CN107730516B - Brain MR image segmentation method based on fuzzy clustering - Google Patents

Brain MR image segmentation method based on fuzzy clustering Download PDF

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CN107730516B
CN107730516B CN201710970162.1A CN201710970162A CN107730516B CN 107730516 B CN107730516 B CN 107730516B CN 201710970162 A CN201710970162 A CN 201710970162A CN 107730516 B CN107730516 B CN 107730516B
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葛洪伟
陆海青
葛阳
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Methuselah Wuxi Medical Technology Co.,Ltd.
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Abstract

The invention discloses a brain MR image segmentation method based on fuzzy clustering, which mainly solves the problem that the traditional FCM algorithm and the improvement method thereof cannot simultaneously eliminate noise and a bias field in the brain MR image segmentation process. The method fully utilizes local spatial information, local gray scale information and non-local information in the image to respectively construct a plurality of local information fuzzy factors and non-local weights, and maintains image details as much as possible while improving the noise resistance of the algorithm; meanwhile, a bias field model is established to remove gray unevenness in the brain MR image; and finally, embedding the proposed multiple local information fuzzy factors and non-local weights into an FCM (fuzzy C-means) method with a bias field model to realize brain MR (magnetic resonance) image segmentation under the conditions of noise and a bias field. The method can effectively inhibit the noise in the brain MR image, can effectively eliminate the influence of the bias field on the brain MR image segmentation, and has better segmentation performance.

Description

Brain MR image segmentation method based on fuzzy clustering
Technical Field
The invention belongs to the technical field of cluster analysis and intelligent information processing, and relates to segmentation of brain MR images in noise and bias field environments. In particular to a brain MR image segmentation method based on fuzzy clustering, which can be used in the fields of medical image analysis, disease diagnosis and the like.
Background
Magnetic Resonance Imaging (MRI) is an important medical Imaging technology, and has become an essential technical means in medical diagnosis, surgical planning, three-dimensional reconstruction and other links, and the segmentation of brain MR images is a hot problem in Magnetic Resonance Imaging research. The brain tissue is generally divided into three parts, namely Gray Matter (GM), White Matter (WM), and cerebral medulla Fluid (CSF), and accurate and effective segmentation of the brain tissue will greatly help accurate diagnosis of brain diseases. Due to the complexity of the brain tissue structure and the influence of factors such as partial volume effect in the medical imaging process, the acquired image often has the characteristics of more noise, low contrast, uneven gray distribution, unclear target boundary and the like, so that great difficulty is brought to accurate segmentation of the brain MR image.
There are many segmentation methods for brain MR images, such as expectation maximization, level set, fuzzy clustering, etc., where fuzzy clustering is a more common method. Fuzzy C-Means (FCM) is the most classical method in Fuzzy clustering and has wide application in medical image segmentation. Different from the traditional hard clustering method, the FCM adopts fuzzy membership to evaluate the degree of the pixels belonging to a certain class, so that the problem of classifying the pixels into one cut is avoided. However, the conventional FCM algorithm does not include spatial neighborhood information of pixels, and thus is very sensitive to noise, and the FCM algorithm cannot solve the problem of gray level non-uniformity in brain MR images. Therefore, various scholars at home and abroad propose related improved algorithms, such as an FCM algorithm based on space constraint, a space FCM algorithm based on neighborhood mean and median, and a fast generalized FCM algorithm. In 2010, Krinidis et al proposed a Fuzzy Local Information C-Means algorithm (FLICM, see: Krinidis S, Chatzis V.A. robust Fuzzy Local Information C-Means, IEEE Transactions on Image Processing,2010,19(5):1328-1337) by constructing a spatial blurring factor and embedding it into the original FCM algorithm to reflect the spatial neighborhood Information of the Image pixels. However, for images under a complex background, the segmentation accuracy of these algorithms is still not high enough, especially for brain MR images commonly used in the medical field, which often include a large amount of complex factors such as noise and bias field, and these algorithms are mostly difficult to effectively segment brain MR images under a strong noise background, and cannot eliminate the bias field existing therein.
In the research of the bias field correction problem, scholars at home and abroad propose a plurality of improved methods based on fuzzy clustering, such as an adaptive fuzzy C-mean algorithm, an adaptive spatial fuzzy clustering algorithm and a coherent local gray level clustering algorithm. In recent years, Li et al propose a new energy minimization Model (MICO), which realizes correction of the bias field and automatic segmentation of the brain MR image by constructing a new energy functional and adding prior information of the brain MR image into the new energy functional. However, the above method is sensitive to noise or abnormal points, and cannot perfectly eliminate the noise in the brain MR image, especially when the noise intensity of the image is large, the segmentation quality of the algorithm will be significantly reduced, and thus the method does not have good noise-resisting performance.
Disclosure of Invention
In view of the above disadvantages, the present invention provides a brain MR image segmentation method based on fuzzy clustering, that is, a brain MR image segmentation method based on an improved fuzzy C-means algorithm, so as to solve the problem of brain MR image segmentation under the background of noise and offset field, and better suppress noise and maintain image details while correcting the offset field.
The key technology for realizing the invention is as follows: firstly, comprehensively utilizing the spatial distance and the local gray scale information of each pixel in an image to design a new multi-local information fuzzy factor so as to improve the accuracy of pixel gray scale calculation; then, a non-local weight term is constructed by using non-local information of the image, and the anti-noise performance of the algorithm is further improved; and finally, modeling the bias field in the observation image, and combining the model with the FCM algorithm to enable the target function of the FCM algorithm to contain bias field information so as to estimate and correct the bias field.
In order to achieve the above object, the specific implementation steps are as follows:
(1) setting an aggregation number c, wherein the fuzzy index m is 2, an iteration termination threshold epsilon, a maximum iteration time iter _ max, and a current iteration time t is 1;
(2) random initialization membership degree matrix U(0)Cluster center V(0)Bias field
Figure BDA0001434231700000021
Wherein
Figure BDA0001434231700000022
Satisfy the requirement of
Figure BDA0001434231700000023
c is the number of clusters, n is the total number of pixels in an image,
Figure BDA0001434231700000024
the gray values of c pixels in the image can be randomly selected as
Figure BDA0001434231700000025
Is set to the initial value of (a),
Figure BDA0001434231700000026
each of which may be in the range of [0, g-1 ]]Selecting randomly, wherein g is the maximum gray level of the image;
(3) computing multiple local information ambiguity factors
Figure BDA0001434231700000027
(4) Computing non-local weights
Figure BDA0001434231700000028
Figure BDA0001434231700000029
Wherein
Figure BDA00014342317000000210
Representing the similarity weight, i.e. the non-local weight,
Figure BDA00014342317000000211
representing all pixels in a window centered on pixel i and having radius r, ZiTo normalize the terms, PiRepresenting a 3X 3 image block, X (P) centered on pixel ii) For image block PiA one-dimensional vector of gray values of the respective pixels, PjRepresenting a 3X 3 image block, X (P), centred on pixel jj) For image block PjThe one-dimensional vector is formed by the gray value of each pixel, | | | · | |, represents a 2-norm, and h is a filtering parameter and is used for controlling the smoothness degree of the image;
(5) calculating new membership degree matrix U ═ Uki}∈Rc×n：
Figure BDA0001434231700000031
Wherein
Figure BDA0001434231700000032
Which is the grey value of the pixel i in the real image,
Figure BDA0001434231700000033
is the gray value of the pixel i in the bias field, vkIs the k-th cluster center, and m is the fuzzy index;
(6) calculating a new cluster center V ═ V1,v2,…,vc}：
Figure BDA0001434231700000034
Wherein
Figure BDA0001434231700000035
Is the combination of local gray level term and local space distance term;
(7) calculating a new bias field
Figure BDA0001434231700000036
Figure BDA0001434231700000037
(8) Calculating new objective function values
Figure BDA0001434231700000038
Figure BDA0001434231700000039
(9) If it is
Figure BDA00014342317000000310
Or if the current iteration time t is more than iter _ max, terminating the iteration and outputting a membership matrix U, a clustering center V and a bias field
Figure BDA00014342317000000311
Otherwise, returning to the step (5) and continuing the next iteration;
(10) defuzzification is carried out to realize image segmentation: determining the category of each pixel according to the maximum membership principle to realize image segmentation,i.e. ci＝argk{max(uki) In which c isiIndicating the class to which pixel i belongs.
The invention has the following advantages:
(1) by introducing multiple local information fuzzy factors and non-local weights, the method can effectively inhibit noise and retain structural information in the image;
(2) the invention fuses the bias field model in the FCM algorithm, and corrects the bias field in the image while segmenting the brain MR image.
(3) In the process of segmenting the brain MR image, the method has certain advantages in the aspects of segmentation quality, noise resistance and bias field correction performance.
Drawings
FIG. 1 is an overall flow diagram of the method of the present invention;
fig. 2(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method and the present invention method under 5% noise and 20% bias field (N5F20) for the simulated brain MR image (brainnweb 64), respectively, and (F) shows the standard segmentation results;
fig. 3(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method and the present invention method under 5% noise and 40% bias field (N5F40) for the simulated brain MR image (brainnweb 64), respectively, and (F) shows the standard segmentation results;
fig. 4(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method and the present invention method under 7% noise and 40% bias field (N7F40) for the simulated brain MR image (brainnweb 64), respectively, and (F) shows the standard segmentation results;
fig. 5(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method and the present invention method under 5% noise and 20% bias field (N5F20) for the simulated brain MR image (brainnweb 97), respectively, and (F) shows the standard segmentation results;
fig. 6(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the flimc method, the MICO method and the method of the present invention for the simulated brain MR image (brainnweb 97) under 5% noise and 40% bias field (N5F40), respectively, and (F) shows the standard segmentation results;
fig. 7(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method and the present invention method under 7% noise and 40% bias field (N7F40) for the simulated brain MR image (brainnweb 97), respectively, and (F) shows the standard segmentation results;
fig. 8(a) is an original image, (b), (c), (d) and (e) are segmentation result graphs of a conventional FCM method, an FLICM method, an MICO method and an actual brain MR image (axial) by the method of the present invention, respectively, (f) is a bias field result graph estimated by the method of the present invention, and (g) is a result graph after bias field correction by the method of the present invention;
fig. 9(a) shows an original image, (b), (c), (d), and (e) show segmentation results of a conventional FCM method, an FLICM method, an MICO method, and a real brain MR image (coronal) by the method of the present invention, respectively, (f) shows a bias field result estimated by the method of the present invention, and (g) shows a result obtained by correcting a bias field by the method of the present invention.
Detailed Description
Introduction of basic theory
FCM Algorithm
Consider a dataset consisting of n p-dimensional samples, X ═ X1,x2,…,xn}∈Rn×pThe FCM algorithm is aimed at targeting the objective function JFCMMinimization is performed to achieve fuzzy partitioning of the sample data, i.e.
Figure BDA0001434231700000051
Wherein U is { U ═ki}∈Rc×nIs a membership matrix, satisfies
Figure BDA0001434231700000052
V＝{v1,v2,…,vcIs a cluster center set, c belongs to [2, n ]]For the number of clusters, m ∈ [1, + ∞) ] is the ambiguity index, often given by m ═ m2. Using Lagrange multiplier method to pair JFCMPerforming iterative update to minimize the objective function
Figure BDA0001434231700000053
Figure BDA0001434231700000054
And (4) iterating the equation (2) and the equation (3) repeatedly until the FCM algorithm converges.
FLICM Algorithm
Space constraint information is not introduced into the traditional FCM algorithm, and the segmentation result is not accurate enough. To this end, Krinidis et al propose a Fuzzy Local Information C-Means algorithm (FLICM) to improve the segmentation accuracy of the algorithm by introducing a spatial blurring factor into the objective function. Having an objective function of
Figure BDA0001434231700000055
Wherein xiIs the gray value of pixel i, GkiRepresenting spatial blurring factors in particular form
Figure BDA0001434231700000056
Wherein N isiRepresenting a local neighborhood centered on pixel i, l being a local neighborhood NiPixel of (2), dilIs the spatial distance between the pixels i, l. Compared with the traditional FCM algorithm, the FLICM algorithm can obtain better segmentation performance and can reduce the influence of noise to a certain extent, however, the robustness of the algorithm to the noise is not strong enough, and therefore, the segmentation effect of the FLICM algorithm to the image under the background of strong noise is not good enough. Furthermore, for brain MR images commonly used in clinical medicine, the FLICM algorithm cannot eliminate the gray level inhomogeneities present therein.
Secondly, the invention relates to a brain MR image segmentation method based on fuzzy clustering
Referring to fig. 1, the specific implementation steps of the present invention are as follows:
step 1, setting a clustering number c, wherein a fuzzy index m is 2, an iteration termination threshold epsilon, a maximum iteration time iter _ max, and a current iteration time t is 1;
step 2, randomly initializing membership degree matrix U(0)Cluster center V(0)Bias field
Figure BDA0001434231700000057
Wherein
Figure BDA0001434231700000058
Satisfy the requirement of
Figure BDA0001434231700000061
c is the number of clusters, n is the total number of pixels,
Figure BDA0001434231700000062
the gray values of c pixels in the image can be randomly selected as
Figure BDA0001434231700000063
Is set to the initial value of (a),
Figure BDA0001434231700000064
each of which may be in the range of [0, g-1 ]]Selecting randomly, wherein g is the maximum gray level of the image;
step 3, calculating a plurality of local information fuzzy factors
Figure BDA0001434231700000065
(3.1) defining a local gray level difference measure ClThe gray level distribution uniformity degree is used for representing the uniformity degree of each pixel gray level distribution in the local neighborhood, and the smaller the value of the gray level distribution uniformity degree is, the gentler the gray level change of the pixels in the local neighborhood is, and the flatter the area is; on the contrary, there are more abrupt gray parts in the region, and the gray distribution is more uneven. In a specific form of
Figure BDA0001434231700000066
Figure BDA0001434231700000067
Wherein xlRepresenting the gray value of the neighborhood pixel l, NiRepresenting a 3 x 3 neighborhood, n, centered on pixel iiRepresenting a neighborhood NiThe total number of pixels in (a) is,
Figure BDA0001434231700000068
representing a neighborhood NiAverage gray of middle pixel;
(3.2) the contribution degree of each pixel in the local neighborhood to the gray level of the central pixel is defined as
Figure BDA0001434231700000069
Figure BDA00014342317000000610
Wherein gamma isilRepresenting the gray level contribution degree of the neighborhood pixel l to the central pixel i;
(3.3) As a measure of unifying data, gammailIs normalized, i.e.
Figure BDA00014342317000000611
Meanwhile, the specific definition of the local gray level term in the invention is given as follows:
Figure BDA00014342317000000612
(3.4) to compensate for the spatial distance term in the FLICM Algorithm
Figure BDA00014342317000000613
The defect of small variation amplitude is that an improved local space distance term is adopted and defined as
Figure BDA00014342317000000614
Wherein d isilRepresents the spatial distance between pixels i, l;
(3.5) combining the proposed local gray level term and local spatial distance term to construct a multi-local information blurring factor
Figure BDA00014342317000000615
In a specific form of
Figure BDA00014342317000000616
Wherein
Figure BDA0001434231700000071
(4) Computing non-local weights
Figure BDA0001434231700000072
Figure BDA0001434231700000073
Figure BDA0001434231700000074
Wherein
Figure BDA0001434231700000075
Representing the similarity weight, i.e. the non-local weight,
Figure BDA0001434231700000076
representing all pixels in a window centered on pixel i and having radius r, ZiTo normalize the terms, PiRepresenting a 3X 3 image block, X (P) centered on pixel ii) For image block PiOne-dimensional vector formed by gray values of each pixel，PjRepresenting a 3X 3 image block, X (P), centred on pixel jj) For image block PjThe one-dimensional vector is formed by the gray value of each pixel, | | | · | |, represents a 2-norm, and h is a filtering parameter and is used for controlling the smoothness degree of the image;
(5) calculating new membership degree matrix U ═ Uki}∈Rc×n：
Figure BDA0001434231700000077
Wherein
Figure BDA0001434231700000078
Which is the grey value of the pixel i in the real image,
Figure BDA0001434231700000079
is the gray value of the pixel i in the bias field, vkIs the clustering center of the kth class;
(6) calculating a new cluster center V ═ V1,v2,…,vc}：
Figure BDA00014342317000000710
(7) Calculating a new bias field
Figure BDA00014342317000000711
Figure BDA00014342317000000712
(8) Calculating new objective function values
Figure BDA00014342317000000713
Figure BDA0001434231700000081
(9) If it is
Figure BDA0001434231700000082
Or if the current iteration time t is more than iter _ max, terminating the iteration and outputting a membership matrix U, a clustering center V and a bias field
Figure BDA0001434231700000083
Otherwise, returning to the step (5) and continuing the next iteration;
(10) defuzzification: determining the class of each pixel according to the maximum membership principle to realize image segmentation, namely ci＝argk{max(uki) In which c isiIndicating the class to which pixel i belongs.
The effects of the present invention can be further illustrated by the following simulation experiments.
1. Simulation conditions and parameters
Experiments were performed using two sets of simulated Brain MR images (respectively, bratinnweb 64 and bratinnweb 97) from the Brain Web simulated Brain MR image library of the McConnell Brain Imaging center of the Institute of molecular neurology, McGill university, and real Brain MR images (respectively, axil and coronal) from the International Brain tissue Segmentation image library (IBSR), each test image being T1-weighted and having a layer thickness of 1 mm. In order to obtain good experimental effect, the parameters in the experiment are set as follows: c is 4, m is 2, epsilon is 10-5Iter _ max is 500, neighborhood NiIs 3 × 3 (i.e., 3 × 3 neighborhood), Wi rIs 7 × 7, image block PiIs 3 × 3, and the filter parameter h is 20. The experimental environment was Matlab R2014 a.
2. Simulation results and analysis
In a simulation experiment, the method is compared with the traditional FCM method, FLICM method and MICO method, and the experiment is mainly carried out from the following two aspects.
Experiment 1: qualitative evaluation experiment for simulating brain MR image segmentation
Two simulated brain MR images (braiin web64 and braiin web97) were respectively added with 5% noise and 20% bias field (N5F20), 5% noise and 40% bias field (N5F40), and 7% noise and 40% bias field (N7F40), and were respectively segmented using the above 4 methods.
Fig. 2(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method and the method of the present invention for the simulated brain MR image (brainnweb 64) under 5% noise and 20% bias field (N5F20), respectively, and (F) shows the standard segmentation results.
Fig. 3(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method, and the method of the present invention for the simulated brain MR image (brainnweb 64) under 5% noise and 40% bias field (N5F40), respectively, and (F) shows the standard segmentation results.
Fig. 4(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method, and the method of the present invention for the simulated brain MR image (brainnweb 64) under the noise of 7% and the bias field of 40% (N7F40), respectively, and (F) shows the standard segmentation results.
Fig. 5(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method, and the method of the present invention for the simulated brain MR image (brainnweb 97) under the 5% noise and 20% bias field (N5F20), respectively, and (F) shows the standard segmentation results.
Fig. 6(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method, and the method of the present invention for the simulated brain MR image (brainnweb 97) under 5% noise and 40% bias field (N5F40), respectively, and (F) shows the standard segmentation results.
Fig. 7(a) shows the original image, (b), (c), (d), (e) show the segmentation results of the conventional FCM method, the FLICM method, the MICO method, and the method of the present invention for the simulated brain MR image (brainnweb 97) under the conditions of 7% noise and 40% bias field (N7F40), and (F) shows the standard segmentation results.
As can be seen from the figure, the method can keep more detailed information while effectively suppressing noise, can well correct the bias field existing in the brain MR image, and is closer to the standard segmentation result compared with other 3 methods, so that the method can obtain a better segmentation effect on the simulated brain MR image under the environments of different-strength noise and bias fields.
Experiment 2: quantitative evaluation experiment for simulating brain MR image segmentation
Jacard Similarity (JS) is adopted as an objective evaluation index for the segmentation performance of the simulated brain MR image, and the evaluation index is defined as
Figure BDA0001434231700000091
Wherein S1Representing the result, S, obtained by a segmentation algorithm2The standard segmentation result (ground truth) is shown. JS reflects the segmentation precision of the image, and the larger the value of JS, the higher the segmentation precision, and the closer the obtained segmented image is to the standard segmentation result. While using a Partition Coefficient (V)pc) And Partition Entropy (V)pe) Further evaluating the clustering performance of each method, and respectively defining the clustering performance as
Figure BDA0001434231700000092
Figure BDA0001434231700000093
Wherein u iskiRepresenting the fuzzy membership of the ith pixel to the kth class, and n is the total number of pixels. It can be seen that VpcAnd VpeReflecting the fuzzy degree, V, of the divided matrixpcThe larger the segmentation matrix is, the smaller the calculated ambiguity of the segmentation matrix is, the more clear the classification of the pixels is, and the better the segmentation effect is; accordingly, VpeThe smaller the clustering performance of the algorithm, the better.
Table 1 compares the JS values of the methods for different tissues (grey matter, white matter, cerebral spinal fluid), with the thickened part being the optimal value. As can be seen from table 1, for the same tissue, under the condition that the image noise and the bias field strength are fixed, the JS value of the method of the present invention is substantially higher than those of the other 3 methods, and as the noise and the bias field strength increase, the JS value of each algorithm decreases, while the method of the present invention can still obtain a relatively higher JS value, which indicates that the method of the present invention has better segmentation performance than those of the other methods.
Table 2 shows the partition coefficient V of each method for the simulated brain MR imagepcAnd dividing entropy VpeWherein the thickened part is an optimal value. As can be seen from Table 2, the process of the invention has a higher V than the remaining 3 processespcValue and lower VpeThe value shows that the membership matrix obtained by calculation of the method has better partition performance and higher clustering accuracy, and can obtain good segmentation effect on images under different degrees of noise and bias field backgrounds. Therefore, the method has certain superiority in clustering segmentation performance.
TABLE 1 JS values of algorithms for different organizations
Figure BDA0001434231700000101
TABLE 2 partition coefficients and partition entropies (V) for the algorithmspc/Vpe)
Figure BDA0001434231700000102
Experiment 3: qualitative evaluation experiment for real brain MR image segmentation
The two real brain MR images (axial and coronal) were segmented separately using the 4 methods described above.
Fig. 8(a) is an original image, (b), (c), (d) and (e) are segmentation result graphs of a real brain MR image (axial) by the conventional FCM method, the FLICM method, the MICO method and the method of the present invention, respectively, (f) is a bias field result graph estimated by the method of the present invention, and (g) is a result graph after bias field correction by the method of the present invention.
Fig. 9(a) shows an original image, (b), (c), (d), and (e) show segmentation results of a conventional FCM method, an FLICM method, an MICO method, and a real brain MR image (coronal) by the method of the present invention, respectively, (f) shows a bias field result estimated by the method of the present invention, and (g) shows a result obtained by correcting a bias field by the method of the present invention.
As can be seen from the figure, the method effectively overcomes the influence of noise, more reasonably segments the details of the brain tissue, well balances the relation between noise suppression and detail preservation, simultaneously fuses a bias field model, effectively corrects the bias field in the brain MR image, and the corrected brain tissue gray scale is more uniform. Therefore, the method of the present invention is superior to the other 3 methods in both visual quality and segmentation performance.
Experiment 4: quantitative evaluation experiment for real brain MR image segmentation
For real brain MR images, there is generally no completely accurate segmentation result as a reference in practical clinical applications. Therefore, in order to objectively verify the segmentation performance of each method on the real brain MR image, two evaluation indexes of Coefficient of Variation (CV) and Joint Coefficient of Variation (CJV) are selected and respectively defined as
Figure BDA0001434231700000111
Wherein sigmaTExpressing the standard deviation of the gray scale, mu, of a certain brain tissue TTMean value of the gray scale, σ, representing the brain tissue TGMGray scale standard deviation, σ, representing gray matterWMRepresenting the gray scale standard deviation, mu, of white matterGMMean value of gray levels, mu, representing gray matterWMRepresenting the mean of the grey levels of white matter. It can be seen that CV and CJV can well reflect the segmentation quality of the brain tissue and the correction effect of the bias field, the smaller the CV and CJV value is, the better the removal effect of the gray level non-uniformity in the brain tissue is, and the more smooth and uniform the corrected bias field shows that the algorithm performance is better.
Table 3 shows CV and CJV values of the bias field correction result graphs of the respective methods, wherein the bold part is the optimal value. As can be seen from table 3, compared to the MICO method, the method of the present invention obtains smaller CV and CJV values for both real brain MR images, which indicates that the method of the present invention can effectively eliminate gray level non-uniformity in brain tissue and has good performance in bias field correction.
Table 3 CV and CJV values for each algorithm versus bias field correction map
Figure BDA0001434231700000112

Claims (1)

1. A brain MR image segmentation method based on fuzzy clustering comprises the following steps:
(1) setting an aggregation number c, wherein the fuzzy index m is 2, an iteration termination threshold epsilon, a maximum iteration time iter _ max, and a current iteration time t is 1;
(2) random initialization membership degree matrix U(0)Cluster center V(0)Bias field
Figure FDA0002262401570000011
Wherein
Figure FDA0002262401570000012
Satisfy the requirement of
Figure FDA0002262401570000013
c is the number of clusters, n is the total number of pixels in an image,
Figure FDA0002262401570000014
the gray values of c pixels in the image can be randomly selected as
Figure FDA0002262401570000015
Is set to the initial value of (a),
Figure FDA0002262401570000016
each of which may be in the range of [0, g-1 ]]Selecting randomly, wherein g is the maximum gray level of the image;
(3) computing multiple local information ambiguity factors
Figure FDA0002262401570000017
(4) Computing non-local weights
Figure FDA0002262401570000018
Figure FDA0002262401570000019
Wherein
Figure FDA00022624015700000110
Representing the similarity weight, i.e. the non-local weight,
Figure FDA00022624015700000111
representing all pixels in a window centered on pixel i and having radius r, ZiTo normalize the terms, PiRepresenting a 3X 3 image block, X (P) centered on pixel ii) For image block PiA one-dimensional vector of gray values of the respective pixels, PjRepresenting a 3X 3 image block, X (P), centred on pixel jj) For image block PjThe one-dimensional vector is formed by the gray value of each pixel, | | | · | |, represents a 2-norm, and h is a filtering parameter and is used for controlling the smoothness degree of the image;
(5) calculating new membership degree matrix U ═ Uki}∈Rc×n：
Figure FDA00022624015700000112
Wherein
Figure FDA00022624015700000113
Which is the grey value of the pixel i in the real image,
Figure FDA00022624015700000114
is the gray value of the pixel i in the bias field, vkIs the k-th cluster center, and m is the fuzzy index;
(6) calculating a new cluster center V ═ V1,v2,…,vc}：
Figure FDA0002262401570000021
Wherein
Figure FDA0002262401570000022
Is the combination of local gray level term and local space distance term;
(7) calculating a new bias field
Figure FDA0002262401570000023
Figure FDA0002262401570000024
(8) Calculating new objective function values
Figure FDA0002262401570000025
Figure FDA0002262401570000026
(9) If it is
Figure FDA0002262401570000027
Or if the current iteration time t is more than iter _ max, terminating the iteration and outputting a membership matrix U, a clustering center V and a bias field
Figure FDA0002262401570000028
Otherwise, returning to the step (5) and continuing the next iteration;
(10) defuzzification is carried out to realize image segmentation: determining the class of each pixel according to the maximum membership principle to realize image segmentation, namely ci＝argk{max(uki) In which c isiRepresents the category to which the pixel i belongs;
the step (3) is carried out according to the following processes:
(3.1) defining a local gray level difference measure ClFor representing the degree of uniformity of the gray level distribution of each pixel in the local neighborhood, the specific form is
Figure FDA0002262401570000029
l∈Ni，
Figure FDA00022624015700000210
Wherein xlRepresenting the gray value of the neighborhood pixel l, NiRepresenting a 3 x 3 neighborhood, n, centered on pixel iiRepresenting a neighborhood NiThe total number of pixels in;
(3.2) the contribution degree of each pixel in the local neighborhood to the gray level of the central pixel is defined as
Figure FDA00022624015700000211
l∈Ni，
Figure FDA00022624015700000212
Wherein gamma isilRepresenting the gray level contribution degree of the neighborhood pixel l to the central pixel i;
(3.3) As a measure of unifying data, gammailIs normalized, i.e.
Figure FDA00022624015700000213
Meanwhile, the specific definition of the local gray level term in the invention is given as follows:
Figure FDA00022624015700000214
l∈Ni；
(3.4) defining a local spatial distance term:
Figure FDA0002262401570000031
wherein d isilRepresents the spatial distance between pixels i, l;
(3.5) combining the proposed local gray level term and local spatial distance term to construct a multi-local information blurring factor
Figure FDA0002262401570000032
In a specific form of
Figure FDA0002262401570000033
Wherein
Figure FDA0002262401570000034
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