CN110647887A - Extraction method of internal markers for coal slime flotation foam image segmentation - Google Patents

Extraction method of internal markers for coal slime flotation foam image segmentation Download PDF

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CN110647887A
CN110647887A CN201910667822.8A CN201910667822A CN110647887A CN 110647887 A CN110647887 A CN 110647887A CN 201910667822 A CN201910667822 A CN 201910667822A CN 110647887 A CN110647887 A CN 110647887A
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coal slime
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田慕玲
王跃龙
孟海涛
武亚雄
武培雄
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Taiyuan University of Technology
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Abstract

一种用于煤泥浮选泡沫图像分割中内部标记符的提取方法是针对煤泥浮选泡沫图像噪声较大、对比度低、气泡难以分割等特点，将粒子群优化算法与一维直方图加权的模糊C均值聚类算法两种算法进行融合，将两种算法获取的内部标记符进行叠加，作为图像分割的内部标记符，用于提取常规标记点，并捕捉气泡较暗的亮点并去除伪亮点，该方法获得的内部标记符克服了经其中一种算法获取到的内部标识点的不足，相互补充，防止遗漏，使内部标识点比较准确、真实，使得分水岭图像分割更为准确，更适用于各种选煤厂的煤泥浮选泡沫图像的分水岭图像分割中内部标记符的提取。

Figure 201910667822

A method for extracting internal markers in coal slime flotation foam image segmentation is based on the characteristics of large noise, low contrast, and difficult bubble segmentation in coal slime flotation foam images. The fuzzy C-means clustering algorithm based on the fuzzy C-means clustering algorithm is combined with the two algorithms, and the internal markers obtained by the two algorithms are superimposed as the internal markers of image segmentation, which are used to extract regular marker points, capture the bright spots with darker bubbles and remove false ones. The bright spot is that the internal markers obtained by this method overcome the shortcomings of the internal identification points obtained by one of the algorithms, complement each other, prevent omission, make the internal identification points more accurate and true, and make the watershed image segmentation more accurate and applicable. Extraction of internal markers in watershed image segmentation of slime flotation foam images in various coal preparation plants.

Figure 201910667822

Description

用于煤泥浮选泡沫图像分割中内部标记符的提取方法Extraction method of internal markers for coal slime flotation foam image segmentation

技术领域technical field

本发明涉及一种煤泥浮选泡沫图像分割的内部标记，具体是一种煤泥浮选泡沫图像形态学分水岭分割中内部标记符的提取方法，属于数字图像处理及煤泥浮选领域。The invention relates to an internal marker for coal slime flotation foam image segmentation, in particular to a method for extracting internal markers in coal slime flotation foam image morphological watershed segmentation, belonging to the field of digital image processing and coal slime flotation.

背景技术Background technique

煤泥浮选泡沫图像是在实际的浮选生产过程中使用工业CCD相机及配套装置实时采集而获得的图像，不同于有色金属及矿物浮选泡沫，煤泥浮选泡沫图像存在其自身的特殊性，其颜色、亮度信息不明显，同时浮选现场的粉尘较多，条件恶劣，因此所获取的浮选泡沫图像的对比度较差，气泡间互相粘连、边缘模糊，这样很难将气泡其从背景中分离，使得气泡边缘难以提取，因此要在煤泥浮选泡沫图像分割中提取有效的图像内部标记符与外部分割线，对梯度图像进行标定，在此基础上对标定后的图像进行分割。The coal slime flotation foam image is an image acquired in real time using industrial CCD cameras and supporting devices in the actual flotation production process. Different from the non-ferrous metal and mineral flotation foam, the coal slime flotation foam image has its own special features. The color and brightness information is not obvious. At the same time, there is a lot of dust in the flotation site and the conditions are bad, so the contrast of the obtained flotation foam image is poor, the bubbles are sticking to each other and the edges are blurred, so it is difficult to separate the bubbles from the bubbles. Separation from the background makes it difficult to extract the bubble edge. Therefore, it is necessary to extract effective image internal markers and external segmentation lines in the coal slime flotation foam image segmentation, and calibrate the gradient image. On this basis, the calibrated image is segmented. .

由于分水岭图像分割的外部分割线是对通过内部标记符进行变换后的标记图像，提取其分水岭脊线后得到的，因此内部标记符是外部分割线的基础；其次内部标记符与外部分割线又是梯度图像进行形态学极小值标定的依据，由二者共同决定着最后分水岭分割的准确性，因此内部标记符提取是分水岭图像分割的关键所在，若内部标识符提取不足，则可能丢失掉应有的标记点，使得分割区域减少，导致分水岭分割的欠分割；相反若提取过多，会增加许多不必要的伪标记点，使标记点过多，从而导致分水岭分割中的过分割，只有提取到正确的内部标记符，才能对图像进行准确分割，从而获取浮选泡沫图像气泡尺寸特征，获得对于浮选工况把握，实现对产品灰分做出准确预测。Since the outer segmentation line of watershed image segmentation is obtained by extracting the watershed ridge line of the marked image transformed by the inner marker, the inner marker is the basis of the outer segmentation line; secondly, the inner marker and the outer segmentation line are also It is the basis for the morphological minimum calibration of the gradient image. The two together determine the accuracy of the final watershed segmentation. Therefore, the extraction of internal markers is the key to the segmentation of watershed images. If the internal identifier extraction is insufficient, it may be lost. There should be marked points, so that the segmentation area is reduced, resulting in under-segmentation of watershed segmentation; on the contrary, if there are too many extractions, many unnecessary pseudo-marked points will be added, resulting in too many marked points, resulting in over-segmentation in watershed segmentation, only Only by extracting the correct internal markers can the image be accurately segmented, so as to obtain the bubble size characteristics of the flotation foam image, obtain a grasp of the flotation working conditions, and achieve accurate prediction of the ash content of the product.

发明内容SUMMARY OF THE INVENTION

本发明所要解决的技术问题是：如何在对浮选泡沫图像进行分水岭图像分割时，更好地提取到浮选泡沫图像分割时使用的内部标记符，并提供一种用于煤泥浮选泡沫图像分割中内部标记符的提取方法。The technical problem to be solved by the present invention is: how to better extract the internal markers used in the segmentation of the flotation froth image when performing the watershed image segmentation on the flotation froth image, and provide a method for flotation froth for coal slime Extraction methods for internal markers in image segmentation.

为实现上述目的，本发明所采用的技术方案是：用于煤泥浮选泡沫图像分割中内部标记符的提取方法，对从选煤厂浮选现场获取的煤泥浮选泡沫图像，在煤泥浮选泡沫图像分割中提出了一种基于粒子群优化算法与一维直方图加权的模糊C均值聚类算法融合的内部标记符提取的优化算法。In order to achieve the above object, the technical solution adopted in the present invention is: an extraction method for internal markers in the segmentation of coal slime flotation foam images, for the coal slime flotation foam images obtained from the coal preparation plant flotation site, An optimization algorithm for internal marker extraction based on the fusion of particle swarm optimization algorithm and one-dimensional histogram-weighted fuzzy C-means clustering algorithm is proposed in the segmentation of mud flotation foam images.

内部标记符包括是由粒子群优化算法获取的标识点与一维直方图加权的模糊C均值聚类算法所获取的标识点，将两种标识点进行形态学处理后并叠加作为最终的图像分割的内部标记符。运用粒子群优化算法，将二维阈值作为粒子群算法中的粒子的位置，以二维最大熵的局部熵作为粒子群算法的适应度函数，根据粒子群粒子的速度和位置公式，对粒子的速度与位置不断进行调整，找到截至这一代每个粒子经过的最好位置

Figure 718657DEST_PATH_IMAGE001
与当前的全局最好位置
Figure 508759DEST_PATH_IMAGE002
，经过若干代的迭代运算，使粒子的位置不断更新，当达到设定的终止条件时，最终寻找出使二维局部熵获得最大的二维阈值，使其作为二维阈值向量，对图像进行双阈值二值化分割，提取二值图像最大值区域，通过形态学的腐蚀运算，将其结果作为标识点。The internal markers include the identification points obtained by the particle swarm optimization algorithm and the identification points obtained by the one-dimensional histogram-weighted fuzzy C-means clustering algorithm. The two identification points are morphologically processed and superimposed as the final image segmentation. internal marker of . Using the particle swarm optimization algorithm, the two-dimensional threshold is used as the position of the particle in the particle swarm algorithm, and the local entropy of the two-dimensional maximum entropy is used as the fitness function of the particle swarm algorithm. Speed and position are constantly adjusted to find the best position each particle has passed by up to this generation
Figure 718657DEST_PATH_IMAGE001
with the current global best position
Figure 508759DEST_PATH_IMAGE002
, after several generations of iterative operations, the position of the particle is continuously updated. When the set termination condition is reached, the two-dimensional threshold value that maximizes the two-dimensional local entropy is finally found, which is used as a two-dimensional threshold vector. Double-threshold binarization segmentation, extracts the maximum value area of the binary image, and uses the result as the identification point through the morphological erosion operation.

采用一维直方图加权模糊C均值聚类算法对浮选泡沫图像进行聚类，样本

Figure 325405DEST_PATH_IMAGE003
，
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为灰阶，这里
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，共256个样本，取初始的聚类中心为
Figure 77963DEST_PATH_IMAGE006
其中
Figure 319589DEST_PATH_IMAGE007
为图像的灰度值，
Figure 391450DEST_PATH_IMAGE008
为图像灰度的最小值，为图像灰度的中值，
Figure 104508DEST_PATH_IMAGE010
为图像灰度的最大值，
Figure 895747DEST_PATH_IMAGE011
，
Figure 974561DEST_PATH_IMAGE012
取一个0-1的随机数，计算隶属度矩阵与聚类中心
Figure 509765DEST_PATH_IMAGE014
，同时根据聚类目标函数式计算目标函数
Figure 725982DEST_PATH_IMAGE015
，经过不断迭代更新，当满足
Figure 948102DEST_PATH_IMAGE016
，迭代终止，输出模糊划分矩阵
Figure 35007DEST_PATH_IMAGE017
和聚类中心，对煤泥浮选泡沫灰度图像通过一维直方图加权的模糊C均值聚类算法对图像进行聚类运算，对聚类后的图像采用局部极大值的方法对聚类后图像提取局部极大值区域，并经过形态学的腐蚀运算，提取标识点；将两种标识点进行叠加运算，作为最终的分水岭图像分割的内部标记符。One-dimensional histogram weighted fuzzy C-means clustering algorithm is used to cluster the flotation foam images.
Figure 325405DEST_PATH_IMAGE003
,
Figure 327996DEST_PATH_IMAGE004
for grayscale, here
Figure 585802DEST_PATH_IMAGE005
, a total of 256 samples, take the initial cluster center as
Figure 77963DEST_PATH_IMAGE006
in
Figure 319589DEST_PATH_IMAGE007
is the gray value of the image,
Figure 391450DEST_PATH_IMAGE008
is the minimum value of the image gray level, is the median value of the image gray level,
Figure 104508DEST_PATH_IMAGE010
is the maximum value of the image gray level,
Figure 895747DEST_PATH_IMAGE011
,
Figure 974561DEST_PATH_IMAGE012
Take a random number from 0-1 to calculate the membership matrix with cluster centers
Figure 509765DEST_PATH_IMAGE014
, and calculate the objective function according to the clustering objective function formula
Figure 725982DEST_PATH_IMAGE015
, after continuous iterative update, when the
Figure 948102DEST_PATH_IMAGE016
, iterative termination, output fuzzy partition matrix
Figure 35007DEST_PATH_IMAGE017
and cluster centers , the coal slime flotation foam grayscale image is clustered by the one-dimensional histogram weighted fuzzy C-means clustering algorithm, and the local maximum value method is used for the clustered image to extract the local value of the clustered image. The maximum value area is extracted, and the identification points are extracted through morphological erosion operation; the two identification points are superimposed and used as the internal markers of the final watershed image segmentation.

本发明在采用了上述方案后，其最大优点在于而粒子群算法对于阈值优化的过程中只需通过内部速度进行更新，没有繁杂的交叉与变异环节，使得在二维阈值选取的过程更加简单、高效，融合一维直方图加权模糊C均值聚类算法对浮选图像进行聚类，使气泡上一些较暗的亮点完全从气泡本身中凸显出来，而一些由于发射作用而出现的伪亮点经聚类后去除，通过粒子群算法与一维直方图加权模糊C均值聚类算法两种算法所获得的内部标记符互为补充，防止遗漏，使得分水岭图像分割更为准确、合理，从而使得最后整个分水岭分割的结果更加准确，能产生较好的图像分割效果，同时摒弃了基于扩展最大变换算法中通过控制最大值最小值深度参数H进行调节获得的内部标记点的通用算法，克服了由于H选定的盲目性所造成内部标记符失真，而导致图像分割中产生的过度分割或欠分割。After adopting the above scheme, the biggest advantage of the present invention is that the particle swarm algorithm only needs to update the internal speed in the process of threshold optimization, and there is no complicated crossover and mutation link, which makes the process of selecting the two-dimensional threshold simpler and more efficient. Efficiently, the flotation images are clustered with a one-dimensional histogram-weighted fuzzy C-means clustering algorithm, so that some darker bright spots on the bubbles are completely highlighted from the bubbles themselves, while some false bright spots appearing due to emission are clustered. Post-class removal, the internal markers obtained by the particle swarm algorithm and the one-dimensional histogram weighted fuzzy C-means clustering algorithm complement each other to prevent omission, making the watershed image segmentation more accurate and reasonable, so that the final whole The result of watershed segmentation is more accurate, and it can produce better image segmentation effect. At the same time, the general algorithm based on the internal marker points obtained by adjusting the maximum and minimum depth parameters H in the extended maximum transformation algorithm is abandoned, which overcomes the limitation of H selection. The internal markers are distorted due to certain blindness, which leads to over-segmentation or under-segmentation in image segmentation.

附图说明Description of drawings

图1为煤泥浮选泡沫图像二维直方图。Figure 1 is a two-dimensional histogram of the coal slime flotation foam image.

具体实施方式Detailed ways

下面对本发明的具体实施方式作出进一步的详细说明。The specific embodiments of the present invention will be further described in detail below.

如附图1所述，实施本发明上述所提供的一种用于煤泥浮选泡沫图像分割中内部标记符的提取方法，运用粒子群优化算法，以二维最大熵的局部熵作为适应度函数，获得图像二值化分割的二维阈值，从而提取图像经双阈值二值化后图像的最大值区域，获取标识点。As shown in FIG. 1, a method for extracting internal markers in coal slime flotation froth image segmentation provided by the present invention is implemented, particle swarm optimization algorithm is used, and the local entropy of two-dimensional maximum entropy is used as fitness function to obtain the two-dimensional threshold of image binarization segmentation, so as to extract the maximum value area of the image after the image is binarized by double thresholds, and obtain the identification point.

1、随机形成

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个粒子，选取 ；其位置分别为，粒子的位置
Figure 546760DEST_PATH_IMAGE022
，维数为
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，由于是对图像二值化阈值的优化，即寻找使二维局部熵获得最大的二维阈值
Figure 227457DEST_PATH_IMAGE024
；此时粒子的位置即为二维阈值，因此选取
Figure 85692DEST_PATH_IMAGE025
；区间为
Figure 370042DEST_PATH_IMAGE026
，其中为灰度图像的灰阶，
Figure 76147DEST_PATH_IMAGE028
；粒子的速度，相应地粒子速度矢量为，维数也为，即，区间为，这里取最大速度，即速度范围为
Figure 788888DEST_PATH_IMAGE029
。1. Randomly formed
Figure 477807DEST_PATH_IMAGE019
particles, choose ; its locations are , the position of the particle
Figure 546760DEST_PATH_IMAGE022
, the dimension is
Figure 471991DEST_PATH_IMAGE023
, because it is the optimization of the image binarization threshold, that is, to find the two-dimensional threshold that maximizes the two-dimensional local entropy
Figure 227457DEST_PATH_IMAGE024
; At this time, the position of the particle is the two-dimensional threshold, so select
Figure 85692DEST_PATH_IMAGE025
; the interval is
Figure 370042DEST_PATH_IMAGE026
,in is the grayscale of the grayscale image,
Figure 76147DEST_PATH_IMAGE028
; The speed of the particle, correspondingly the particle speed vector is , and the dimension is also , that is, the interval is
Figure 788888DEST_PATH_IMAGE029
.

2、选取一幅通过工业CCD 相机在煤泥浮选生产现场所获取的泡沫图像，其像素尺寸为256×256，对于每个粒子，其位置的二维取值分别代入对应二维阈值中的与，应用粒子群算法，对于每个粒子的适应度的值进行计算，即2. Select a foam image obtained by an industrial CCD camera at the coal slime flotation production site, and its pixel size is 256 × 256. For each particle, the two-dimensional value of its position is substituted into the corresponding two-dimensional threshold. And, apply the particle swarm algorithm to calculate the fitness value of each particle, that is

(1) (1)

其中表示抗体群中的第个粒子的适应度，为二维局部熵where represents the fitness of the first particle in the antibody population, and is the two-dimensional local entropy

其中

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，in
Figure 675122DEST_PATH_IMAGE031
,

，

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,
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， ,

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，
Figure 988292DEST_PATH_IMAGE036
Figure 618490DEST_PATH_IMAGE035
,
Figure 988292DEST_PATH_IMAGE036

为联合频度：

Figure 675625DEST_PATH_IMAGE037
is the joint frequency:
Figure 675625DEST_PATH_IMAGE037

附图1为二维直方图示意图，横坐标 为像素点处的灰度值，纵坐标

Figure 520587DEST_PATH_IMAGE040
为像素点
Figure 531268DEST_PATH_IMAGE041
右邻域点处的灰度值，向量
Figure 30383DEST_PATH_IMAGE042
为图像分割的二维阈值，通过这两个阈值，二维直方图矩阵被分割成四个区，分别设为A，B，C 和D四个区域。Accompanying drawing 1 is two-dimensional histogram schematic diagram, abscissa for pixels gray value at , ordinate
Figure 520587DEST_PATH_IMAGE040
for pixels
Figure 531268DEST_PATH_IMAGE041
gray value at right neighbor point, vector
Figure 30383DEST_PATH_IMAGE042
It is the two-dimensional threshold for image segmentation. Through these two thresholds, the two-dimensional histogram matrix is divided into four regions, which are set as four regions A, B, C and D respectively.

Figure 126515DEST_PATH_IMAGE043
表示同时满足当前点灰度为
Figure 369277DEST_PATH_IMAGE044
，其右邻域点的灰度为
Figure 500044DEST_PATH_IMAGE045
的所有满足条件的总的灰度对，，为图像的行数，
Figure 3204DEST_PATH_IMAGE048
图像的列数，由于浮选泡沫图像的像素尺寸为256×256，这里
Figure 519636DEST_PATH_IMAGE049
。
Figure 126515DEST_PATH_IMAGE043
Indicates that the current point grayscale is satisfied at the same time
Figure 369277DEST_PATH_IMAGE044
, the grayscale of its right neighbor point is
Figure 500044DEST_PATH_IMAGE045
The total grayscale pairs of all satisfying conditions, , is the number of lines in the image,
Figure 3204DEST_PATH_IMAGE048
The number of columns of the image, since the pixel size of the flotation foam image is 256×256, here
Figure 519636DEST_PATH_IMAGE049
.

3、对每个微粒，根据其适应度值，确定每个粒子的最好位置

Figure 829394DEST_PATH_IMAGE050
和当前的全局最好位置
Figure 634539DEST_PATH_IMAGE051
；每个粒子的初始值为粒子的初始位置值，
Figure 58885DEST_PATH_IMAGE051
初始值为所有粒子
Figure 70703DEST_PATH_IMAGE053
的最大值。3. For each particle, determine the best position of each particle according to its fitness value
Figure 829394DEST_PATH_IMAGE050
and the current global best position
Figure 634539DEST_PATH_IMAGE051
; each particle The initial value of is the initial position value of the particle,
Figure 58885DEST_PATH_IMAGE051
The initial value is all particles
Figure 70703DEST_PATH_IMAGE053
the maximum value of .

4、根据(2)、(3)式调整微粒速度和位置；4. Adjust the particle speed and position according to formulas (2) and (3);

Figure 628723DEST_PATH_IMAGE054
(2)
Figure 628723DEST_PATH_IMAGE054
(2)

(3) (3)

其中，

Figure 711266DEST_PATH_IMAGE056
，
Figure 893985DEST_PATH_IMAGE057
是该群体中粒子的总数，
Figure 673723DEST_PATH_IMAGE058
是粒子的速度；
Figure 68932DEST_PATH_IMAGE059
是每个粒子当前自己的最好位置；是群体中所有粒子所经历最好位置； 是0到1之间的随机数，
Figure 707221DEST_PATH_IMAGE062
称为惯性因子，运用线性递减权值策略，即in,
Figure 711266DEST_PATH_IMAGE056
,
Figure 893985DEST_PATH_IMAGE057
is the total number of particles in the population,
Figure 673723DEST_PATH_IMAGE058
is the velocity of the particle;
Figure 68932DEST_PATH_IMAGE059
is the current best position of each particle; is the best position experienced by all particles in the group; is a random number between 0 and 1,
Figure 707221DEST_PATH_IMAGE062
is called the inertia factor, and a linear decreasing weight strategy is used, that is,

Figure 234017DEST_PATH_IMAGE063
(4)
Figure 234017DEST_PATH_IMAGE063
(4)

其中

Figure 902896DEST_PATH_IMAGE064
和
Figure 427418DEST_PATH_IMAGE065
是
Figure 181747DEST_PATH_IMAGE066
的最大最小值，取
Figure 184338DEST_PATH_IMAGE067
，
Figure 238882DEST_PATH_IMAGE068
；
Figure 403147DEST_PATH_IMAGE069
和
Figure 175931DEST_PATH_IMAGE070
分别是当前迭代次数和最大迭代次数，其中
Figure 716634DEST_PATH_IMAGE071
，取，
Figure 429692DEST_PATH_IMAGE073
是第
Figure 893034DEST_PATH_IMAGE074
个粒子的当前位置，
Figure 237428DEST_PATH_IMAGE075
和
Figure 797722DEST_PATH_IMAGE076
是学习因子，选取
Figure 569369DEST_PATH_IMAGE077
。in
Figure 902896DEST_PATH_IMAGE064
and
Figure 427418DEST_PATH_IMAGE065
Yes
Figure 181747DEST_PATH_IMAGE066
The maximum and minimum value of , take
Figure 184338DEST_PATH_IMAGE067
,
Figure 238882DEST_PATH_IMAGE068
;
Figure 403147DEST_PATH_IMAGE069
and
Figure 175931DEST_PATH_IMAGE070
are the current number of iterations and the maximum number of iterations, respectively, where
Figure 716634DEST_PATH_IMAGE071
,Pick ,
Figure 429692DEST_PATH_IMAGE073
is the first
Figure 893034DEST_PATH_IMAGE074
the current position of each particle,
Figure 237428DEST_PATH_IMAGE075
and
Figure 797722DEST_PATH_IMAGE076
is the learning factor, choose
Figure 569369DEST_PATH_IMAGE077
.

5、重新计算每个微粒的新的适应度，并对其进行更新。5. Recalculate the new fitness of each particle and update it.

6、对每个微粒，与其经过的最好位置的适应度作比较，若其适应度优于

Figure 933671DEST_PATH_IMAGE079
，则将其作为当前的最好位置
Figure 286155DEST_PATH_IMAGE080
；求取最好的
Figure 963124DEST_PATH_IMAGE081
，即为最新的
Figure 401059DEST_PATH_IMAGE082
，使其更新全局最好位置。6. For each particle, the best position it passes through The fitness of , if its fitness is better than
Figure 933671DEST_PATH_IMAGE079
, take it as the current best position
Figure 286155DEST_PATH_IMAGE080
; seek the best
Figure 963124DEST_PATH_IMAGE081
, which is the latest
Figure 401059DEST_PATH_IMAGE082
, so that it updates the global best position .

7、令

Figure 622142DEST_PATH_IMAGE084
，检查是否达到结束条件，结束条件为达到
Figure 395243DEST_PATH_IMAGE086
或群体的连续两代的
Figure 619551DEST_PATH_IMAGE087
的差小于等于
Figure 274523DEST_PATH_IMAGE088
；未达到结束条件，则转4；若满足结束条件，即为最优解， 其中为最大的迭代数，选取
Figure 236980DEST_PATH_IMAGE090
，
Figure DEST_PATH_IMAGE091
。7. Order
Figure 622142DEST_PATH_IMAGE084
, check whether the end condition is reached, the end condition is achieve
Figure 395243DEST_PATH_IMAGE086
or two consecutive generations of the group
Figure 619551DEST_PATH_IMAGE087
difference is less than or equal to
Figure 274523DEST_PATH_IMAGE088
; If the end condition is not met, go to 4; if the end condition is met, is the optimal solution, where For the maximum number of iterations, choose
Figure 236980DEST_PATH_IMAGE090
,
Figure DEST_PATH_IMAGE091
.

8、获取的

Figure 264979DEST_PATH_IMAGE092
为二维阈值向量
Figure DEST_PATH_IMAGE093
，对图像进行双阈值二值化分割，提取二值图像最大值区域，通过形态学的腐蚀运算，将其结果作为标识点。8. Obtained
Figure 264979DEST_PATH_IMAGE092
is a two-dimensional threshold vector
Figure DEST_PATH_IMAGE093
, perform double-threshold binarization segmentation on the image, extract the maximum value area of the binary image, and use the result as the identification point through the morphological erosion operation.

采用一维直方图加权模糊C均值聚类算法对浮选泡沫图像进行聚类，提取聚类图像的极大值区域，获取标识点。The one-dimensional histogram weighted fuzzy C-means clustering algorithm is used to cluster the flotation foam images, and the maximum value area of the clustered image is extracted to obtain the identification points.

9、确定一维直方图加权的模糊C均值聚类算法聚类的种类数

Figure 977720DEST_PATH_IMAGE094
，由于泡沫图像按灰度大体分为三类，即气泡顶点、气泡表面、背景的灰度，因此取聚类种类
Figure DEST_PATH_IMAGE095
。9. Determine the number of types of clusters by the one-dimensional histogram-weighted fuzzy C-means clustering algorithm
Figure 977720DEST_PATH_IMAGE094
, because the foam image is roughly divided into three categories according to the grayscale, namely the grayscale of the bubble vertex, the bubble surface, and the background, so the clustering type is selected.
Figure DEST_PATH_IMAGE095
.

10、确定聚类中心的初始值

Figure 964130DEST_PATH_IMAGE096
，聚类中心，
Figure 598374DEST_PATH_IMAGE098
为聚类个数。取
Figure DEST_PATH_IMAGE099
，初始的聚类中心为
Figure 695643DEST_PATH_IMAGE100
，其中
Figure 997311DEST_PATH_IMAGE007
为图像的灰度值，
Figure DEST_PATH_IMAGE101
为图像灰度的最小值，
Figure 154623DEST_PATH_IMAGE102
为图像灰度的中值，
Figure DEST_PATH_IMAGE103
为图像灰度的最大值，
Figure 807321DEST_PATH_IMAGE104
，
Figure DEST_PATH_IMAGE105
取一个0-1的随机数。10. Determine the initial value of the cluster center
Figure 964130DEST_PATH_IMAGE096
, the cluster center ,
Figure 598374DEST_PATH_IMAGE098
is the number of clusters. Pick
Figure DEST_PATH_IMAGE099
, the initial cluster center is
Figure 695643DEST_PATH_IMAGE100
,in
Figure 997311DEST_PATH_IMAGE007
is the gray value of the image,
Figure DEST_PATH_IMAGE101
is the minimum value of the image gray level,
Figure 154623DEST_PATH_IMAGE102
is the median value of the image gray level,
Figure DEST_PATH_IMAGE103
is the maximum value of the image gray level,
Figure 807321DEST_PATH_IMAGE104
,
Figure DEST_PATH_IMAGE105
Take a random number from 0-1.

11、根据式（5）计算隶属度矩阵

Figure 708281DEST_PATH_IMAGE106
；11. Calculate the membership matrix according to formula (5)
Figure 708281DEST_PATH_IMAGE106
;

Figure 864456DEST_PATH_IMAGE107
（5）
Figure 864456DEST_PATH_IMAGE107
(5)

为待聚类分析的全体样本，其中每个对象为

Figure 661511DEST_PATH_IMAGE108
，
Figure 801505DEST_PATH_IMAGE109
为自然数。对于浮选泡沫图像为8bits的灰度图像，则样本取
Figure 709418DEST_PATH_IMAGE110
为灰阶，这里
Figure 219214DEST_PATH_IMAGE112
，共256个样本；聚类中心，
Figure 26950DEST_PATH_IMAGE098
为聚类个数，取
Figure 423296DEST_PATH_IMAGE114
；取
Figure 562154DEST_PATH_IMAGE115
；
Figure 676740DEST_PATH_IMAGE116
指第j个样本隶属于第i个聚类的隶属度，并满足
Figure 192035DEST_PATH_IMAGE117
，
Figure 911730DEST_PATH_IMAGE118
为第i个聚类中心与第j个样本
Figure 752647DEST_PATH_IMAGE119
间的欧氏距离。is the whole sample to be clustered, and each object is
Figure 661511DEST_PATH_IMAGE108
,
Figure 801505DEST_PATH_IMAGE109
is a natural number. For the grayscale image of flotation foam image with 8bits, the sample is taken as
Figure 709418DEST_PATH_IMAGE110
for grayscale, here
Figure 219214DEST_PATH_IMAGE112
, a total of 256 samples; cluster centers ,
Figure 26950DEST_PATH_IMAGE098
is the number of clusters, take
Figure 423296DEST_PATH_IMAGE114
;Pick
Figure 562154DEST_PATH_IMAGE115
;
Figure 676740DEST_PATH_IMAGE116
Refers to the membership degree that the jth sample belongs to the ith cluster, and satisfies the
Figure 192035DEST_PATH_IMAGE117
,
Figure 911730DEST_PATH_IMAGE118
is the i -th cluster center and the j -th sample
Figure 752647DEST_PATH_IMAGE119
Euclidean distance between.

12、根据聚类目标函数式(6)计算目标函数；12. Calculate the objective function according to the clustering objective function formula (6) ;

Figure 876777DEST_PATH_IMAGE121
(6)
Figure 876777DEST_PATH_IMAGE121
(6)

其中为各个灰度级出现的频度；设图像的尺寸为

Figure 728376DEST_PATH_IMAGE123
，in is the frequency of occurrence of each gray level; let the size of the image be
Figure 728376DEST_PATH_IMAGE123
,

Figure 286396DEST_PATH_IMAGE124
(7)
Figure 286396DEST_PATH_IMAGE124
(7)

式中表示灰度为的像素在图像中出现的次数，

Figure 20500DEST_PATH_IMAGE127
为灰阶，
Figure 331395DEST_PATH_IMAGE128
；
Figure 726605DEST_PATH_IMAGE129
表示图像的尺寸，由于浮选泡沫图像的像素尺寸为256×256，这里
Figure 72135DEST_PATH_IMAGE130
，且满足
Figure 894598DEST_PATH_IMAGE131
。in the formula Indicates grayscale as the number of times the pixel appears in the image,
Figure 20500DEST_PATH_IMAGE127
is grayscale,
Figure 331395DEST_PATH_IMAGE128
;
Figure 726605DEST_PATH_IMAGE129
represents the size of the image, since the pixel size of the flotation foam image is 256×256, here
Figure 72135DEST_PATH_IMAGE130
, and satisfy
Figure 894598DEST_PATH_IMAGE131
.

13、用(8)式更新聚类中心

Figure 161631DEST_PATH_IMAGE132
；13. Use the formula (8) to update the cluster center
Figure 161631DEST_PATH_IMAGE132
;

Figure 891690DEST_PATH_IMAGE133
(8)
Figure 891690DEST_PATH_IMAGE133
(8)

14、若，迭代停止，取；输出模糊划分矩阵

Figure 42682DEST_PATH_IMAGE136
和聚类中心
Figure 779694DEST_PATH_IMAGE137
；否则令
Figure 834238DEST_PATH_IMAGE138
，返回11。14. If , the iteration stops, take ; output fuzzy partition matrix
Figure 42682DEST_PATH_IMAGE136
and cluster centers
Figure 779694DEST_PATH_IMAGE137
; otherwise let
Figure 834238DEST_PATH_IMAGE138
, which returns 11.

15、对煤泥浮选泡沫灰度图像通过一维直方图加权的模糊C均值聚类算法对图像进行聚类运算。15. Perform a clustering operation on the coal slime flotation foam grayscale image through a one-dimensional histogram weighted fuzzy C-means clustering algorithm.

16、采用局部极大值的方法对聚类后图像提取局部极大值区域，并经过形态学的腐蚀运算，提取标识点。16. The method of local maxima is used to extract the local maxima region from the clustered image, and the identification points are extracted through the morphological erosion operation.

17、将8与16提取的标识点进行叠加运算，作为最终的分水岭运算的内部标记符。17. Perform a superposition operation on the identification points extracted by 8 and 16, as the final internal marker of the watershed operation.

Claims (3)

1.一种用于煤泥浮选泡沫图像分割中内部标记符的提取方法，其特征在于：所述提取算法是将粒子群优化算法与一维直方图加权的模糊C均值聚类算法两种算法进行融合，将两种算法获取的内部标记符进行叠加，作为图像分割的内部标记符，用于提取常规标记点，并捕捉气泡较暗的亮点并去除伪亮点。1. an extraction method for internal markers in coal slime flotation foam image segmentation, it is characterized in that: described extraction algorithm is two kinds of fuzzy C-means clustering algorithm weighted by particle swarm optimization algorithm and one-dimensional histogram The algorithm is fused, and the internal markers obtained by the two algorithms are superimposed as the internal markers of image segmentation, which are used to extract regular markers, capture the bright spots with darker bubbles, and remove false bright spots. 2.如权利要求1所述的用于煤泥浮选泡沫图像分割中内部标记符的提取方法，其特征在于：所述粒子群优化算法是将二维阈值作为粒子群算法中的粒子的位置，将二维最大熵的局部熵作为粒子群算法的适应度函数，经算法的迭代更新，获取使二维局部熵获得最大的二维阈值，将其作为二维阈值向量，对图像进行双阈值二值化分割，提取二值图像最大值区域，通过形态学的腐蚀运算，将其结果作为内部标识点。2 . The method for extracting internal markers in coal slime flotation froth image segmentation according to claim 1 , wherein the particle swarm optimization algorithm uses a two-dimensional threshold as the position of particles in the particle swarm optimization algorithm. 3 . , take the local entropy of the two-dimensional maximum entropy as the fitness function of the particle swarm algorithm, and through the iterative update of the algorithm, obtain the two-dimensional threshold that maximizes the two-dimensional local entropy, and use it as a two-dimensional threshold vector to double-threshold the image. Binarization segmentation, extracts the maximum value area of the binary image, and uses the result as the internal identification point through the morphological erosion operation. 3.如权利要求1所述的用于煤泥浮选泡沫图像分割中内部标记符的提取方法，其特征在于：所述煤泥浮选泡沫图像的灰度是通过一维直方图加权的模糊C均值聚类算法对图像进行聚类运算，对聚类后的图像采用局部极大值的方法对煤泥浮选图像进行聚类，并对聚类图像提取局部极大值区域，并经过形态学的腐蚀运算，提取标识点。3. The method for extracting internal markers in coal slime flotation froth image segmentation according to claim 1, wherein the grayscale of the coal slime flotation froth image is a fuzzy weighted by one-dimensional histogram The C-means clustering algorithm performs clustering operations on the images, uses the local maxima method for the clustered images to cluster the coal slime flotation images, and extracts the local maxima regions from the clustered images. Learn the corrosion operation to extract the identification points.
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