mean square error, which minimizes the overall mean square error in the inverse filtering and noise smoothing process. The Wiener filtering is a linear estimate of the original image.

(2) EM  ( Expected value - Maximum value ) algorithm

The EM algorithm is one of a series of algorithms for finding the maximum likelihood as an iterative method. The EM algorithm is a widely used method for estimating the density of data points within a non-geographic clustering. The EM algorithm includes iteratively performing an alternation of the expected value E and the maximized M until the result converges. The likelihood expectation value is calculated by including the latent variable in the step (E), and the maximum likelihood of the variable is performed by maximizing the expected likelihood on the M step based on the final E step. Based on the variables found on the M step, another E step is started and the process is repeated until convergence is achieved. The EM algorithm can be used in a wide variety of fields including medical image processing and image interpolation (Lama et al., 2016).

An Expectation Maximization (EM) algorithm was used to partition the images into clusters. Data points are only partially allocated to other clusters, instead of being assigned to only one cluster. Clustering is a type of unsupervised learning that attempts to find clusters that best describe given data without labeling data. Classifying data requires labeling of the data and each piece of data, but most of the data is present, but the label or category of the data is unclear. Therefore, it is necessary to explain the data by a method other than classfication. In the present invention, each cluster according to the EM algorithm can be modeled using a probability distribution for partial allocation. Thus, the data points are associated with a particular probability cluster and, unlike K-mean clustering, belong to the highest probability cluster in the final allocation. For reference, the K-means algorithm assigns each data point to a cluster closest to its center. Next, for each cluster, the cluster center is updated according to the assigned data point, and this process is repeated until the cluster label is no longer changed. The K-means clustering algorithm is simple but tends to be more easily localized than K-means. The EM algorithm required initialization of the Gaussian mixture model parameters. It is estimated as the rational number of a probability distribution function called K of the gray level, and the distribution of each pixel can be modeled by one Gaussian. The following formula shows the probability density of this mixture.

(1)

(One)

및

이다. 유사하게, 매개변수

는

,

, 및

로 구성되고,

이다. 그러므로, Here, x is a feature vector,

And

to be. Similarly,

The

,

, And

≪ / RTI >

to be. therefore,

(2)

(2)

Lt;

For each step,

, 공분산이

, 혼합계수가

일때, 다음 로그 공산값이 초기값을 평가한다.1. Initialization

, Covariance

, The mixing coefficient is

, The next logarithmic value evaluates the initial value.

2. E (Expectation) step

At step E, we evaluated the expected value using the current parameter values.

(3)

(3)

3. Maximization step

At the M-step, we updated the parameters.

The updated average may be calculated as Equation (4) below.

(4)

(4)

The updated covariance may be calculated as: < EMI ID = 5.0 >

(5)

(5)

The updated mixing coefficient can be calculated by the following equation (6).

(6)

(6)

here,

이다.

to be.

4. The log likelihood is evaluated by the following equation (7).

(7)

(7)

Log likelihood values were computed to detect convergence using Equation 7. If the convergence criterion is not met, the algorithm returns to step E.

(3) Threshold processing

가 임계값 T에서

의 임계 버전이면, 하기 식 (8)을 만족한다.Threshold processing is a widely used method for image segmentation due to its simplicity. Threshold processing is an important part of image segmentation because it separates the gray levels of the pixels belonging to the object into the gray levels of the pixels belonging to the background. Thus, it plays an important role in separating objects from the background. Threshold processing is used by default because it provides high-speed operation and ease of implementation. if

Lt; RTI ID = 0.0 > T &

The following expression (8) is satisfied.

(8)

(8)

(4) Restoration work

이 되도록 할때, M으로부터 N의 침식의 복원은 안정성에 도달할 때까지 M "above" N의 그레이 스케일 침식을 반복하여 얻어진다.There are two grayscale images M and N defined in the same domain,

, The recovery of M to N erosion is obtained by repeating the gray scale erosion of M "above" N until stability is reached.

(9)

(9)

의

기본 침식을 하기와 같이 얻었다. Next grayscale image

of

Basic erosion was obtained as follows.

(10)

(10)

는 점의 최대를 나타내고,

는 b라고 명시한 평면구조 요소에 의한 M의 침식을 나타낸다.here

Represents the maximum of points,

Represents the erosion of M by a planar structural element denoted b.

The reconstruction by expansion of M to N can be obtained by repeating the gray scale delay calculation of M "under" N until stability is reached.

(11)

(11)

그레이 스케일 이미지의

기본팽창을 하기와 같이 얻을 수 있다.

Of a grayscale image

The basic expansion can be obtained as follows.

(12)

(12)

는 점의 최소를 나타내고,

는 b로 표시된 평면구조요소에 의한 M의 팽창이다. here

Represents the minimum of the points,

Is the expansion of M by a planar structural element denoted b.

(5) Marker  extraction

As described above, direct application of the water-shear transformation on the gradient image produces over-division due to irregularities and noise included in the MRI. Thus, the EM algorithm and restoration work are applied to efficiently display brain tissue. Restoration operations, such as erosion-based and expansion-based grayscale image restoration, were performed. Both are identical, the difference being that the present inventors changed the erosion work to expansion and vice versa. A foreground marker within the region of interest and an embedded background marker within the background can be obtained from the restore operation. These markers are very important because they help to modify the gradient image obtained from the EM algorithm by the minima imposition technology. A water sample performed on a modified gradient size helps to partition brain tissue efficiently.

The present invention provides a method for effectively distinguishing and obtaining a brain image. Therefore, it can be used clinically to analyze brain images and diagnose or monitor brain diseases or lesions.

Claims (4)

Obtaining a brain MR image and subjecting it to Wiener filtering to obtain a filtered image;
Applying the filtered brain MR image to an expectation-maximization algorithm (EM algorithm) to obtain a clustered image and performing a reconstruction operation on the filtered brain MR image, Wherein the operation is to perform erosion based and expansion based grayscale image restoration to obtain foreground and background markers;
Thresholding is performed on the clustered image using the average value of the brightest clusters as a threshold value to obtain a binary image and then Sobel filtering is performed to obtain an initial gradient image step; And
For the initial gradient image, introducing a minimum value based on the foreground marker and background marker to obtain a marker-adjusted gradient image, and then applying a Watershed segmentation.
A method for segmenting brain gray matter, white matter, and cerebrospinal fluid images by combining an EM algorithm and a marker-adjusted water-shedding split.
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