Skip to content

Advertisement

  • Research
  • Open Access

Image segmentation method based on K-mean algorithm

EURASIP Journal on Image and Video Processing20182018:81

https://doi.org/10.1186/s13640-018-0322-6

  • Received: 12 June 2018
  • Accepted: 15 August 2018
  • Published:

Abstract

The image is an important way for people to understand the world. How to make the computer have image recognition function is the goal of image recognition research. In image recognition, image segmentation technology is one of the important research directions. This paper uses gray-gradient maximum entropy method to extract features from the image, uses K-mean method to classify the images, and uses average precision (AP) and intersection over union (IU) evaluation methods to evaluate the results. The results show that the method of K-mean can achieve image segmentation very well.

Keywords

  • Image segmentation
  • K-mean
  • Clustering
  • Gray-level co-occurrence matrix (GLCM)
  • Maximum entropy

1 Introduction

With the development of human society and the advancement of science and technology, people have to process a large amount of information data from measurement or observation every day for further management and use. At any time, images play an important role in the process of human receiving, processing, and transmitting information. This is because image information is visual, intuitive, easy to understand, and informative, so it is the most exposed in our daily production and life. One of the types of information is also the most important and effective way for people to access and communicate information. However, in the large amount of image information that humans obtain through vision, not all information content is required by us, which requires processing the obtained image to meet people’s needs in various situations. People have found that useful information exists in certain areas of the image, so we need to separate these specific areas from other areas by a certain technique to divide the input image into several meaningful target areas. Technology is image segmentation.

Image segmentation, feature extraction, and target recognition constitute three major tasks in the field of computer vision from low to high. Therefore, image segmentation is a basic computer vision technology, which is the main problem in low-level vision in the field of computer vision. It is a key step before analyzing and understanding the processed image data. The main goal of image segmentation is to divide the image into components that have strong correlations with the real-world objects or regions contained therein. In image analysis, the target objects in the image are often the content we are interested in, and the regions occupied by these target objects in the image are often different. It is necessary to detect, extract features, and extract different target objects in the image. Classification recognition, the separation of meaningful objects in the image from the background, and the separation of these objects into different meanings must be done. For example, to determine the area of forest arable land in the aerial image, you first need to separate these areas from the image; to identify certain words in the image file, you also need to sort these words; to identify and calibrate the micrographs, the chromosomes also need to use image segmentation techniques. Successful segmentation facilitates subsequent higher levels of image recognition and understanding. In the practical problem of computer vision, the quality of image segmentation will directly affect the feature extraction description, recognition, and classification of subsequent targets. Therefore, image segmentation is one of the most important and key research issues in the field of image processing. With the deepening of image segmentation technology, the application fields of image segmentation are becoming more and more extensive, such as communication, military, remote sensing image analysis, medical diagnosis, and intelligent transportation. In the fields of agricultural modernization and industrial automation, image segmentation is inseparable.

Image segmentation is a cross-discipline research direction, involving artificial intelligence, machine learning, pattern recognition, and other disciplines. Neurophysiology and psychological research results show that in the visual cognitive process, there is a visual clustering and segmentation process [1] in the brain. Exogenous areas of the brain provide an image analysis process that combines low-level feature expression obtained from the visual cortex V1 region with attention selection and object recognition [2]. The experiments of these neural mechanisms confirmed the existence of the segmentation process in the cognitive process, which also provided a theoretical basis for the image segmentation technology.

With the deepening of research, image segmentation technology has made great progress. In 1997, Shi J [3] and others proposed an image segmentation method that aims at extracting global features of images and proposed a new global standard. The normalized cutting criterion measures the dissimilarity between different groups and the similarity between groups. In the static image segmentation, the results show that the segmentation effect can be well achieved. Felzenszwalb P F [4] and others studied the regional problems of image segmentation. In their research results, predicates were used to measure the boundary between two regions and represented by images, and then a predicate-based segmentation method was used. The greedy algorithm performs the segmentation that satisfies the global attribute. The simulation results of the image segmentation show that this method can preserve the details of the low-variation image region and can ignore the details of the hyper-variable region. Cox I J [5] and others published an image segmentation algorithm in their research results. In this algorithm, the segmentation region includes both the external boundary cost and the internal benefit associated with the boundary. The optimal segmentation of the image is achieved by minimizing the ratio between the external border cost and the internal benefit by calculating the effective image segmentation method. Keegan M S [6] and others proposed a multichannel-based image segmentation method, which allows users to combine their own information channels and define multiobjective functions by using the two-phase logic framework to achieve image segmentation. Pham D L [7] and others proposed a fuzzy image segmentation algorithm. For the effect of intensity inhomogeneity, this algorithm deals with the inhomogeneity in image segmentation by modifying the objective function method in K-mean algorithm. So that the iterative algorithm which minimizes the objective function is applied to the fuzzy segmentation algorithm, and it is proven to be effective on multiple sets of image test sets. Image segmentation technology has been applied in many fields and has achieved a lot of achievements in recent years [812].

Due to the complexity of algorithms and the large differences between the segmentation results and the reality, the current image segmentation research results limit the application of image segmentation results. The main reason is that there is a large loss of information between the continuous expression of the image and the discrete expression of the segmentation. This loss is often due to the generation of boundary information during the classification process. As a clustering method, K-mean has been successfully applied to the classification research of many studies. For example, Kang S H [13] and others proposed a data clustering model based on a variational approach. This model is an extension of the classical K-mean method, a regularized K-mean method, by selecting a parameter that automatically gives a reasonable number of clusters. The Walvoort D J J [14] team chose the mean squared shortest distance (MSSD) as an objective function to minimize it using K-mean clustering. The results describe two K-mean methods: one for unequal areas and the other for equal-area-segmentation; the results of simulation experiments on soil samples show that the algorithm gives satisfactory results within reasonable calculations. Friggstad Z [15] described how to solve better worst-case approximation guarantee problem in the results. Friggstad Z and others settle this problem by showing that a simple local search algorithm provides a polynomial time approximation scheme (PTAS) for K-means for a Euclidean space for any fixed point. Due to the advantage of K-mean in clustering, clustering studies in many fields today use K-mean as a classification tool and achieved good results [1620].

This paper uses gray-gradient maximum entropy method to extract features from the image, uses K-mean method to classify the images, and uses AP and IU evaluation methods to evaluate the results. The results show that the K-mean method can be used to achieve good image segmentation. The main contributions of this paper are:
  1. 1)

    A feature extraction method based on gray-gradient maximum entropy method and an image segmentation method using K-mean method is defined

     
  2. 2)

    Contrast the difference between subjective evaluation and objective evaluation

     
  3. 3)

    Study the six scenarios using the same method

     

2 Proposed method

2.1 Gray-level co-occurrence matrix

Gray-level co-occurrence matrix (GLCM) refers to a common method for describing texture by studying the spatial correlation characteristics of grayscale. Because the texture is formed by the repeated occurrence of the gray distribution in the spatial position, there will be a certain gray relationship between two pixels at a certain distance in the image space, that is, the spatial correlation characteristics of the gray in the image. A grayscale histogram is a result of statistics on a single pixel having a certain grayscale on the image, and a GLCM is obtained by statistically obtaining a state in which two pixels having certain distances on the image each have a certain grayscale.

Take any point (x, y) in the image (N × N) and another point (x + a, y + b) that deviates from it and set the gray value of the point pair to (g1, g2). Point (x, y) moves on the whole picture, then a variety of (g1, g2) values are obtained. The series of gray values is k, and the combination of (g1, g2) has a square of K. For the whole picture, count the number of occurrences of each (g1, g2) value and arrange them into a square matrix, and then, the total number of (g1, g2) appears to be normalized to the occurrence probability P (g1, g2), which is called the GLCM. The distance difference values (a, b) can be combined with different values to obtain a joint probability matrix under different conditions. The values of (a, b) are selected according to the characteristics of the periodic distribution of the texture. For finer textures, small difference values, such as (1, 0), (1, 1), and (2, 0) are selected. When a = 1, b = 0, the pixel pair is horizontal, that is 0° scanning. When a = 0, b = 1, the pixel pair is vertical, that is 90° scanning. When a = 1, b = 1, the pixel pair is right diagonal, that is 45° scanning. When a = − 1, b = 1, the pixel pair is left diagonal, that is 135° scanning. In this way, the probability of simultaneous occurrence of two pixel gray-level converts the spatial coordinates of (x, y) to the description of “gray pair” (g1, g2), forming a GLCM.

The method of normalizing the GLCM is as follows:
$$ p\left({g}_1,{g}_2\right)=\frac{p\left({g}_1,{g}_2\right)}{R} $$
(1)
The calculation method of R is:
$$ R=\left\{\begin{array}{c}N\left(N-1\right)\kern2em \theta =0\mathrm{or}\theta =90\\ {}{\left(\mathrm{N}\hbox{-} 1\right)}^2\kern1.5em \theta =45\mathrm{or}\theta =135\end{array}\right. $$
(2)

If the image is composed of blocks of pixels with similar gray values, the diagonal elements of the GLCM will have relatively large values; if the image pixel gray values change locally, then the elements that deviate from the diagonal will have bigger value.

Angular second moment (ASM) energy reflects the uniformity of the gray distribution of the image and the texture thickness. If all values of the co-occurrence matrix are equal, the ASM value is small; conversely, if some of the values are large and the other values are small, the ASM value is large. When the elements in the co-occurrence matrix are concentrated, the ASM value is large at this time. A large ASM value indicates a more uniform and regular texture pattern. The ASM calculation method for image G is as follows:
$$ ASM={\sum}_{i=1}^k{\sum}_{j=1}^k{\left(G\left(i,j\right)\right)}^2 $$
(3)

Entropy is a measure of the amount of information an image has. The texture information also belongs to the information of the image and is a measure of randomness. When all elements in the co-occurrence matrix have the greatest randomness and all values in the spatial co-occurrence matrix are almost equal, the elements of a co-occurrence matrix are distributed, the entropy is large. It indicates the degree of non-uniformity or complexity of the texture in the image.

The entropy E(G) for the image G is calculated as follows:
$$ E(G)=-{\sum}_i^k{\sum}_{j=1}^kG\left(i,j\right)\log G\left(i,j\right) $$
(4)

2.2 Maximum entropy of grayscale gradient

The co-occurrence matrix of image G is an Lf × Lg dimensional matrix. If (Lf − 1) × (Lg − 1) represents a two-dimensional histogram of the size of the image region, as shown in Fig. 1, the origin of the co-occurrence matrix coordinate system is the upper left corner, where the x-axis is the gradient of the image and y is the gray value. The threshold is set to (s, t). Since the gray level and the gradient value are clearly distinguished at the threshold, the gray value of the target is lower and the gray value of the background is higher, so the co-occurrence matrix can be divided into four areas: A, B, C, and D.
Fig. 1
Fig. 1

Four areas of the co-occurrence matrix

The gray value of the image and background does not change much, so the gray value is relatively small. Using A(0 ≤ i ≤ s, 0 ≤ j ≤ t) to represent images, D(s + 1 ≤ i ≤ Lf − 1, 0 ≤ j ≤ t) represents the background. As t becomes larger, the probability of the boundary between the target and the background of the corresponding pixel increases. Therefore, the element kij of the co-occurrence matrix in B(0 ≤ i ≤ s, t + 1 ≤ j ≤ Lg − 1) is the image of gray scale i, and the gradient j belongs to the number of edge transitions. The element kij of the co-occurrence matrix in C(s + 1 ≤ i ≤ Lf − 1, t + 1 ≤ j ≤ Lg − 1) is the gray scale i belongs to the background, and the gradient j belongs to the number of edge transitions. From this, we can get the pixels for the four regions in Fig. 1 as follows:
$$ {\displaystyle \begin{array}{l}{P}_A={\sum}_{i=0}^s{\sum}_{j=0}^t{p}_{ij}\kern2.5em {P}_B={\sum}_{i=0}^s{\sum}_{j=t}^{L_g-1}{p}_{ij}\kern0.5em \\ {}{P}_C={\sum}_{i=s}^{L_f-1}{\sum}_{j=0}^t{p}_{ij}\kern2.5em {P}_D={\sum}_{i=s}^{L_f-1}{\sum}_{j=t}^{L_g-1}{p}_{ij}\kern0.5em \end{array}} $$
(5)
Regularize pij:
$$ {P}_{ij}^A=\frac{P_{ij}}{P_A}={k}_{ij}/\left({\sum}_{i=0}^s{\sum}_{j=0}^t{k}_{ij}\right) $$
(6)
Thus, the conditional entropy formula can be obtained:
$$ {\displaystyle \begin{array}{l}H\left(\mathrm{edge},\mathrm{object}\right)=-\sum \limits_{i=0}^s\sum \limits_{j=t+1}^{L_g-1}{p}_{ij}^B\log {p}_{ij}^B\\ {}H\left(\mathrm{edge},\mathrm{background}\right)=-\sum \limits_{i=s+1}^{L_f-1}\sum \limits_{j=t+1}^{L_g-1}{p}_{ij}^C\log {p}_{ij}^C\end{array}} $$
(7)
Finally, the conditional entropy of the image can be calculated:
$$ H\left(s,t\right)=\left(H\left(\mathrm{edge},\mathrm{object}\right)+H\left(\mathrm{edge},\mathrm{background}\right)\right)/2 $$
(8)

According to the maximum entropy theory, the maximum value of s and t obtained by H is the best threshold.

2.3 K-mean segmentation

The K-mean algorithm is a classical distance-based algorithm. The similarity is evaluated by the distance. That is to say, the longer the two objects are, the smaller the similarity is, and the closer the distance is, the greater the similarity is. So the algorithm eventually gets a compact and independent cluster.

The algorithm process is as follows:
  1. 1)

    K clusters are arbitrarily selected from the overall N categories as cluster centers.

     
  2. 2)

    Calculate the distance to each cluster center for each other category and classify the category as the nearest cluster center.

     
  3. 3)

    Recalculate the cluster centers of each class that have been separated.

     
  4. 4)

    Iterate through steps (2) to (3) until the new center is equal to or less than the specified threshold, and the algorithm ends.

     
Mean clustering algorithm divides objects into K categories Kc = {c1, c2, …, ck}, each ck has a cluster center μk; apply the Euclidean distance formula to calculate the sum of the squares of the distances from the points in the class to the cluster center μk:
$$ \mathrm{Mean}\ \left({c}_k\right)=\sum \limits_{x_i\in {c}_k}{\left|{x}_i-{\mu}_k\right|}^2 $$
(9)

The goal of clustering is to minimize square sum mean (Kc) = \( \sum \limits_{k=1}^K\mathrm{mean}\ \left({c}_k\right) \) of distance. The clustering method in this paper is to replace the original values of the same kind of pixels with their defined values (colors) and take each color component of the RGB as the input parameter to replace the pixels of the same kind of the original image. The resulting categories are displayed on an image without displaying them one by one.

The K-mean algorithm has less space requirements because it only needs to store data points and centers. The required storage capacity is O (n + K), where n is the number of data points and the K-mean algorithm has less time requirements. Basically, it has a linear relationship with the number n of data points, that is, O (IKn), where I is the number of iterations of convergence, I is usually small, and can be bounded, that is, most of the changes usually occur in general. In the first few iterations, the K-mean algorithm is the most widely used algorithm because of its simplicity and high complexity. However, the K-mean algorithm also has many disadvantages.

The K-mean algorithm is only applicable to the case where the cluster mean value is meaningful. The number of clusters K must be specified in advance. However, it is difficult to select the K value in general, which means that it is difficult to determine how many clusters are finally divided. It is suitable for finding non-convex shapes. The results of clustering are greatly influenced by the selection of the initial centroid, which makes the clustering results very unstable.

2.4 Image segmentation evaluation method

The image segmentation evaluation method is divided into subjective evaluation and objective evaluation. As an evaluation system, it should have the following three characteristics:
  1. 1)

    Consistency, the results of automatic segmentation algorithm segmentation and artificially specified real segmentation regions should be matched as closely as possible, and the boundaries should be as close as possible;

     
  2. 2)

    The stability of the parameters, according to the predetermined parameters, the segmentation result should be consistent with the real value as much as possible;

     
  3. 3)

    The stability of the image, corresponding to different images, the segmentation results selected in the same parameters should be consistent.

     

Because the results of subjective evaluation methods are not controllable, this paper chooses quantitative standard methods to evaluate image segmentation algorithms.

2.4.1 AP

This method draws on the accuracy and recall rate in text retrieval, first marking the segmented image, and mapping the relevance of the tag to the text, so that the performance evaluation in the text retrieval can be introduced into the image segmentation performance evaluation. The accuracy rate P refers to the ratio of all pixel markers whose correct pixel markings match the artificial results. The recall rate R refers to the proportion of pixels marked correctly in the mark of the result of artificial marking. Gupta S [21] and others used AP as the evaluation standard parameter for image segmentation in research results.

The AP standard calculation method is:
$$ \mathrm{AP}={\int}_0^1P(r) dr $$
(10)

2.4.2 IU

Long J [22] defines IU in their research results to evaluate segmentation methods.

For the two regions R and R’, their overlap calculations are as follows:
$$ O\;\left(R,{R}^{\hbox{'}}\right)=\frac{\mid R\cap {R}^{\hbox{'}}\mid }{\mid R\cup {R}^{\hbox{'}}\mid } $$
(11)
The IU indicator can be calculated as follows:
$$ \mathrm{IU}\left({S}^{\hbox{'}}\to S\right)=\frac{1}{N}\sum \limits_{R\in S}\mid R\mid \times \underset{R^{\hbox{'}}\in {S}^{\hbox{'}}}{\max }O\left(R,{R}^{\hbox{'}}\right) $$
(12)

3 Experimental results

3.1 Simulation environment

  1. 1)

    Processor: Intel’s fourth-generation Core i7-4710HQ @ 2.50 GHz quad-core

    Speed: 2.50 GHz (100 MHz × 25.0)

    Number of processors: core number: 4/number of threads: 8

     
  2. 2)

    Main board: Chipset: Intel Haswell - Lynx Point

    BIOS: Guangda NL8HP192_T1/date of manufacture: October 16, 2014

    The size of BIOS: 4096 KB

     
  3. 3)

    Memory information: ChannelA-DIMM0 Kingston DDR3L 1600 MHz 4G B

     
  4. 4)

    Operating system: Windows 7 Ultimate 64-bit SP1

     
  5. 5)

    Software environment: MATLAB R2014b 8.4

     

3.2 Image source

The images used in this paper are photographs taken by the author using a millet 5 mobile phone, including buildings, trees on the street, vehicle, roads with people, streets with cars only, and indoor scenes. Each of them has 300 pictures, each with a size of 720 × 960 and a resolution of 96dpi. Each scene is shown in Fig. 2.
Fig. 2
Fig. 2

The scene pictures taken in this paper

3.3 Sample division

Cross validation is a practical method of statistically cutting a sample of data into smaller subsets. The basic idea is to group the data set in a sense, one part as a training set and the other as a validation set or test set. First, train the classifier with the training set, and then use the validation set to test the trained model, and use it as a performance indicator for evaluating the classifier. This paper selects 10-fold cross validation to divide the data set into ten parts and takes 9 of them as training and 1 of them as verification. The average of the 10 results is used as an estimate of the accuracy of the algorithm.

4 Discussion

4.1 Subjective effect analysis

As shown in Fig. 3, using the above method to process the picture, the following results can be obtained.
Fig. 3
Fig. 3

Effect of gray-gradient maximum entropy method

As can be seen from Fig. 3, the use of this method for image segmentation, the performance of antinoise in different scenes is different. The results of Fig. 3 show that this method is effective for street segmentation with less construction vehicles and scenery. For example, the details of the building (upper left in Fig. 3) can be well recognized. However, for the trees in the street and indoor scenes, there is poor segmentation (top and bottom right in Fig. 3). The main reason for this is that the light in the trees and the indoor environment is dark, and the boundary is not as good as the street under the strong light. At the same time, because the shape of the building and vehicle is large, the contour boundary is clear, especially the building, and there are special signs between the boundaries.

Find the entropy values in four directions (0o, 45o, 90o, 135o) for the above six scenes; the results are shown in Table 1. The entropy values of the six scenes in the four directions are consistent at 00 and 135o. In the four directions, the entropy value of 0o is the smallest and the entropy value of 135o is the largest.
Table 1

Entropy of different scenes in four directions

 

0o

45o

90o

135o

Scene 1

3.86

4.04

3.9

4.07

Scene 2

4.22

4.49

4.33

4.45

Scene 3

4.06

4.21

3.99

4.17

Scene 4

4.02

4.18

4.01

4.21

Scene 5

3.74

3.79

3.76

3.94

Scene 6

3.6

3.84

3.58

3.85

The results in Table 1 also show that the entropy values of different scenes are not the same, with scene 2 being the largest and scene 6 being the smallest.

4.2 Analysis of AP and IU results

Subjective methods can only describe the results qualitatively, so it is difficult to accurately evaluate the segmentation results. This paper uses AP and UI methods to quantitatively evaluate image segmentation.

It can be seen from the results of Fig. 4 that the AP value of the architecture is 85.03, the AP value of the tree is 76.49, the AP value of the vehicle is 74.03, the AP value of the road with people is 77.61, the AP value of the road with car is 82.11, and the AP value of the indoor is 73.56. Compared with subjective evaluation, the quantitative results provided by AP values are more accurate. It can be seen from the definition of AP that the larger the AP value, the better the result of image segmentation. Therefore, the results of Fig. 4 can be seen that the architecture and road with car distinguish the best, but the indoor is the worst. Different from subjective evaluation, there is little difference between the AP of the tree and the AP of road with people, but the effect of vehicle is worse than that of trees and road with people. After checking 300 scene photos, it was found that two of the photos were blurred due to the close arrangement of multiple vehicles. The above results are also reflected in the IU value; Fig. 5 shows the IU mean for 6 groups of 300 photos in each category. From the IU mean value, it can be clearly seen that IU and AP show the same quantitative evaluation results, and this consistency is not found in subjective evaluation.
Fig. 4
Fig. 4

AP values for different scenarios (the x coordinate is six different scenes and the y coordinate is the AP value)

Fig. 5
Fig. 5

The IU results of six scenarios

As shown in Fig. 6, the image is classified by K-mean method. Figure 6 shows that the different elements of the image are clustered into different “blocks” before and after clustering, and the image is processed by K-mean method. The biggest difference between segmentation and other segmentation methods is that the different elements in the image are not classified according to strict boundaries, but are clustered according to the differences in the elements in the image, so the distance between the classes is not fixed.
Fig. 6
Fig. 6

Analogy before and after splitting (left is the original image, right is the split graph)

Comparison of different segmentation methods can be achieved by using AP and UI as parameters. Table 2 shows the comparison between Silberman [23], Gupta [24], Dollar [25], and this paper. From the results of Table 2, the AP values of the four scenarios are larger than other methods, which show that the image segmentation can be better achieved by the method of this paper.
Table 2

Comparison of different methods

Ref

AP

Silberman

56.2

Gupta

62.9

Dollar

67.9

Our

85.3,6.4,74.1,77.6

5 Conclusions

Cluster analysis is an important means of data mining, and its application fields include statistics, image processing, medical diagnosis, information retrieval, biology, and machine learning. The clustering algorithm can obtain a good segmentation effect when applied to image segmentation and has been widely concerned and applied. Image segmentation is the basis of image recognition research. The quality of image segmentation directly affects the result of image recognition. This paper uses gray-gradient maximum entropy method to extract features from the image, uses K-mean method to classify the images, and uses AP and IU evaluation methods to evaluate the results. The result shows that the image segmentation can be realized well by using the method of K-mean.

Abbreviations

AP: 

Average precision

ASM: 

Angular second moment

GLCM: 

Gray-level co-occurrence matrix

IU: 

Intersection over union

MSSD: 

Mean squared shortest distance

PTAS: 

Polynomial time approximation scheme

Declarations

Acknowledgements

The authors thank the editor and anonymous reviewers for their helpful comments and valuable suggestions.

About the Authors

Xi′an University of Science and Technology, No. 58 Yanta middle road, Beilin District, Xi′an, Shaanxi, People’s Republic of China

Shan Pengfei was born in Huaibei, Anhui, People’s Republic of China, in 1987. He received the doctor’s degree from Xi′an University of Science and Technology, People’s Republic of China. Now, he works in School of Energy Engineering, Xi′an University of Science and Technology. His research interest includes rock dynamic mechanics and its image process.

Funding

Financial support for this work was provided by the 973 Key National Basic Research Program of China (no. 2015CB251602), the National Natural Science Foundation of China (nos. 51504184 and 51604264), the China Postdoctoral Science Foundation (no. 2017M196372XB), the Doctoral and Post-doctoral Start Foundation of Xi’an University of Science and Technology (nos. 2016QDJ048 and 2017QDJ060), and the Open Projects of Research Center of Coal Resources Safe Mining and Clean Utilization, Liaoning (no. LNTU17KF08). Support from these agencies is gratefully acknowledged, Natural Science Foundation of Shaanxi Province (no. 2018JQ5194).

Availability of data and materials

We can provide the data.

Authors’ contributions

The author makes contributions to all the works described in this paper. The author read and approved the final manuscript.

Ethics approval and consent to participate

Approved.

Consent for publication

Approved.

Competing interests

The authors declare that they have no competing interests. And all authors have seen the manuscript and approved for submission and confirmed that the content of the manuscript has not been published or submitted for publication elsewhere.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors’ Affiliations

(1)
School of Energy Engineering, Xi′an University of Science and Technology, Xi′an, Shaanxi, People’s Republic of China

References

  1. R. Shapley, N. Rubin, D. Ringach, Visual segmentation and illusory contours. Vis. Neurosci. 2, 1119–1128 (2004)Google Scholar
  2. R. Von Der Heydt, Image parsing mechanisms of the visual cortex. Vis. Neurosci., 1139–1150 (2003)Google Scholar
  3. J. Shi, J. Malik, Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (1997)Google Scholar
  4. P.F. Felzenszwalb, D.P. Huttenlocher, Efficient graph-based image segmentation. Int. J. Comput. Vis. 59(2), 167–181 (2004)View ArticleGoogle Scholar
  5. I.J. Cox, S.B. Rao, Y. Zhong, “Ratio regions”: a technique for image segmentation, vol 2 (2017), pp. 557–557Google Scholar
  6. M.S. Keegan, B. Sandberg, T.F. Chan, A multiphase logic framework for multichannel image segmentation [J]. Inverse Prob. Imaging 6(1), 95–110 (2017)MathSciNetView ArticleMATHGoogle Scholar
  7. D.L. Pham, J.L. Prince, An adaptive fuzzy c-means algorithm for image segmentation in the presence of intensity inhomogeneities [J]. Pattern Recogn. Lett. 20(1), 57–68 (2016)View ArticleMATHGoogle Scholar
  8. Moreno R, Grana M, Ramik D, et al. Image segmentation by spherical coordinates 2018Google Scholar
  9. Dewi M P, Armiati A, Alvini S. Image segmentation using minimum spanning tree. 2018, 335(1):012135Google Scholar
  10. Q. Huang, Y. Luo, Q. Zhang, Breast ultrasound image segmentation: a survey. Int. J. Comput. Assist. Radiol. Surg. 12(3), 1–15 (2018)Google Scholar
  11. Romero A, Drozdzal M, Erraqabi A, et al. Image segmentation by iterative inference from conditional score estimation. 2018Google Scholar
  12. Y. Yu, C. Fang, Z. Liao, Piecewise flat embedding for image segmentation (2018), pp. 1368–1376Google Scholar
  13. S.H. Kang, B. Sandberg, A.M. Yip, A regularized k-means and multiphase scale segmentation. Inverse Prob. Imaging 5(2), 407–429 (2017)MathSciNetView ArticleMATHGoogle Scholar
  14. D.J.J. Walvoort, D.J. Brus, J.J. De Gruijter, An R package for spatial coverage sampling and random sampling from compact geographical strata by k-means. Comput. Geosci. 36(10), 1261–1267 (2018)View ArticleGoogle Scholar
  15. Z. Friggstad, M. Rezapour, M.R. Salavatipour, in Foundations of Computer Science. IEEE. Local search yields a PTAS for k-means in doubling metrics (2016), pp. 365–374Google Scholar
  16. S. Shahrivari, S. Jalili, Single-pass and linear-time k-means clustering based on MapReduce. Inf. Syst. 60(C, 1–12 (2016)View ArticleGoogle Scholar
  17. Bachem O, Lucic M, Hassani H, et al. Fast and provably good seedings for k-means. 2016Google Scholar
  18. Yang B, Fu X, Sidiropoulos N D, et al. Towards K-means-friendly spaces: simultaneous deep learning and clustering. 2016Google Scholar
  19. P. Arora, Deepali, S. Varshney, Analysis of k-means and k-medoids algorithm for big data. Procedia Comput Sci 78, 507–512 (2016)View ArticleGoogle Scholar
  20. S.M. Ferrandez, T. Harbison, T. Weber, et al., Optimization of a truck-drone in tandem delivery network using k-means and genetic algorithm. J Ind Eng Manag 9(2), 374 (2016)Google Scholar
  21. S. Gupta, R. Girshick, P. Arbeláez, et al., in European Conference on Computer Vision. Learning rich features from RGB-D images for object detection and segmentation (Springer, Cham, 2014), pp. 345–360Google Scholar
  22. J. Long, E. Shelhamer, T. Darrell, Fully convolutional networks for semantic segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 39(4), 640–651 (2017)View ArticleGoogle Scholar
  23. N. Silberman, D. Hoiem, P. Kohli, et al., in European Conference on Computer Vision. Indoor segmentation and support inference from RGBD images (Springer, Berlin, 2012), pp. 746–760Google Scholar
  24. S. Gupta, P. Arbelaez, J. Malik, in Computer Vision and Pattern Recognition. IEEE. Perceptual organization and recognition of indoor scenes from RGB-D images (2013), pp. 564–571Google Scholar
  25. P. Dollar, C.L. Zitnick, in IEEE International Conference on Computer Vision. IEEE. Structured forests for fast edge detection (2014), pp. 1841–1848Google Scholar

Copyright

© The Author(s). 2018

Advertisement