CN107392914A - Nuclear magnetic resonance image dividing method based on self-adaption cluster algorithm - Google Patents
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Abstract
The invention discloses a kind of nuclear magnetic resonance image dividing method based on self-adaption cluster algorithm, belong to image segmentation field.The present invention proposes a kind of cluster segmentation algorithm based on k means algorithms for distinguishing cerebral magnetic resonance image, and the algorithm can automatically and efficiently determine cluster numbers with segmentation object nuclear magnetic resonance image, so as to replace artificial method.Test result indicates that the inventive method has certain advantage relative to other methods and criterion.The inventive method can not only correctly find an appropriate number of cluster numbers, and have higher precision and efficiency compared to other method.Meanwhile the present invention tests the inventive method with reference picture, and segmentation result is demonstrated using quantitative assessment.As a result show that the inventive method has higher precision and robustness.
Description
Technical field
The present invention relates to image segmentation field, more particularly to a kind of nuclear magnetic resonance image based on self-adaption cluster algorithm point
Segmentation method.
Background technology
In field of medical image processing, tissue typing has become a kind of important medical science of progress reported as precisely as possible and ground
Study carefully.Nuclear magnetic resonance figures seems that the sophisticated medical imaging technology of enough information is provided for people's class soft tissue.Researcher needs accurate
Segmentation brain magnetic resonance image.In some medical researches, cerebral magnetic resonance image still checked manually by medical expert and
Segmentation, this is a kind of inaccurate and time-consuming way.
In medical image research, the research to cerebral magnetic resonance image anatomical structure is necessary.If people
If work point is analysed, then substantial amounts of view data can cause very big difficulty to analysis.Many researchers propose in recent years
To the computer-aid method of portion's nuclear magnetic resonance image segmentation.Many different methods are used for splitting cerebral magnetic resonance image,
Such as cluster, threshold value, region growing etc..
Partitioning algorithm based on cluster is a kind of unsupervised sorting algorithm.The purpose of clustering algorithm is to make the pixel in class
Difference is small, and the pixel difference between class is big.The advantages of cluster be it is directly perceived, quickly, it is easy to accomplish etc..However, researcher generally needs
To be that these algorithms set some parameters, no matter they are k mean algorithms, Fuzzy C-Mean Algorithm or mountain peak algorithm.If hand
Dynamic arrange parameter, it will had a huge impact to result.
It is known, for example, that k-means algorithms are a kind of cost function minimums for making distance metric in data set to seek
Look for the algorithm of data clusters.Traditional k-means clustering algorithms need randomly to select k pixel from image as initial
Cluster centre.Then pixel is assigned in each cluster by the algorithm according to minimum Eustachian distance.By a number of iteration,
Make each pixel minimum apart from summation to cluster centre, until cluster centre no longer changes.In general, k-means
Algorithm needs to set some parameters to complete task.Initialization calculates the time for reducing, and obtains meaningful cluster knot
Fruit is very important.Clusters number k is by one of most important parameter of user's selection.K is arranged to 2 to 16 herein,
And select wherein K optimum value.Need to select k point from image as initial cluster center.Generally, selected with randomized
Initial cluster center.Although this is feasible, but unstability be present.So it is easily ensnared into Local Minimum.In addition, with
Machine method can increase iterations and run time.If abnormity point is arrived in algorithm random selection, it will obtain bad knot
Fruit.
The content of the invention
In order to make up the deficiencies in the prior art, solve in the prior art based on the partitioning algorithm of cluster in manual arrange parameter
When the problem of result being made a big impact, the invention provides a kind of nuclear magnetic resonance image based on self-adaption cluster algorithm
Dividing method.
The technical scheme is that：
A kind of nuclear magnetic resonance image dividing method based on self-adaption cluster algorithm, including step：
1) nuclear magnetic resonance image is inputted；
2) biased field is adjusted；
Using the modification method of the uneven normalization algorithm N3 of nonparametric inhomogeneities, one is found smoothly at double
To maximize the distribution in organisational level high frequency components, the image of correcting offset field；
3) improved k-means algorithms segmentation figure picture is used；
First, initial cluster center is found using the method for quantile；After obtaining all initial cluster centers, changed
Generation segmentation nuclear magnetic resonance image；Using Euclidean distance as distance metric；For each pixel, all calculate the pixel and arrive
The Euclidean distance of the average value each clustered；If pixel is not pressing close to the cluster of oneself most, it must be transferred into recently
Cluster in；In the cluster closest to oneself, if that does not just have to move it pixel；If distance metric is less than one
The threshold values of individual fixation is less than a fixed threshold values compared to iteration before, then the process will terminate；
4) clusters number is determined.
For the term in the present invention：
The uneven normalization algorithm of nonparametric (N3)：N3 is a kind of iterative algorithm, and a kind of asymmetric correction method.
The present invention make N3 purpose be find a field smoothly at double so that maximize organisational level high frequency components point
Cloth.This method is a kind of known automatic algorithms, it is not necessary to which any prior information, the algorithm are never applied to nuclear magnetic resonance image
In segmentation field.
K-means algorithms：A kind of algorithm that data clusters are found in data set, allows the cost function of Diversity measure
(object function) reaches minimum.
Traditional k-means clustering algorithms need randomly to select k pixel from image as initial cluster center.
Then pixel is assigned in each cluster by the algorithm according to minimum Eustachian distance.By a number of iteration, make each picture
Element is minimum apart from summation to cluster centre, until cluster centre no longer changes.In general, k-means algorithms need
Some parameters are set to complete task.Initialization calculates the time for reducing, and it is very to obtain meaningful cluster result
Important.Clusters number k is by one of most important parameter of user's selection.K is arranged to 2 to 16 herein, and selects it
Middle K optimum value.Need to select k point from image as initial cluster center.Generally, initial clustering is selected with randomized
Center.Although this is feasible, but unstability be present.So it is easily ensnared into Local Minimum.In addition, random device meeting
Increase iterations and run time.If abnormity point is arrived in algorithm random selection, it will obtain bad result.
Improved k-means algorithms of the present invention are will randomly to select K in traditional k-means algorithms from image
Pixel is improved to find initial cluster center using the method for quantile as initial cluster center.
Initial cluster center is found with being randomly chosen using the method for quantile in the improved k-means algorithms of the present invention
Initial cluster center is compared, and drastically increases the efficiency of k-means algorithms.
Preferably, the method for quantile described in step 3) is specially：
Pixel is become into a vector, the vectorial quantile PiCalculated by formula (I), i=1,2 ..., K；Formula (I)
In, i=1,2 ..., K, K be cluster numbers；
Pass through PiIt is multiplied by vector and obtains all initial cluster centers.
Preferably, the method for determination clusters number is specially in step 4)：
It is shown as evaluation function, the function such as formula (II) to define G values；
In formula (II), SinIt is difference in class, it represents the standard error in a class between the pixel value of all pixels；
Divide the image into K classes：C1,C2…CK, shown in its calculation formula such as formula (III)：
In formula (III), n is the number of all pixels point in image；X is represented in class CiIn each pixel gray value；
It is the average gray value of all pixels point in i-th of class；
In formula (II), SoutIt is class inherited, represents the standard deviation between all initial cluster centers；SoutIt is defined as
Formula (IV)：
In formula (IV), K is clusters number, CiIt is the gray value at ith cluster center,It is all initial cluster centers
Average gray value；
Evaluation function tendency chart is generated using G values, wherein, x-axis represents clusters number k, and y-axis represents G value；The curve map
The point of middle maximum curvature is used as the number of cluster；It is monotonic increase on the left of ancon, and the right side of ancon is straight line.
Beneficial effects of the present invention are：
1st, method proposed by the present invention can be used for the classification of brain tissue and accurately anatomical structure.To cerebral magnetic resonance
During graphical analysis, the change of the method analysis brain can be utilized, delimit the intervention of pathological regions, surgery planning and image guiding
Measure.
Furthermore it is possible to more specifically split with reference to other algorithms, such as adaptive statistical model, color transfer algorithm and
Markov or Bayes's distribution.Most of all, this method can replace visual verification to illustrate a kind of algorithm the shortcomings that or
Person verifies the desired cluster result of nuclear magnetic resonance image.
2nd, the skew of nuclear magnetic resonance image is eliminated with the uneven method for normalizing of nonparametric first in the methods of the invention
.The performance of algorithm will be improved and reduce distortion by correcting the image of biased field.
3rd, the present invention proposes to be combined using G value functions and ancon rule to select an appropriate number of cluster numbers.It is solved
Need to set cluster numbers K in advance and influence the problem of result in k-means algorithms.The inventive method has higher precision
And robustness.
Embodiment
Embodiment 1
The present invention is tested and verified with internet brain segmentation storehouse (IBSR).It can provide original brain nuclear-magnetism
Resonance image and corresponding reference picture.The present invention is carried out real with the different slice positions of each three-dimensional cerebral magnetic resonance image
Test, obtained result carries out quality evaluation compared with different evaluation criterions, while to the image of division.
A kind of nuclear magnetic resonance image dividing method based on self-adaption cluster algorithm, including step：
1) nuclear magnetic resonance image is inputted；
2) biased field is adjusted；
Due to the structural complexity and gray scale of brain tissue and the disequilibrium of noise, the segmentation of cerebral magnetic resonance image
Get up than other medical image segmentations more difficult.Especially when cerebral magnetic resonance image has very strong biased field, at present
There is no suitable method to obtain satisfied segmentation result.
The present invention has found one smoothly using the modification method of the uneven normalization algorithm N3 of nonparametric inhomogeneities
Field at double is to maximize the distribution in organisational level high frequency components, the image of correcting offset field；This method be it is a kind of from
Dynamic algorithm, it is not necessary to any prior information.The performance of algorithm will be improved and reduce distortion by correcting the image of biased field
3) improved k-means algorithms segmentation figure picture is used；
First, initial cluster center is found using the method for quantile；After obtaining all initial cluster centers, changed
Generation segmentation nuclear magnetic resonance image；Using Euclidean distance as distance metric；For each pixel, all calculate the pixel and arrive
The Euclidean distance of the average value each clustered；If pixel is not pressing close to the cluster of oneself most, it must be transferred into recently
Cluster in；In the cluster closest to oneself, if that does not just have to move it pixel；If distance metric is less than one
The threshold values of individual fixation is less than a fixed threshold values compared to iteration before, then the process will terminate；
The method of quantile described in step 3) is specially：
Pixel is become into a vector, the vectorial quantile PiCalculated by formula (I), i=1,2 ..., K；Formula (I)
In, i=1,2 ..., K, K be cluster numbers；
Pass through PiIt is multiplied by vector and obtains all initial cluster centers.
4) clusters number is determined.The method for determining clusters number is specially：
In order to determine suitable clusters number in k-means algorithms, a kind of evaluation criterion, existing clusters number are defined
All determined by ancon rule.
It is shown as evaluation function, the function such as formula (II) that the present invention defines G values；
In formula (II), SinIt is difference in class, it represents the standard error in a class between the pixel value of all pixels；
Divide the image into K classes：C1,C2…CK, shown in its calculation formula such as formula (III)：
In formula (III), n is the number of all pixels point in image；X is represented in class CiIn each pixel gray value；
It is the average gray value of all pixels point in i-th of class；
In formula (II), SoutIt is class inherited, represents the standard deviation between all initial cluster centers；SoutIt is defined as
Formula (IV)：
In formula (IV), K is clusters number, CiIt is the gray value at ith cluster center,It is all initial cluster centers
Average gray value；
Evaluation function tendency chart is generated using G values, wherein, x-axis represents clusters number k, and y-axis represents G value；The curve map
The point of middle maximum curvature is used as the number of cluster；It is monotonic increase on the left of ancon, and the right side of ancon is straight line.
5) other several evaluation criterions are contrasted
Checking of the selection of evaluation criterion to method is critically important.If valuation functions do not have corresponding algorithmic match, just very
The rare result to satisfaction.
In traditional K-means algorithms, the most frequently used measuring is cost function J；By traditional evaluation criterion cost function J
It is added to contrast test.Cost function J is based in CiPixel x number and corresponding cluster centre c in groupiBetween Euclidean
Distance, it can be defined as：
Here,It is the cost function in i-th group, the k for passing through varying number using formula (V)
Cluster to calculate.Then these values are connected into a curve and finds flex point.
In addition, the objective evaluation index for being referred to as normalization Uniform measurement (NU) and valuation functions F is also added into and compared
Process.NU is defined as：
Wherein f (x, y) represents cerebral magnetic resonance image.ZiIt is i-th of cut zone, Ai is Zi area, and C is normalizing
Change the factor.NU is the major criterion for splitting picture quality by unsupervised algorithm measurement.NU values mean more greatly output image
Quality is better.
It is valuation functions F that another, which assesses measurement, and it is defined as：
Wherein my i is image to be split, and K is number of clusters, AiIt is the area of ith zone, eiIt is defined as original graph
The Euclidean distance sum of the characteristic vector of each pixel between picture and segmentation figure picture in region.
The inventive method determines each image k exact amount.However, in cost function J, as a result do not make us full
Meaning.There are several jumps in some cost function J tendency chart, therefore can not find suitable ancon as K values.This method
Major limitation is that elbow rule may be without stable jump.
Certainly, compared with the first two evaluation index, NU and F (I) trend do not have convincingness.NU values mean more greatly defeated
Going out image has more preferable segmentation result.But NU trend is to be increased monotonically.This means clusters number more multimass more
Good, this is not convincing.In the same way, F (I) the smaller segmentation result of value is better.However, the trend list due to F (I)
Adjust and decline, without obvious turning point, still can not find appropriate k values.Therefore, in general the inventive method has uniqueness
Advantage.
6) quality evaluation of segmentation figure picture
It is most important come assessment algorithm by the precision for testing segmentation figure picture.As a result standard Jaccard similitudes can be used
Index (JS) is verified.JS indexes are used to assess the proposed segmentation result of algorithm and the similarity of reference picture, are defined
For：
Wherein S1 is the reference picture provided by IBSR, and S2 is the segmentation result obtained by the algorithm proposed.JS indexes
Represent that the degree of accuracy of segmentation is higher close to 1.Image is mainly divided into white matter and grey matter by reference picture.Therefore here only with white matter and
Grey matter carries out contrast test.
The JS indexes of the white matter on four width cerebral magnetic resonance images, grey matter and weighted average are calculated respectively.From knot
Fruit can be seen that in every width cerebral magnetic resonance image corresponding to average JS maximum number of clusters always with the inventive method
Obtained preferable clustering number amount is consistent.In white matter and grey matter part, cluster numbers are higher than me corresponding to the maximum of JS indexes
Select.But the JS values of white matter and grey matter corresponding to the number of clusters in our selections are all very big.In general, originally
The result of inventive method has obvious advantage than the methods of cost function J.As a result show that the inventive method has higher precision
And robustness.
Claims (3)
1. a kind of nuclear magnetic resonance image dividing method based on self-adaption cluster algorithm, it is characterised in that including step：
1) nuclear magnetic resonance image is inputted；
2) biased field is adjusted；
Using the modification method of the uneven normalization algorithm N3 of nonparametric inhomogeneities, find a field smoothly at double with
Maximize the distribution in organisational level high frequency components, the image of correcting offset field；
3) improved k-means algorithms segmentation figure picture is used；
First, initial cluster center is found using the method for quantile；After obtaining all initial cluster centers, it is iterated point
Cut nuclear magnetic resonance image；Using Euclidean distance as distance metric；For each pixel, the pixel is all calculated to each
The Euclidean distance of the average value of cluster；If pixel is not pressing close to the cluster of oneself most, it must be transferred into nearest gather
In class；In the cluster closest to oneself, if that does not just have to move it pixel；If distance metric is solid less than one
Fixed threshold values is less than a fixed threshold values compared to iteration before, then the process will terminate；
4) clusters number is determined.
2. the nuclear magnetic resonance image dividing method based on self-adaption cluster algorithm as claimed in claim 1, it is characterised in that step
3) method of quantile described in is specially：
Pixel is become into a vector, the vectorial quantile PiCalculated by formula (I), i=1,2 ..., K；In formula (I), i
=1,2 ..., K, K be cluster numbers；
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3. the nuclear magnetic resonance image dividing method based on self-adaption cluster algorithm as claimed in claim 1 or 2, it is characterised in that
The method of determination clusters number is specially in step 4)：
It is shown as evaluation function, the function such as formula (II) to define G values；
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As being divided into K classes：C1,C2…CK, shown in its calculation formula such as formula (III)：
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In formula (II), SoutIt is class inherited, represents the standard deviation between all initial cluster centers；SoutIt is defined as formula
(Ⅳ)：
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In formula (IV), K is clusters number, CiIt is the gray value at ith cluster center,It is being averaged for all initial cluster centers
Gray value；
Evaluation function tendency chart is generated using G values, wherein, x-axis represents clusters number k, and y-axis represents G value；In the curve map most
The point of deep camber is used as the number of cluster；It is monotonic increase on the left of ancon, and the right side of ancon is straight line.
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| CN109949298A (en) * | 2019-03-22 | 2019-06-28 | 西南交通大学 | A kind of image segmentation quality evaluating method based on clustering learning |
| CN109949298B (en) * | 2019-03-22 | 2022-04-29 | 西南交通大学 | Image segmentation quality evaluation method based on cluster learning |
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