CN106875402B - A kind of digital image processing method based on the clustering algorithm for choosing suitable clusters number - Google Patents
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Abstract
The present invention relates to a kind of digital image processing methods based on the clustering algorithm for choosing suitable clusters number, and specific steps include: (1) input gray level image；(2) setting needs the number of iteration cluster numbers K；(3) it searches for initial cluster center: finding initial cluster center using the concept of quantile；(4) image segmentation, the segmented image of output are carried out according to the k-means sorting procedure of standard；(5) optimum segmentation result is selected using optimization criterion.The invention proposes one can determine the optimization criterion of clusters number in segmented image.It, which uses in class difference and the concept of class inherited, can obtain optimal segmentation result with less clusters number.The present invention has enough efficiency and stability, in terms of run time advantageously than traditional k-means algorithm.
Description
Technical field
The present invention relates to a kind of digital image processing methods based on the clustering algorithm for choosing suitable clusters number, belong to poly-
Class algorithm segmentation technology.
Background technique
In field of image processing, image segmentation is very important being classified and being handled for image.Therefore, Wo Menxu
These images are divided into different regions, and extract interested object.In different image Segmentation Technologies, cluster
It is important one of method, and is widely used in the image segmentation of gray level image.There are many clustering algorithms at present:
K-means cluster；Fuzzy c-means cluster；Mountain clustering and ISODATA method etc..The algorithm of most common of them is k-
Means clustering algorithm.K-means algorithm is a kind of Unsupervised clustering algorithm, it have it is intuitive, the spies such as quickly and easily realize
Property.Although this algorithm be it is very popular, it still has some defects.Wherein, most importantly k-means cluster needs
Cluster numbers are known in advance, this will reduce its robustness and stability.
Image segmentation is exactly a process for coming out feature or extracted region significant in image.Especially in medical treatment
Field, medical investigator need to extract interested region from background.It would therefore be desirable to which these images are divided into difference
Region, and extract interested object.Meanwhile the pixel in each region answers similitude with higher, region it
Between pixel answer otherness with higher.Image segmentation is very widely used, it is occurred nearly in about at image
It is also important step that all spectra of reason, which is a basis in image procossing,.
In different image Segmentation Technologies, cluster is important one of method, and in the image segmentation of gray level image
On be widely used.Cluster is that one group of object of grouping enters the treatment process of similarly feature class.It is in many necks
Domain is widely used, and is included in statistics, machine learning, pattern-recognition, data mining and image procossing etc..In Digital Image Processing
In, it is essential for being segmented in iamge description and classification.The technology is (i.e. conventional commonly used in many consumption electronic products
Digital picture), or in a specific application field, such as medical digital images.Algorithm is typically based on similitude and particularity,
Different classifications can be divided into, such as threshold value, template matching, region growing, edge detection and cluster.Clustering algorithm has also been employed that
In various fields, such as engineering, computer and mathematics Digital Image Segmentation technology.Recently, the application of clustering algorithm is further
It is applied in medical field, especially in biomedical image analysis, it is characterised in that image is generated by medical imaging devices
's.Previous studies prove that the interested specific region in medical image can be divided and be determined to clustering algorithm.It is cured in biology
It learns in image segmentation task, clustering algorithm, which is typically considered, to be suitble to be partitioned into interested knot from known anatomic information
Structure.
In the clustering method of objective function based on the form of minimum, most widely used is exactly K-means cluster.K-
Means algorithm is also referred to as K mean algorithm, is that one kind obtains most widely used clustering algorithm.It will be in each cluster subset
All data samples representative point of the mean value as the cluster, the main thought of algorithm is that data set is drawn by iterative process
Be divided into different classifications so that evaluation clustering performance criterion function be optimal, thus make generate each cluster in it is compact,
It and is independent between class.This algorithm is not suitable for processing discrete type attribute, but has preferable cluster effect for continuous type
Fruit, for image segmentation have the characteristics that it is intuitive, quickly, be easily achieved.Although this algorithm be it is very popular, it is still
With some defects.Firstly, k-means cluster process is easily trapped into local minimum.Secondly, it be not suitable for processing have from
Dissipate the data of attribute.In addition, it is it is also possible to ignore some small clusters.It is worth noting that k-means cluster needs to shift to an earlier date
Know cluster numbers, this will reduce its robustness and stability.
Summary of the invention
Summary of the invention
In view of the deficiencies of the prior art, the present invention provides a kind of numbers based on the clustering algorithm for choosing suitable clusters number
Word image processing method；
Invention describes a kind of optimization criterions to solve influence of the clusters number to final segmented image.We are based on
Pixel difference defines a formula between pixel difference and class in class.By the standard, can be obtained with clusters number few as far as possible
To preferable segmentation result.Measurement NU and F (I) is tested by objective assessment, we demonstrate the stabilization of the standard performance
Property.In addition, utilizing quantile strategy invention also improves the method for determining initial cluster center in traditional k-means algorithm
Instead of randomly selected method.Determine that initial cluster center can make segmented image more stable using quantile, while can
To save runing time.
Detailed description of the invention
Term is explained
1, quantile, quantile, that is, quantile are for taking quartile, i.e., ascending all numerical value in statistics
Quarter is arranged and is divided into, the numerical value in three cut-point positions is exactly quartile.In the present invention, if cluster numerical digit K,
The ascending arrangement of all pixels of the image to be divided is divided into K equal portions, finds out the central value of every equal portions as initial poly-
Class center.
2, K-means is clustered, a kind of algorithm for finding data clusters in data set, allows the cost function of Diversity measure
(objective function) reaches minimum.
Technical scheme is as follows:
A kind of digital image processing method based on the clustering algorithm for choosing suitable clusters number, specific steps include:
(1) input gray level image；
(2) setting needs the number of iteration cluster numbers K；The initial value of K is 2；
It is well known that iteration cluster numbers K is unknown in traditional k-means algorithm.In fact, for most of
Iteration cluster numbers K is set as 2 by digital picture and micro-image, this is to be not enough to appropriate carry out image segmentation.Also have one
A little experimenters select the value of k according to the experience of oneself, for example, the region that head medicine image includes is soft tissue, bone, rouge
Fat and background area, so the value of k is set as 4 by they.In order to determine that the optimal value of k, the present invention find a kind of measurement standard,
Automatically determine optimal k value.Before being clustered, setting k from 2 to 16 is recycled, to replace a fixed assumption value.It provides
More intuitive trend is to help our to analyze.
(3) it searches for initial cluster center: finding initial cluster center using the concept of quantile；Specific steps include:
A, all pixels in the gray level image of step (1) input are subjected to ascending order arrangement according to gray value, obtain vector,
That is: the size m*m of the described gray level image is a matrix, by the matrix conversion at 1*m2Vector, then by 1*m2Vector in
All elements obtain the vector by ascending order arrangement from small to large；The quantile P of the vectoriIt is calculated by formula (I), i=
1,2 ..., K:
B, K quantile, including P are calculated by step A1,P2,...,Pi, P1,P2,...,PiRespectively correspond step
Vector described in rapid A, P1,P2,...,PiThe as initial cluster center of the gray level image of step (1) input；
For example, K=4, is calculated four quantiles: P1,P2,P3,P4, P1,P2,P3,P4The result of four values are as follows: 12.5,
37.5,62.5,87.5.These values correspond to the initial cluster center of vector.
According to traditional K- means clustering algorithm, need to randomly choose k point from image as initial cluster center.Then
Data point is assigned in each cluster by the algorithm according to minimum Eustachian distance.By the iteration of certain number, it is to greatest extent
Ground reduces the sum of the distance from each object to cluster centre, until these mass centers will not change again.But this tradition
Method low efficiency, runing time is more long.And it is that very efficiently, it compares and seeks at random that the present invention, which finds initial cluster center,
The method looked for saves runing time.In next explanation, contrast test will do it to verify its efficiency.
(4) image segmentation, the segmented image of output are carried out according to the k-means sorting procedure of standard；
(5) optimum segmentation is selected as a result, specific steps include: using optimization criterion
1. seeking difference value S in the class of the segmented image of output by formula (II)in, difference value S in classinRefer at one
Standard deviation in cluster between the pixel value of all pixels:
In formula (II), C1,C2,C3,......,CiRefer to the initial cluster center P that step (3) is sought1,P2,...,PiIt is right
The cluster answered, n are the quantity of pixel in current segmented image, and x is represented in cluster CiIn each pixel pixel value,It is i-th
The average value of the pixel value of all pixels in class；
2. seeking the class inherited value S of the segmented image of output by formula (III)out, class inherited value SoutRefer at the beginning of i
Standard deviation between the pixel value of beginning cluster centre, value are the bigger the better.
In formula (III), K refers to cluster numbers, PiRefer to i-th of initial cluster center (pixel value),It is all initial poly-
The average pixel value at class center；
3. seeking optimal standards by formula (IV) is G, as follows:
4. successively being sought according to above step corresponding when K is 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
Optimal standards is G, obtains best segmentation effect according to the corresponding optimal standards G sought.
According to the present invention preferably, the step (4), specific steps include:
A, cluster centre P is initializedi；
B, subordinated-degree matrix u is determinedij: as the pixel value X of j-th of pixeljBelong to CiWhen, uijIt is 1, is otherwise 0；That is:
If PiIt is in all initialization cluster centres closest to XjCentral point, then XjBelong to Ci；
C, cost function J is calculated by formula (V):
When the cost function J being calculated is lower than 0.005, then stop calculating cost function, otherwise continues to calculate cost
Function；
D, Optimal cluster centers are obtained according to formula (VI), is cluster CiAverage value:
In formula (VI), | Ci| it is CiSize；
E, segmented image is exported.
The invention has the benefit that
1, the invention proposes one can determine the optimization criterion of clusters number in segmented image.It uses class
Interior difference and the concept of class inherited can obtain optimal segmentation result with less clusters number.The experimental results showed that should
Criterion has enough efficiency and stability.In addition, other evaluation methods also obtain consistent result.
2, the present invention is by improving the k-means algorithm for finding initial cluster center method also than traditional k-means calculation
Method is in terms of run time advantageously.
Detailed description of the invention
Fig. 1 is the process of the digital image processing method of the present invention based on the clustering algorithm for choosing suitable clusters number
Schematic diagram；
Fig. 2 is the trend chart that the optimal standards obtained under different K values obtained in embodiment is G；
Specific embodiment
The present invention is further limited with embodiment with reference to the accompanying drawings of the specification, but not limited to this.
Embodiment
A kind of digital image processing method based on the clustering algorithm for choosing suitable clusters number, the present embodiment Southern California
The USC-SIPI image measurement library of university is verified, as shown in Figure 1, specific steps include:
(1) input gray level image；
(2) setting needs the number of iteration cluster numbers K；The initial value of K is 2；
It is well known that iteration cluster numbers K is unknown in traditional k-means algorithm.In fact, for most of
Iteration cluster numbers K is set as 2 by digital picture and micro-image, this is to be not enough to appropriate carry out image segmentation.Also have one
A little experimenters select the value of k according to the experience of oneself, for example, the region that head medicine image includes is soft tissue, bone, rouge
Fat and background area, so the value of k is set as 4 by they.In order to determine that the optimal value of k, the present invention find a kind of measurement standard,
Automatically determine optimal k value.Before being clustered, setting k from 2 to 16 is recycled, to replace a fixed assumption value.It provides
More intuitive trend is to help our to analyze.
(3) it searches for initial cluster center: finding initial cluster center using the concept of quantile；Specific steps include:
A, all pixels in the gray level image of step (1) input are subjected to ascending order arrangement according to gray value, obtain vector,
That is: the size m*m of the described gray level image is a matrix, by the matrix conversion at 1*m2Vector, then by 1*m2Vector in
All elements obtain the vector by ascending order arrangement from small to large；The quantile P of the vectoriIt is calculated by formula (I), i=
1,2 ..., K:
B, K quantile, including P are calculated by step A1,P2,...,Pi, P1,P2,...,PiRespectively correspond step
Vector described in rapid A, P1,P2,...,PiThe as initial cluster center of the gray level image of step (1) input；
Four quantiles: P are calculated in K=41,P2,P3,P4, P1,P2,P3,P4The result of four values are as follows: 12.5,37.5,
62.5,87.5.These values correspond to the initial cluster center of vector.
According to traditional K- means clustering algorithm, need to randomly choose k point from image as initial cluster center.Then
Data point is assigned in each cluster by the algorithm according to minimum Eustachian distance.By the iteration of certain number, it is to greatest extent
Ground reduces the sum of the distance from each object to cluster centre, until these mass centers will not change again.But this tradition
Method low efficiency, runing time is more long.And it is that very efficiently, it compares and seeks at random that the present invention, which finds initial cluster center,
The method looked for saves runing time.In next explanation, contrast test will do it to verify its efficiency.
(4) image segmentation, the segmented image of output are carried out according to the k-means sorting procedure of standard；Specific steps include:
A, cluster centre P is initializedi；
B, subordinated-degree matrix u is determinedij: as the pixel value X of j-th of pixeljBelong to CiWhen, uijIt is 1, is otherwise 0；That is:
If PiIt is in all initialization cluster centres closest to XjCentral point, then XjBelong to Ci；
C, cost function J is calculated by formula (V):
When the cost function J being calculated is lower than 0.005, then stop calculating cost function, otherwise continues to calculate cost
Function；
D, Optimal cluster centers are obtained according to formula (VI), is cluster CiAverage value:
In formula (VI), | Ci| it is CiSize；
E, segmented image is exported.
(5) optimum segmentation is selected as a result, specific steps include: using optimization criterion
1. seeking difference value S in the class of the segmented image of output by formula (II)in, difference value S in classinRefer at one
Standard deviation in cluster between the pixel value of all pixels:
In formula (II), C1,C2,C3,......,CiRefer to the initial cluster center P that step (3) is sought1,P2,...,PiIt is right
The cluster answered, n are the quantity of pixel in current segmented image, and x is represented in cluster CiIn each pixel pixel value,It is i-th
The average value of the pixel value of all pixels in a class；
2. seeking the class inherited value S of the segmented image of output by formula (III)out, class inherited value SoutRefer at the beginning of i
Standard deviation between the pixel value of beginning cluster centre, value are the bigger the better.
In formula (III), K refers to cluster numbers, PiRefer to i-th of initial cluster center (pixel value),It is all initial poly-
The average pixel value at class center；
3. seeking optimal standards by formula (IV) is G, as follows:
4. successively being sought according to above step corresponding when K is 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
Optimal standards is G, obtains best segmentation effect according to the corresponding optimal standards G sought.As shown in Fig. 2, the change of G value
Change trend will be as shown in Fig. 2.We have found that the trend of G value tends to be horizontal after cluster numbers are more than 4.We
It can be construed to when K is less than 4, these clusters are not enough to image carrying out good classification.And when K is greater than 4, G value is almost
Restrain it is in alignment, illustrate K be equal to 4 after, the classifying quality of every width segmented image does not have big change, that is, has had
Enough cluster numbers classify.Therefore when k is equal to 4, we can obtain best segmentation effect.
Optimization criterion: when we using before improved k-means clustering algorithm, to be first arranged the number of iterations K come into
Row experiment.We attempt to go to obtain different segmentation results using different K because we need to be assessed with optimization criterion
Which value can bring best segmentation result to us.Many criterion have been developed for determining the effective of k-means cluster
Property, all these criterion all attempt to find the best cluster numbers of segmentation effect.For example, Bezdek et al. is in view of modification
Hubert statistics, Davies-Bouldin and Dunn index propose some new indexs of Cluster Validity.Milligan etc.
People tests many programs and goes to determine the number that a data concentrate cluster.Cooper et al. is tested to be clustered in clustering
Influence of the number to measurement error.
As a clustering algorithm, we certainly want to the difference minimum in the class of all clusters in a cluster, together
When one all classes of width digital picture class inherited it is maximum.It is S that we, which define difference value in class,in, it represents the institute in a class
There is the standard deviation between the pixel value of pixel.Assuming that initial cluster center is C1,C2,C3,......,Ci, then SinIs defined as:
It is obtained by calculating the standard deviation between all cluster centres, is defined as:
Consider difference value and class inherited value in above-mentioned class, it would be desirable to combine them and become ratio as measurement
Standard.Because class inherited value is maximized, so we should put difference value in class it is desirable that minimizing difference value in class
Onto molecule, class inherited value is put on denominator, formula are as follows:
We determined that optimized results only need to find the minimum value of ratio.Pass through multiple experiment, it has been found that when making
When going segmented image with our algorithm, SinThe trend being gradually reduced, S is presentedoutIncrease first and then gradually tends to hold
It is flat.But SinVariation be faster than Sout, it is on a declining curve that this will will lead to ratio.If the result is that such, we if cannot be true
Surely the optimal number clustered.Therefore we need to modify formula to solve this problem, rearrange displaying formula:
That is formula (IV).
By rearrangement formulae it was found that intermediate one is 2 power, and constant K is first power.So if it only multiplies
With K, which will lead to monotonic decreasing.In order to solve this problem, we on original formula multiplied by K so that rear two
The exponential of item is identical.It thus can produce the optimal standards that we propose herein.
In order to further prove the ability and applicability of proposition method, we by with Fuzzy C-means algorithm and
The method for comparing to examine us of OTSU algorithm.Firstly, we use the gray level image for being referred to as normalization measurement (NU)
Parameter is objectively evaluated to compare segmentation result.Normalize the formula of measurement:
NU=1-GU/C (VIII)
F (x, y) is a width gray level image, ZiIt is i-th of cut zone, AiIt is region ZiArea, C is normalized parameter,
GU is the normalization measurement of f (x, y).The feature consistency in one region can be by calculating each region in the side of affiliated area
Difference is evaluated.Therefore, a better segmentation result should have biggish NU value.We use Fuzzy C-means respectively
Algorithm and improved k-means algorithm calculate original image and segmented image the value of NU, and the value of K is respectively set to 2,3,4.
Meanwhile we also add the result of the OTSU algorithm when K is equal to 2.
Because OTSU output is bianry image, we can only show result when its two cluster.Pass through experiment
It can be concluded that the maximum value of NU is the result divided when k is equal to 4 with improved k-means algorithm.This conclusion and lead to before
It is consistent to cross the conclusion that optimization criterion obtains.Furthermore we demonstrate calculated in all clusters numbers with improved k-means
Method all has better segmentation result than fuzzy c-means.
For part and global evaluation result simultaneously, we have used the evaluation function of Liu and Yang again.Evaluation function is fixed
Justice are as follows:
Wherein I is for divided image, and k is cluster numbers, AiIt is the area of ith zone, eiIt is defined as original graph
The Euclidean distance summation of the feature vector of picture and segmented image between each pixel in this region.
The function will not have an impact conclusion because of artificial setting parameter.The value of F (I) is smaller just to illustrate segmentation knot
Fruit is better.We can also draw a conclusion, i.e., had most by the segmented image that the cluster numbers that our optimization criterion generates are 4
Small F (I) value.Verification result also confirms that, is best segmentation result by the selected segmented image of our optimization criterion.
In addition, improved K-means algorithm than traditional K-means algorithm processing the time on more efficiently.We from
5 width images have been selected to be tested in database.The processing time of each image be cluster numbers k from 2 to 6 circular treatment it is total when
Between.The improved k-means algorithm of the results show has obtained shorter runing time compared to traditional k-means algorithm.
This result also illustrates that algorithm presents higher efficiency after the method for improving new move initial cluster center.
Claims (2)
1. a kind of digital image processing method based on the clustering algorithm for choosing suitable clusters number, which is characterized in that specific step
Suddenly include:
(1) input gray level image；
(2) setting needs the number of iteration cluster numbers K；The initial value of K is 2；
(3) it searches for initial cluster center: finding initial cluster center using the concept of quantile；Specific steps include:
A, the size m*m of the gray level image is a matrix, by the matrix conversion at 1*m2Vector, then by 1*m2Vector
In all elements by from small to large ascending order arrangement, obtain the vector；The quantile P of the vectoriIt is counted by formula (I)
It calculates, i=1,2 ..., K:
B, K quantile, including P are calculated by step A1,P2,...,Pi, P1,P2,...,PiRespectively correspond step A institute
State vector, P1,P2,...,PiThe as initial cluster center of the gray level image of step (1) input；
(4) image segmentation, the segmented image of output are carried out according to the k-means sorting procedure of standard；
(5) optimum segmentation is selected as a result, specific steps include: using optimization criterion
1. seeking difference value S in the class of the segmented image of output by formula (II)in, difference value S in classinRefer in a cluster
Standard deviation between the pixel value of all pixels:
In formula (II), C1,C2,C3,......,CiRefer to the initial cluster center P that step (3) is sought1,P2,...,PiIt is corresponding poly-
Class, n are the quantity of pixel in current segmented image, and x is represented in cluster CiIn each pixel pixel value,It is institute in i-th of class
There is the average value of the pixel value of pixel；
2. seeking the class inherited value S of the segmented image of output by formula (III)out, class inherited value SoutRefer to that i are initially gathered
Standard deviation between the pixel value at class center；
In formula (III), K refers to cluster numbers, PiRefer to i-th of initial cluster center,It is the average picture of all initial cluster centers
Element value；
3. seeking optimal standards by formula (IV) is G, as follows:
4. successively being sought according to above step corresponding optimal when K is 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16
Change standard is G, obtains best segmentation effect according to the corresponding optimal standards G sought.
2. a kind of Digital Image Processing side based on the clustering algorithm for choosing suitable clusters number according to claim 1
Method, which is characterized in that the step (4), specific steps include:
A, cluster centre P is initializedi；
B, subordinated-degree matrix u is determinedij: as the pixel value X of j-th of pixeljBelong to CiWhen, uijIt is 1, is otherwise 0；That is: if Pi
It is in all initialization cluster centres closest to XjCentral point, then XjBelong to Ci；
C, cost function J is calculated by formula (V):
When the cost function J being calculated is lower than 0.005, then stop calculating cost function, otherwise continues to calculate cost function；
D, Optimal cluster centers are obtained according to formula (VI), is cluster CiAverage value:
In formula (VI), | Ci| it is CiSize；
E, segmented image is exported.
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