CN106504260B - FCM image segmentation method and system - Google Patents
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Abstract
The invention provides an FCM image segmentation method and an FCM image segmentation system. A FCM image segmentation method is provided,the method is used for solving the technical problem that the robustness of the existing image segmentation for strong noise is poor. The iteration process comprises the following steps: in the current iteration of the iteration process, the cluster center V of the previous iteration is determined by the neighborhood point of the sample pointiter‑1Difference in gray level, membership U of previous iterationiter‑1And the space Euclidean distance to form a fuzzy factor G of the current iterationiterThe cluster center V of the previous iterationiter‑1The method comprises the steps of presetting a number of clustering centers; in the current iteration of the iterative process, the blurring factor G is passed through the current iterationiterAnd the clustering center V of the previous iterationiter‑1Forming a degree of membership U of the current iterationiter(ii) a In the current iteration of the iteration process, the membership degree U of the current iteration is determinediterForming a cluster center V for the current iterationiter。
Description
Technical Field
The invention relates to an FCM image segmentation method and system, in particular to an image segmentation method and system based on fuzzy clustering segmentation.
Background
Image segmentation is an important process of image processing and computer vision. Image segmentation is a technique and process for segmenting an image into specific regions with unique properties and presenting objects of interest. Fuzzy clustering methods (i.e., FCM algorithms) in cluster segmentation methods have been successfully applied in various aspects of medical image processing, artificial intelligence, pattern recognition, and the like.
The FCM algorithm adds a membership function on the basis of hard classification, so that each sample point does not belong to a certain class any more, but belongs to different classes in a certain percentage. The FCM algorithm objective function is as follows:
n represents the number of sample points in an image, and the number of the sample points is generally the same as that of pixel points in the image; c is the number of clusters, c belongs to [1, N ]](ii) a i is the central pixel point of the selected neighborhood window (e.g., a window of 3 x 3 size); x is the number ofiRepresenting the gray value of the ith point in the image, vkA gray value representing the k-th cluster center; | xi-vk| | represents the gray value difference between the ith point and the kth clustering center in the original image; u. ofkiIs the degree of membership of the ith point to the kth class, i.e. the ith point belongs to the kth cluster centerProbability of, and
m ∈ [1, + ∞) is a weighted index of membership, typically set to 2. This enables more image information to be retained for a harder classification of the conventional FCM.
However, the information of surrounding neighborhoods is not considered in the FCM algorithm, so that the FCM algorithm is very sensitive to noise, cannot distinguish noise points from non-noise points, and is relatively low in noise robustness. With the increase of noise, the performance of the algorithm is worse and worse, and even effective image segmentation under a low-noise environment cannot be realized.
The FCM _ S algorithm considers the information of the surrounding neighborhood on the basis of the FCM algorithm, so that the category of the central point is influenced by the categories of surrounding neighborhood points, and the robustness to noise and singular points is greatly enhanced. However, the surrounding neighborhood points are calculated in each iteration process, which makes the algorithm very time-consuming.
The EnFCM algorithm and the FGFCM algorithm perform a weight operation on an original picture and a local neighborhood thereof to obtain a new linear weight picture, and then cluster the pictures according to pixel gray levels, so that the speed of the clustering algorithm is greatly improved. But the weighting operations blur the detailed parts of the image.
The algorithms other than the FCM algorithm all require parameter control, and the selection of parameters needs experience and a lot of experiments to determine, so the algorithm is not autonomous. The FLICM algorithm does not need any parameter set manually, and meanwhile, local space and local gray value information are added, so that the algorithm has certain robustness on noise while maintaining image details. However, the FLICM algorithm does not achieve good clustering when the noise fraction is large.
Disclosure of Invention
In view of this, an object of the embodiments of the present invention is to provide an FCM image segmentation method and system, which solve the technical problem that the fuzzy clustering method cannot effectively complete image segmentation in a high noise environment.
The FCM image segmentation method comprises an iteration process, wherein the iteration process comprises the following steps:
in the current iteration of the iteration process, the cluster center V of the previous iteration is determined by the neighborhood point of the sample pointiter-1Difference in gray level, membership U of previous iterationiter-1And the space Euclidean distance to form a fuzzy factor G of the current iterationiterThe cluster center V of the previous iterationiter-1The method comprises the steps of presetting a number of clustering central points;
in the current iteration of the iterative process, the blurring factor G is passed through the current iterationiterAnd the clustering center V of the previous iterationiter-1Forming a degree of membership U of the current iterationiter；
In the current iteration of the iteration process, the membership degree U of the current iteration is determinediterForming a cluster center V for the current iterationiter。
The FCM image segmentation system of the present invention comprises an iteration module for forming an iterative process, the iteration module comprising:
a fuzzy factor generating unit for passing the neighborhood point of the sample point and the clustering center V of the previous iteration in the current iteration of the iteration processiter-1Difference in gray level, membership U of previous iterationiter-1And the space Euclidean distance to form a fuzzy factor G of the current iterationiterThe cluster center V of the previous iterationiter-1The method comprises the steps of presetting a number of clustering central points;
a membership degree generating unit for generating a fuzzy factor G through the current iteration in the current iteration of the iteration processiterAnd the clustering center V of the previous iterationiter-1Forming a degree of membership U of the current iterationiter；
A cluster center generating unit for generating a cluster center according to the membership U of the current iteration in the current iteration of the iteration processiterForming a cluster center V for the current iterationiter。
The FCM image segmentation method and the FCM image segmentation system form a new fuzzy factor on the basis of the traditional FCM algorithm, and introduce the fuzzy factor into the traditional FCM algorithm. The fuzzy factor changes the traditional Euclidean distance constraint mode, the gray value difference between the spatial neighborhood point and the central point is added to the distance constraint, the fuzzy factor has high robustness of strong noise, and the detail of the image edge after the noise image is segmented can be well maintained. The fuzzy factor has self-adaptability, does not need to manually set parameters, and can automatically realize a relatively ideal segmentation effect according to different images and noises with different degrees. Through data verification of a high-noise image segmentation experiment, the FCM image segmentation method disclosed by the invention can realize good clustering under the condition of low noise, and the clustering effect is better than that of other FCM improved algorithms under the condition of high noise.
Drawings
Fig. 1a is a flowchart of an iterative process of image segmentation according to an embodiment of the FCM image segmentation method of the present invention.
Fig. 1b is a flowchart of initialization and iteration processes of inputting an image to be processed, a segmentation membership and a cluster center in an embodiment of the FCM image segmentation method of the present invention.
Fig. 2 is a schematic diagram illustrating the comparison between the effect of one embodiment of the FCM image segmentation method of the present invention and that of other FCM image segmentation methods when performing image segmentation on an image including a mixed noise image.
Fig. 3 is a schematic diagram illustrating the comparison between the FCM image segmentation method of the present invention and other image segmentation methods when performing image segmentation on images containing gaussian noise.
FIG. 4 is a block diagram of an FCM image segmentation system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The step numbers in the drawings are used only as reference numerals for the steps, and do not indicate the execution order.
Fig. 1a is a flowchart of an iterative process of image segmentation in an embodiment of the FCM image segmentation method of the present invention. The iterative processing procedure of image segmentation as shown in fig. 1 includes:
s 11: in the current iteration of the iteration process, the cluster center V of the previous iteration is determined by the neighborhood point of the sample pointiter-1Difference in gray level, membership U of previous iterationiter-1And the space Euclidean distance to form a fuzzy factor G of the current iterationiter；
It should be noted that in the first iteration of the iteration process, the cluster center V of the previous iterationiter-1As an initial cluster center V0Membership U of previous iterationiter-1Is an initial degree of membership U0Initial clustering center V0The method comprises a preset number of clustering center points.
s 12: in the current iteration of the iterative process, the blurring factor G is passed through the current iterationiterAnd the clustering center V of the previous iterationiter-1Forming a degree of membership U of the current iterationiter；
s 13: in the current iteration of the iteration process, the membership degree U of the current iteration is determinediterForming a cluster center V for the current iterationiter。
The FCM image segmentation method of the embodiment is based on an FCM image segmentation algorithm, fuzzy factors are introduced in an iteration processing process, local space information of neighborhood points and gray value information of the neighborhood points and a clustering center are utilized, and anti-interference performance of sample points on noise points can be improved.
Fig. 1b is a flowchart of an FCM image segmentation method according to another embodiment of the present invention, which includes a process of inputting an image to be processed, a process of initializing a segmentation process, and an iterative process. As shown in fig. 1b, the process of inputting the image to be processed includes:
step a: inputting an image to be processed;
the image to be processed contains noise, the types of noise include but are not limited to gaussian noise and salt and pepper noise, and the noise signal to noise ratio is not specifically limited herein.
The initialization process of the segmentation process comprises the following steps:
step b: initializing and setting a fuzzy index m, an iteration stop threshold epsilon and a maximum iteration number maxIter, and initializing a clustering number c and a neighborhood window W;
these basic parameters are the same as in the FCM algorithm. The difference is that the FCM image segmentation method of this embodiment further includes setting a neighborhood window W, which is generally the number of neighborhood points, for example, a window of 3 × 3, where W is equal to 9. The iteration stop threshold ε is typically chosen to be 1e-5, and the maximum number of iterations maxIter is less than 500.
Step c: initializing membership U with a random number between 0 and 10And using the initial membership U0Calculate initialized cluster center V for 0 th (i.e., first iteration)0(ii) a Initializing the clustering center V0C cluster centers are contained;
initialized membership U0Clustering center V for iteration 00And calculating, wherein the calculation process is the same as the initialization process of the FCM algorithm. The initialization process can initialize the cluster center first or the membership degree first, and the initialization sequence is not limited.
The iterative process comprises:
in the current iteration of the iteration process, acquiring neighborhood points of the sample points through the sample points of the image to be processed, and forming a gray value difference between the neighborhood points and the clustering center of the previous iteration;
specifically, for the iter iteration (of the current iteration), iter ═ 1,2, …, maxIter, neighborhood points around the image sample point are calculated, and the neighborhood points and the cluster center V (of the previous iteration) are obtained by using the calculated neighborhood pointsiter-1The gray value difference of (2).
Step e: in the current iteration of the iteration process, a fuzzy factor of the current iteration is formed through the gray value difference between the neighborhood point of the sample point and the clustering center of the previous iteration, the membership degree of the previous iteration and the spatial Euclidean distance;
specifically, for the iter-th iteration (of the current iteration), iter ═ 1,2, …, maxIter, the neighborhood point and cluster center V of the sample point are usediter-1Difference of gray values of (a) previous iteration (membership U)iter-1And the space Euclidean distance between the sample point and the neighborhood point, and calculating the fuzzy factor G of the ith iteration (of the current iteration)iter。
Step f: in the current iteration of the iteration process, the membership degree of the current iteration is formed through the fuzzy factor of the current iteration and the clustering center of the previous iteration;
in particular, using a blurring factor G (of the current iteration)iterAnd cluster center (of the previous iteration) Viter-1Calculating membership U of the iter iteration (of the current iteration)iter，iter＝1,2,…,maxIter。
Step g: in the current iteration of the iteration process, a cluster center of the current iteration is formed according to the membership degree of the current iteration;
in particular, according to the degree of membership U (of the current iteration)iterRecalculating the cluster center V for the iter-th iteration (of the current iteration)iter。
Step h: judging whether the membership value difference before and after iter iteration (of the current iteration) is smaller than an iteration stop threshold epsilon or whether the iteration iter exceeds the maximum iteration maxIter, if not, repeating the step d and the step g to carry out next iteration to calculate the membership and the clustering center until the condition is met;
if yes, executing step i: and finishing image segmentation and outputting the segmented image.
According to the FCM image segmentation method provided by the embodiment of the invention, the balance between the robustness of noise and the image detail retentivity can be automatically controlled by introducing the specific fuzzy factor, and the limitation of any parameter is not required; in addition, the invention utilizes the local space information and the gray value information, so that the algorithm is more flexible, and the details of the picture can be better maintained; meanwhile, the invention has high robustness and can improve the anti-interference performance of the central point to the noise point.
The objective function of the invention is as follows:
in the formula 1, N represents the number of sample points in an image, and the FCM image segmentation method of the embodiment of the invention firstly introduces a new fuzzy factor G based on gray scale space distance constraintkiThe fuzzy factor controls the influence of the neighborhood point on the central pixel point. The ambiguity factor of the present invention is defined as follows:
in the formula 2, NiRepresenting the i-th point neighborhood window (typically 3 x 3) in the original picture. ditThe Euclidean distance from the central point i to the surrounding neighborhood points t controls the influence of the surrounding neighborhood points on the central pixel point, so that the influence of the neighborhood points with long distance on the central pixel point is small, and the influence of the neighborhood points with short distance on the central pixel point is large. k is an element of [1, c ∈ ]]And c is the number of cluster centers, i.e., the images can be classified into several categories.
t is 1,2, …, W, t is the neighborhood point t of the ith pixel point in the image,
uktrepresenting the degree to which the neighborhood point t belongs to the kth cluster center of the previous iteration.
||xt-vkAnd | | l represents the gray value difference between the t-th point and the k-th clustering center in the original image, wherein the t-th point is a point in the ith point neighborhood window in the original image.
The present invention is at Euclidean distance ditThe gray value difference between the neighborhood point and the central point is quoted, and the influence of each point of the neighborhood point on the central point is changed continuously as the gray value of the central point is changed continuously with each iteration. The gray value difference between the neighborhood point and the central point is small, namely the neighborhood point is similar to the central point, and the influence of the neighborhood point on the central point is increased; on the contrary, the gray difference ratio of the neighborhood point to the central point is larger, and the influence of the neighborhood point on the central point is reduced, so the method has stronger robustness on noise and singular points.
On the basis of the above embodiment, in an FCM image segmentation method according to another embodiment of the present invention, a preprocessing process for an image to be processed is included, including:
step a 1: judging whether the image to be processed is a gray image or not, and if not, converting the color image into a gray image;
step a 2: and acquiring the resolution of the image to be processed, including the number of length pixels and the number of width pixels.
The processing procedure can simplify the complexity of the image to be processed and simplify the processing procedure of the color signal when the gray scale information for image segmentation is reserved. By determining the maximum value of the sample point, the processing scale of the iterative process is determined, processing resources are allocated in advance, and the calculation efficiency of the iterative process is improved.
On the basis of the above embodiment, in the FCM image segmentation method according to another embodiment of the present invention, an initial membership U is used0Forming an initial cluster center V0The initial iteration process of (1) initializing the membership value by using a random function to form an initialized membership U0(ii) a Initializing membership U according to characteristic values of each sample point of image0Calculating an initialized clustering center V0. The method specifically comprises the following steps:
step c 1: random initialization of c-1 membership values u by using random functionki，
Step c 2: the c-th degree of membership is calculated,
step c 3: initializing the iteration number to be 0;
step c 4: calculating to obtain the k-th clustering center vkAnd c clustering centers v of the 0 th iteration are obtained by circulating for c timeskTo obtain the clustering center V of the 0 th iteration0＝(v1,v2,…,vc)，k∈[1,c](ii) a Cluster center vkExpressed by the following formula:
in formula 3, vkRepresenting the cluster center of the current iteration, N representing the total number of sample points in the image, m representing the blur index, xiRepresenting the gray value of the ith point in the image, ukiRepresenting the degree to which the neighborhood point i belongs to the kth cluster center in the previous iteration.
The processing procedure obtains the initial membership degree and the clustering center of each sample point of the image to be processed, and forms the operation basis of iterative computation.
On the basis of the above embodiment, the FCM image segmentation method according to another embodiment of the present invention includes a neighborhood point and a cluster center V of a sample pointiter-1A gray value difference forming process, wherein each neighborhood point position in the neighborhood of the sample point is determined according to a preset neighborhood window;
acquiring a gray value of each neighborhood point according to the position of each neighborhood point;
forming each neighborhood point and corresponding clustering center V of previous iterationiter-1The gray value difference of (2).
The method specifically comprises the following steps:
step d 1: determining the positions of neighborhood points in a neighborhood window W of the sample point;
specifically, the positions of all neighborhood points in a neighborhood (window) of an ith sample point are determined, the position of the ith sample point is calibrated by using coordinates (x, y), the position of each neighborhood point in the neighborhood is calibrated by using (x + ii, y + jj), and if the neighborhood window W is p × q, ii belongs to [ -p/2, p/2], and jj belongs to [ -q/2, q/2 ];
step d 2: obtaining the gray value x of the neighborhood point according to the position of the neighborhood point tt；
Specifically, according to the (x + ii, y + jj) coordinate, find the neighborhood point t of the ith sample point, and its gray value is marked as xt；
Step d 3: forming a gray value difference between a neighborhood point t of the sample point and a corresponding clustering center;
in particular, according to | | xt-vkCalculating the gray value difference between the t-th neighborhood point and the k-th clustering center;
and forming gray value differences SUM of all neighborhood points of the ith sample point and the kth clustering center through gray value difference summation.
The processing procedure obtains the difference degree of the gray values between the neighborhood point of the sample point and the corresponding affiliated clustering center of the sample point.
In an embodiment of the invention, the FCM image segmentation method includes a step of forming a current iteration fuzzy factor GiterAccording to the position of the sample point and the position of the neighborhood point of the sample point, the space Euclidean distance d between the sample point and the neighborhood point is obtainedit；
According to
Fuzzy factor G of single neighborhood point relative to a cluster center for forming sample pointkt；
By blurring factor G for all single neighborhood points in the neighborhood window of sample point iktSumming to obtain fuzzy factors of all neighborhood points of the sample point relative to a cluster center
Wherein N isiIs a neighborhood window of sample point i. SUM | | | xt-vkL; i is the sample point number, i belongs to [0, n ]]Wherein n is the number of sample points, and t is the neighborhood point of the neighborhood window of the sample point; u. ofktRepresenting the degree of the neighborhood point t belonging to the kth clustering center in the previous iteration; m represents a blur index.
The method specifically comprises the following steps:
step e 1: if the current sample point is located at the ith sample point and the kth clustering center in the image, according to | | xt-vkCalculating the gray value difference between the t-th neighborhood point of the ith sample point and the kth clustering center, and recording as SUM;
step e 2: determining the position of each neighborhood point in a neighborhood window of the ith sample point, calibrating the position of the ith sample point by using coordinates (x, y), and calibrating the position of each neighborhood point in the neighborhood by using (x + ii, y + jj);
step e 3: in the neighborhoodDetermining the coordinates of a neighborhood point, recording as (x ', y'), calculating the Euclidean distance between the ith sample point (i.e. the central point i) and the neighborhood point t
t＝1,2,…,W；
Step e 4: according to
Form a fuzzy factor G (subject degree space distance constrained) of a single neighborhood point relative to a cluster centerkt；
Step e 5: repeating the steps e3 and e4 to obtain the fuzzy factors G of all neighborhood points (except the central point i) in the neighborhoodktAnd summed to obtain the ambiguity factor GkiT is 1,2, …, W; i.e. the blurring factor of all neighbourhoods of a sample point with respect to a cluster center
Wherein N isiA neighborhood window of sample point i;
step e 6: repeating the steps e3 to e5 c times to obtain c fuzzy factors G of the ith sample pointijJ-1, 2, …, c, i.e. the ambiguity factors of all neighborhood points of a sample point relative to all cluster centers form the ambiguity factor of the current iteration
Where c is the number of cluster centers.
The fuzzy factor G of the neighborhood point of the ith sample point relative to a clustering center is obtained in the processing processkiAnd a blurring factor G with respect to all cluster centers (c)ijI.e. the blurring factor G of the current iterationiter。
On the basis of the above embodiment, in the FCM image segmentation method according to another embodiment of the present invention, a sequence iteration is included to form the membership degree UiterObtaining the gray value of the sample point i;
acquiring gray values of all clustering centers of the previous iteration;
forming a gray value difference between the sample point i and the corresponding clustering center;
according to
Obtaining the membership u of the sample point i relative to all the clustering centers of the previous iterationki(ii) a Wherein xiIs the gray value of a sample point, vkIs the gray value of the clustering center k of the previous iteration, k belongs to [1, c ∈]C is the number of preset clustering centers, j belongs to [1, c ∈ ]]；
Obtaining the membership degrees of all sample points relative to all clustering centers of the previous iteration to form the membership degree U of the current iterationiter。
The method specifically comprises the following steps:
acquiring the gray value of the sample point;
acquiring gray values of all clustering centers;
according to | | xi-vk||2Acquiring gray value differences of sample points and all clustering centers;
according to
And acquiring the membership degree of the sample points relative to all the clustering centers.
In the FCM image segmentation method of an embodiment of the invention, the membership U of a specific forming order iteration is includediterThe process of (2), comprising:
step f 1: if the current sample point is located at the ith sample point and the kth clustering center in the image, according to | | xi-vk||2Calculating the gray value difference between the ith sample point and the kth clustering center;
step f 2: repeating step f1 c times, obtaining the gray value difference between the sample point (i.e. the center point i) and the jth clustering center, j being 1,2, …, c;
step f 3: calculating the membership degree of the central point i belonging to the k-th class center
k＝1,2,…,c；
Step f 4: repeating the steps f1 to f3 for c times, and calculating the membership degrees of the central point i belonging to c different clustering centers;
step f 5: repeating the steps d1 to d3, the steps e1 to e6 and the steps f1 to f4 for N times, and calculating the membership degrees of all sample points (namely the pixel points of the image to be processed) belonging to c different cluster centers.
On the basis of the above embodiment, in the FCM image segmentation method according to another embodiment of the present invention, a cluster center V forming order iteration is includediterThe process of (2), comprising:
step g 1: accumulating the iteration times iter to make iter equal to iter + 1;
step g 2: calculating a clustering center V of the iter iteration according to the membership degree U; namely:
according to
Forming;
n denotes the total number of sample points in the image, m denotes the blur index, xiRepresenting the gray value of the ith point in the image, ukiRepresenting the degree to which the neighborhood point i belongs to the kth cluster center in the previous iteration.
Step g 3: saving the membership degree U in the variable UoldIn (1).
Fig. 2 is a schematic diagram illustrating a comparison between image segmentation effects of an embodiment of the FCM image segmentation method of the present invention and other FCM image segmentation methods. As shown in fig. 2, fig. 2(a) is an original image. Fig. 2(b) is a mixed noise in which gaussian noise with a variance of 0.1 and salt-and-pepper noise of 15% are added to an original image.
As can be seen from fig. 2(c), the processing result of FCM is the worst, most of the noise is not removed, and the image segmentation effect is very poor. From fig. 2(d), it can be seen that the FCM _ S process is better than FCM, but the classification is wrong in the heart and the information is lost completely. It can be seen from fig. 2(e) and 2(f) that the processing effect of EnFCM and FGFCM is better than that of FCM _ S, but since EnFCM and FGFCM filter the picture in advance, the picture is blurred, the detail part cannot be well maintained, especially the background part, and a large number of block noise points exist. From fig. 2(g) it can be seen that the FLICM is able to remove most of the noise, but the background and the flower stem part still retain much of the noise. As can be seen from fig. 2(h), the segmentation method according to the embodiment of the present invention can obtain better effect than the FLICM, and achieves more ideal segmentation effect from the aspect of keeping picture details and robustness to noise.
The ratio of the accuracy (%) of each FCM image segmentation method corresponding to fig. 2 is shown in table 1:
| FCM | FCM_S | EnFCM | FGFCM | FLICM | the invention | |
| Gaussian(δ＝0.05) | 70.99 | 90.42 | 93.53 | 93.73 | 96.06 | 99.78 |
| Gaussian(δ＝0.10) | 65.06 | 82.60 | 86.56 | 86.85 | 90.76 | 94.92 |
| Gaussian(δ＝0.15) | 62.52 | 79.86 | 82.84 | 83.00 | 87.55 | 93.44 |
| Gaussian(δ＝0.20) | 61.27 | 75.63 | 79.02 | 79.45 | 82.81 | 92.42 |
| Salt&Pepper(5％) | 97.45 | 97.56 | 97.55 | 98.98 | 99.94 | 99.96 |
| Salt&Pepper(10％) | 95.02 | 99.15 | 95.16 | 96.53 | 99.86 | 99.94 |
| Salt&Pepper(15％) | 92.25 | 99.64 | 92.75 | 92.59 | 99.78 | 99.84 |
| Salt&Pepper(20％) | 88.59 | 98.94 | 88.95 | 87.10 | 99.67 | 99.80 |
TABLE 1
Adding two noises with different degrees and different types into an original image, wherein one is Gaussian (delta is 0.05-0.20), namely adding Gaussian noise with the variance of 0.05-0.20; the other is Salt and Pepper noise Salt & Pepper (5% -20%), namely 5% -20% of Salt and Pepper noise is added. Then, different FCM algorithms and the FCM image segmentation method of the embodiment of the invention are adopted to cluster the noise images respectively, so as to obtain new cluster images. And comparing the new clustering picture with the original picture to obtain the classification accuracy.
As can be seen from table 1, compared with the original image, the classification accuracy of the image segmentation result obtained by the FCM image segmentation method according to the embodiment of the present invention is higher than that of the FCM algorithm and its improved algorithm no matter under gaussian noise or salt-and-pepper noise, and when the proportion of noise is increased, the result of the present invention has obvious advantages.
Ambiguity factor G of segmentation method of the embodiment of the inventionkiThe balance between the robustness of noise and the image detail retention can be automatically controlled without any parameter limitation. And in each iteration of the algorithm, GkiAre changed, unlike the parameters in FCM _ S, EnFCM, FGFCM algorithms that control the balance of noise robustness and picture detail retention, which cannot be changed once determined. GkiThe local space information and the gray value information are better utilized by changing, so that the algorithm is more flexible, the robustness to noise is higher, and the details of the picture can be better maintained.
Based on the FCM image segmentation method of the above embodiment, in another embodiment of the FCM image segmentation method of the present invention, in another order iterative process of forming the blurring factor, the spatial euclidean distance d between the sample point and the neighborhood point is obtained according to the position of the sample point and the position of the neighborhood point of the sample pointit；
According to
Fuzzy factor G of single neighborhood point relative to a cluster center for forming sample pointkt(ii) a Wherein:
SUM＝||xt-vkl; i is the sample point number, i belongs to [0, n ]]Wherein n is the number of sample points, and t is the neighborhood point of the neighborhood window of the sample point; u. ofktRepresenting the degree of the neighborhood point t belonging to the kth clustering center in the previous iteration; m represents a blur index; gray ═ α xtWherein α is a control parameter;
by blurring factor G for all single neighborhood points in the neighborhood window of sample point iktSumming to obtain fuzzy factors of all neighborhood points of the sample point relative to a cluster center
Wherein N isiIs a neighborhood window of sample point i.
The method specifically comprises the following steps:
step e 11: if the current sample point is located at the ith sample point and the kth clustering center in the imageAccording to | | xt-vkCalculating the gray value difference between the t-th neighborhood point of the ith sample point and the kth clustering center, and summing to obtain SUM;
step e 12: determining the position of each neighborhood point in a neighborhood window of the ith sample point, calibrating the position of the ith sample point by using coordinates (x, y), and calibrating the position of each neighborhood point in the neighborhood by using (x + ii, y + jj);
step e 13: determining the coordinates of a neighborhood point in the neighborhood, recording as (x ', y'), and calculating the Euclidean distance between the central point i and the neighborhood point t
t＝1,2,…,W；
Step e 14: determining a gray value x of a neighborhood point in a neighborhoodtBy gray ═ α xtIn combination with a control parameter α;
step e 15: according to
Form a fuzzy factor G based on the constraint of neighborhood point membership spatial distancekt；
Step e 16: repeating the above steps e13 and e15 to obtain the fuzzy factors G of all neighborhood points (except the sample point i) in the neighborhoodktAnd summed to obtain the ambiguity factor Gki，t＝1，2，…，W；
Step e 17: repeating the steps e13 to e16 c times to obtain c fuzzy factors G of the ith sample pointij，j＝1，2，…，c。
The fuzzy factor G of the neighborhood point of the ith sample point relative to a clustering center is obtained in the processing processkiAnd a blurring factor G with respect to all cluster centers (c)ijI.e. the blurring factor G of the current iterationiter。
Wherein SUM | | | xt-vkL; i is the sample point number, i belongs to [0, n ]]Wherein n is the number of sample points, and t is the neighborhood point of the neighborhood window of the sample point; u. ofktRepresenting that the neighborhood point t belongs to the kth in the previous iterationDegree of clustering center; m represents a blur index; gray ═ α xtWherein α is a control parameter.
FCM image segmentation method of the embodiment, and another embodiment of the FCM image segmentation method, the blurring factor GkiFurther optimization is carried out, so that the accuracy of the image segmentation edge is greatly improved, and the segmentation effect is further improved. Optimized ambiguity factor GkiThe objective function of (2) is as follows:
controlling a parameter alpha, and controlling the influence degree of the gray value gray on the whole fuzzy factor, and the influence degree on the whole algorithm; the larger the value of a is, the larger the influence of the representation gray scale is, the more image details can be kept, but the robustness to noise is reduced; conversely, the smaller the value a, the less the effect on the representation gray value, and the greater the robustness against noise, but the less the retention of image details.
Fig. 3 is a schematic diagram illustrating the comparison between the image segmentation effect of another embodiment of the FCM image segmentation method of the present invention and the image segmentation effect of other FCM image segmentation methods. As shown in fig. 3, fig. 3(a) is an original image. Fig. 3(b) shows the original image with gaussian noise having a variance of 0.05 added thereto. As can be seen from fig. 3(c), the processing result of FCM is the worst, most of the noise is not removed, and the image segmentation effect is very poor.
A comparison of the accuracy of the FCM image segmentation methods corresponding to fig. 3 is shown in table 2:
TABLE 2
Two kinds of noise with different degrees and different types are added into an original image, wherein one kind of noise is Gaussian noise (delta is 0.05-0.20), namely the Gaussian noise with the variance of 0.05-0.20 is added. The other is mixed noise, namely Gaussian noise and salt and pepper noise are added into the image at the same time, the invention adopts the condition that the salt and pepper noise is continuously increased under the condition that the Gaussian noise is not changed, namely 5 to 20 percent of salt and pepper noise is added into the image under the condition that the Gaussian noise with the variance of 0.1 is added into the image. Then, different FCM algorithms and the FCM image segmentation method of the embodiment of the invention are adopted to cluster the noise images respectively, so as to obtain new cluster images. And comparing the new clustering picture with the original picture to obtain the classification accuracy.
As can be seen from table 2, compared with the original image, the image segmentation result obtained by the FCM image segmentation method according to the embodiment of the present invention has a classification accuracy higher than that of the FCM algorithm and its improved algorithm under the mixed noise of gaussian noise, and when the proportion of noise increases, the result of the present invention has a significant advantage.
FIG. 4 is a block diagram of an FCM image segmentation system according to an embodiment of the present invention. As shown in fig. 4, an iteration module 100 is included for forming an iterative process.
The iteration module 100 includes:
a fuzzy factor generating unit 110, configured to pass through a neighborhood point of the sample point and a clustering center V of a previous iteration in a current iteration of the iteration processiter-1Difference in gray level, membership U of previous iterationiter-1And the space Euclidean distance to form a fuzzy factor G of the current iterationiterThe cluster center V of the previous iterationiter-1The method comprises the steps of presetting a number of clustering central points;
a membership degree generating unit 150 for generating a fuzzy factor G through a current iteration of the iterative processiterAnd the clustering center V of the previous iterationiter-1Forming a degree of membership U of the current iterationiter；
A cluster center generating unit 160 for generating the cluster center according to the membership degree U of the current iteration in the current iteration of the iteration processiterForming a cluster center V for the current iterationiter。
In another embodiment of the present invention, the FCM image segmentation system further includes a first iteration unit 105, configured to initialize the membership value using a random function to form an initialized membership U0(ii) a The primary iteration unit may be deployed in the iteration module or outside the iteration module.
Initializing membership U according to characteristic values of each sample point of image0Calculating an initialized clustering center V0。
On the basis of the foregoing embodiment, in an FCM image segmentation system according to an embodiment of the present invention, the blurring factor generation unit 110 includes:
a neighborhood position generating subunit 111, configured to determine, according to a neighborhood window, a position of each neighborhood point in the neighborhood of the sample point;
a neighborhood gray level generation subunit 112, configured to obtain a gray level value of each neighborhood point according to each neighborhood point position;
a neighborhood point gray difference generating subunit 113, configured to form each of the neighborhood points and a corresponding clustering center V of a previous iterationiter-1The gray value difference of (2).
On the basis of the foregoing embodiment, in an FCM image segmentation system according to an embodiment of the present invention, the blur factor generation unit 110 further includes:
a euclidean distance generating subunit 114, configured to obtain a spatial euclidean distance d between the sample point and the neighborhood point according to the position of the sample point and the position of the neighborhood point of the sample pointit；
A first single blurring factor generating subunit 115 for generating a first single blurring factor based on
Form the ambiguity factor Gkt of a single neighborhood of points of the sample point relative to a cluster center;
a single cluster center ambiguity factor generation subunit 119 for generating an ambiguity factor G by applying to all of the single neighborhood points in the neighborhood window of the sample point iktSumming to obtain fuzzy factors of all neighborhood points of the sample point relative to a cluster center
On the basis of the above embodiment, in an FCM image segmentation system according to another embodiment of the present invention, the blurring factor generation means includes a second single blurring factor generation subunit 116 instead of the first single blurring factor generation subunit 115,
for in accordance with
On the basis of the above embodiment, the membership degree generating unit 150 of an FCM image segmentation system according to an embodiment of the present invention includes:
a sample point gray scale generation subunit 151 configured to acquire a gray scale value of the sample point i;
a clustering center gray level generation subunit 152, configured to obtain gray levels of all clustering centers of the previous iteration;
a sample point gray difference value generation subunit 153, configured to form a gray value difference between a sample point i and a corresponding clustering center;
a single sample point membership degree generating subunit 154 for generating a single sample point membership degree according to
Obtaining the membership u of the sample point i relative to all the clustering centers of the previous iterationki；
A membership degree generating subunit 155 for all the sample points, configured to obtain membership degrees of all the sample points with respect to all the clustering centers of the previous iteration, and form a membership degree U of the current iterationiter。
On the basis of the above embodiment, the cluster center generating unit 160 of the FCM image segmentation system according to an embodiment of the present invention includes:
a current iteration cluster center generating subunit 161 for generating a current iteration cluster center according to
And forming a current iteration cluster center.
On the basis of the above embodiment, an FCM image segmentation system according to an embodiment of the present invention further includes:
a gray scale conversion unit 90, configured to convert the color image to be processed into a gray scale image before the iterative process;
an image size identifying unit 95 is configured to obtain a resolution of the grayscale image before the iterative process, and take pixels of the grayscale image as sample points.
On the basis of the foregoing embodiment, the FCM image segmentation system according to another embodiment of the present invention further includes a determining module 200, configured to form a cluster center V of a current iterationiterAnd then, judging the termination of the iteration, wherein the judgment comprises the following steps:
an iteration termination judging unit 210, configured to judge whether a membership value difference before and after the iteration of the current iteration is smaller than an iteration stop threshold epsilon or whether the iteration number exceeds the maximum iteration number.
Specific implementation and beneficial effects of the FCM image segmentation system in the embodiment of the present invention can be referred to as the FCM image segmentation method, and are not described herein again.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and the like that are within the spirit and principle of the present invention are included in the present invention.
Claims (15)
1. An FCM image segmentation method, comprising an iterative process, wherein the iterative process comprises:
in the current iteration of the iteration process, the cluster center V of the previous iteration is determined by the neighborhood point of the sample pointiter-1Difference in gray level, membership U of previous iterationiter-1And the space Euclidean distance to form a fuzzy factor G of the current iterationiterThe cluster center V of the previous iterationiter-1The method comprises the steps of presetting a number of clustering central points;
in the current iteration of the iterative process, the blurring factor G is passed through the current iterationiterAnd the clustering center V of the previous iterationiter-1Forming a degree of membership U of the current iterationiter；
In the current iteration of the iterative processAccording to the degree of membership U of the current iterationiterForming a cluster center V for the current iterationiter；
Wherein the blurring factor GiterThe forming method comprises the following steps:
obtaining the spatial Euclidean distance d between the sample point and the neighborhood point according to the position of the sample point and the position of the neighborhood point of the sample pointit；
According to
SUM＝||xt-vkl; i is the sample point number, i belongs to [0, n ]]Wherein n is the number of sample points, and t is the neighborhood point of the neighborhood window of the sample point; u. ofktRepresenting the degree of the neighborhood point t belonging to the kth clustering center in the previous iteration; m represents a blur index; gray ═ α xtWherein α is a control parameter;
by blurring factor G for all single neighborhood points in the neighborhood window of sample point iktSumming to obtain fuzzy factors of all neighborhood points of the sample point relative to a cluster center
Wherein N isiIs a neighborhood window of sample point i.
2. The image segmentation method of claim 1, further comprising a first iteration of:
initializing the membership value by using a random function to form an initialized membership U0；
Initializing membership U according to characteristic values of each sample point of image0Calculating an initialized clustering center V0。
3. The image segmentation method of claim 1, wherein the neighborhood point of the sample point and the previous timeIterative clustering center Viter-1The gray value difference of (a) includes:
determining each neighborhood point position in the sample point neighborhood according to a preset neighborhood window;
acquiring a gray value of each neighborhood point according to the position of each neighborhood point;
forming each of said neighborhood points and a corresponding cluster center V of a previous iterationiter-1The gray value difference of (2).
4. The image segmentation method of claim 3, the determining each neighborhood point position in the sample point neighborhood according to a neighborhood window comprising:
presetting the size of a neighborhood window as p multiplied by q, wherein p and q are the width and the length of the neighborhood window;
determining the coordinate positions of the sample points as x and y, wherein the x and the y are horizontal and vertical coordinates of the sample points in the image;
determining each neighborhood point position x + ii, y + jj in the neighborhood window of the sample point according to the size of the neighborhood window, wherein ii and jj are the horizontal offset and the vertical offset of the coordinates of the sample point, ii belongs to [ -p/2, p/2], and jj belongs to [ -q/2, q/2 ];
the corresponding clustering center V for forming each neighborhood point and the previous iterationiter-1The gray value difference of (a) includes:
according to | | xt-vk| | forms the gray value difference between the neighborhood point of the sample point and the corresponding clustering center, xt is the gray value of the neighborhood point t of the sample point, vkIs the gray value of the clustering center k of the previous iteration, k belongs to [1, c ∈]And c is the preset number of clustering centers.
5. The image segmentation method of claim 1, forming a degree of membership U for a current iterationiterThe method comprises the following steps:
acquiring a gray value of a sample point i;
acquiring gray values of all clustering centers of the previous iteration;
forming a gray value difference between the sample point i and the corresponding clustering center;
according to
Obtaining the membership u of the sample point i relative to all the clustering centers of the previous iterationki(ii) a Wherein xiIs the gray value of a sample point, vkIs the gray value of the clustering center k of the previous iteration, k belongs to [1, c ∈]C is the number of preset clustering centers, j belongs to [1, c ∈ ]]；
Obtaining the membership degrees of all sample points relative to all clustering centers of the previous iteration to form the membership degree U of the current iterationiter。
6. The image segmentation method of claim 5, the cluster center V forming a current iterationiterIs according to
Forming;
where N represents the total number of sample points in the image, m represents the blur index, xiRepresenting the gray value of the ith point in the image, ukiRepresenting the degree to which the neighborhood point i belongs to the kth cluster center in the previous iteration.
7. The image segmentation method of any of claims 1 to 6, further comprising, prior to the iterative process:
converting the color image to be processed into a gray image;
and acquiring the resolution of the gray image, and taking the pixel of the gray image as a sample point.
8. An image segmentation method as claimed in any one of claims 1 to 6, forming a cluster center V for a current iterationiterThen, the method further comprises the following steps:
judging whether the membership value difference before and after iteration of the current iteration is smaller than an iteration stop threshold epsilon or whether the iteration frequency exceeds a preset maximum iteration frequency, if so, finishing image segmentation and outputting a segmented image; if not, performing next iteration to calculate the membership degree and the clustering center until the condition is met.
9. An FCM image segmentation system comprising an iteration module for forming an iterative process, the iteration module comprising:
a fuzzy factor generating unit for passing the neighborhood point of the sample point and the clustering center V of the previous iteration in the current iteration of the iteration processiter-1Difference in gray level, membership U of previous iterationiter-1And the space Euclidean distance to form a fuzzy factor G of the current iterationiterThe cluster center V of the previous iterationiter-1The method comprises the steps of presetting a number of clustering central points;
a membership degree generating unit for generating a fuzzy factor G through the current iteration in the current iteration of the iteration processiterAnd the clustering center V of the previous iterationiter-1Forming a degree of membership U of the current iterationiter；
A cluster center generating unit for generating a cluster center according to the membership U of the current iteration in the current iteration of the iteration processiterForming a cluster center V for the current iterationiter；
Wherein the blurring factor generation unit includes:
a Euclidean distance generating subunit, configured to obtain a spatial Euclidean distance d between the sample point and the neighborhood point according to the position of the sample point and the position of the neighborhood point of the sample pointit；
A single blurring factor generation subunit for generating a single blurring factor based on
Fuzzy factor G of single neighborhood point relative to a cluster center for forming sample pointkt(ii) a Wherein: SUM | | | xt-vkL; i is the sample point number, i belongs to [0, n ]]Wherein n is the number of sample points, and t is the neighborhood point of the neighborhood window of the sample point; u. ofktRepresenting the degree of the neighborhood point t belonging to the kth clustering center in the previous iteration; m represents a blur index; gray ═ α xtWherein α is a control parameter;
single clusteringA central ambiguity factor generation subunit for generating an ambiguity factor G by applying to all of the single neighborhood points in the neighborhood window of the sample point iktSumming to obtain fuzzy factors of all neighborhood points of the sample point relative to a cluster center
Wherein N isiIs a neighborhood window of sample point i.
10. The image segmentation system of claim 9, further comprising a first iteration unit for initializing the membership values using a random function to form initialized membership U0；
Initializing membership U according to characteristic values of each sample point of image0Calculating an initialized clustering center V0。
11. The image segmentation system of claim 9, the blur factor generation unit comprising:
a neighborhood position generating subunit, configured to determine, according to a neighborhood window, a position of each neighborhood point in the neighborhood of the sample point;
the neighborhood gray level generation subunit is used for acquiring the gray level value of each neighborhood point according to the position of each neighborhood point;
a neighborhood point gray difference value generation subunit for forming each neighborhood point and the corresponding clustering center V of the previous iterationiter-1The gray value difference of (2).
12. The image segmentation system of claim 9, the membership generation unit comprising:
the sample point gray level generation subunit is used for acquiring the gray level value of the sample point i;
a clustering center gray level generation subunit, configured to obtain gray levels of all clustering centers of the previous iteration;
the sample point gray difference value generation subunit is used for forming a gray value difference between the sample point i and the corresponding clustering center;
single sample point membership generationA subunit of
Obtaining the membership u of the sample point i relative to all the clustering centers of the previous iterationki；
A membership degree generating subunit for all the sample points, which is used for obtaining the membership degree of all the sample points relative to all the clustering centers of the previous iteration to form the membership degree U of the current iterationiter。
13. The image segmentation system of claim 12, the cluster center generation unit comprising:
a current iteration cluster center generating subunit for generating
And forming a current iteration cluster center.
14. The image segmentation system of any of claims 9 to 13, further comprising:
the gray level conversion unit is used for converting the color image to be processed into a gray level image before the iterative process;
and the image size identification unit is used for acquiring the resolution of the gray-scale image before the iterative process and taking the pixel of the gray-scale image as a sample point.
15. The image segmentation system of any of claims 9 to 13, further comprising a decision module for forming a cluster center V for a current iterationiterAnd then, judging the termination of the iteration, wherein the judgment comprises the following steps:
and the iteration termination judging unit is used for judging whether the membership value difference before and after the iteration of the current iteration is smaller than the iteration stop threshold epsilon or whether the iteration times exceed the maximum iteration times.
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