发布时间: 2018-09-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.170659 2018 | Volume 23 | Number 9 图像分析和识别

1. 西南财经大学经济信息工程学院, 成都 611130;
2. 四川师范大学工学院, 成都 610101
 收稿日期: 2018-01-03; 修回日期: 2018-03-09 基金项目: 国家自然科学基金项目（61502396）；西南财经大学中央高校基本科研业务费专项基金项目（JBK150503）；西南财经大学中央高校基本科研基金项目（JBK1801076）；四川省教育厅一般基金项目（18ZB0484）；四川师范大学自制仪器设备基金项目（ZZYQ2017001）；陕西省科技厅工业公关项目（2016GY-088）；互联网金融创新及监管四川省协同创新中心；金融智能与金融工程四川省重点实验室资助项目 第一作者简介: 尹诗白, 1984年生, 女, 副教授, 2013年于长安大学获博士学位, 主要从事机器视觉方面的研究。E-mail:shibai.yin@gmail.com;孔垂涵, 男, 在读本科生, 主要从事图像处理方面的研究。E-mail:41504611@2015.swufe.edu.cn;王一斌, 男, 讲师, 博士, 硕士生导师, 主要从事模式识别方面的研究。E-mail:yibeen.wong@gmail.com. 中图法分类号: TP391.4 文献标识码: A 文章编号: 1006-8961(2018)09-1326-09

# 关键词

Unsupervised hierarchical color image segmentation through fuzzy correlation and graph cut
Yin Shibai1, Kong Chuihan1, Wang Yibin2
1. Department of Economic Information Engineering, Southwestern University of Finance and Economics, Chengdu 611130, China;
2. Department of Engineering, Sichuan Normal University, Chengdu 610101, China
Supported by: National Natural Science Foundation of China (61502396)

# Abstract

Objective Image segmentation is a process of dividing an image into different regions such that each region is homogeneous but the union of any two adjacent regions is not. As the first step in image analysis and pattern recognition, image segmentation serves as a fundamental step in numerous computer vision applications, such as object detection, content-based image retrieval, and medical image analysis. Threshold-based methods, which subdivide the image into several homogenous regions on the basis of pixel intensities, are popular segmentation techniques. Numerous algorithms have been proposed in this direction, which include gray-level thresholding and interactive pixel classification. Among these algorithms, the frequently used maximum fuzzy correlations are widely adopted to measure the appropriateness of fuzzy two partitions for the image segmentation purpose due to the unavoidable ambiguities, fuzziness, and uncertainty of the image information. However, this method has some limitations, i.e., the partition number needs to be preset, the results have isolated noise, and maximum fuzzy correlation approach cannot be extended to color image segmentation. Method Most existing gray-level image segmentation techniques could be extended to color image. They can be directly applied to each component of a color space, and then, the result can be combined in a certain way to obtain the final segmentation result. However, one of the problems is how to use the color information as a whole for each pixel and how to select the color representation for segmentation because each color representation has advantages and disadvantages. To address these problems, an unsupervised hierarchical color image segmentation through maximum fuzzy correlation and graph cut is proposed. First, we oversegment the color image into superpixels to improve the efficiency of hierarchical image segmentation. Then, we combine the fast fuzzy correlation with graph cut to form a bi-level segmentation operator, which can suppress the isolated noise caused by the single threshold-based approach and enforce the spatial coherence in the thresholding segmentation approach. Here, an iterative calculation scheme is presented to reduce redundant computations in fuzzy correlation evaluation. Finally, a top-down hierarchical segmentation approach has been designed. By iteratively performing this bi-level segmentation operator, multilevel image segmentation is achieved in a hierarchical manner. Starting from the input color image, our algorithm first selects the color channel that can best segment the image into two labels and then iteratively selects channels to further split each label until convergence. In practice, we partition the 3D color space and adopt the idea of k-d tree to record the segmentation process. Result The presented hierarchical segmentation is implemented in Matlab 7.0. Quantitative and qualitative evaluations are performed to compare with those from the state-of-the-art methods. To test the effectiveness of graph cut on the basis of two fuzzy correlation partitions, we compare our method with maximum fuzzy correlation. The experiment shows that our method can overcome the isolated noise and obtain satisfactory results. To demonstrate the segmentation performance of our algorithm on the color images, the Berkeley segmentation database is used, which consists of 300 natural images of diverse scene categories. We quantitatively compare the performance of our method with existing SAS, Ncut, and JSEG methods. Among these methods, SAS and Ncut are semi-supervised hierarchical superpixel-based color image segmentation methods. However, JSEG is an unsupervised color image segmentation method. By utilizing four widely used metrics, we can find that our method outperforms the Ncut and JSEG methods in terms of precision, and the running time is improved by 20%. Compared with SAS, our method obtains subpar results because it uses only pixel color information and is fully unsupervised. In comparison, the SAS approach uses high-level features, such as texture, edges, and color for segmentation. Conclusion An unsupervised hierarchical image segmentation approach is presented in this paper. The algorithm uses superpixels as segmentation primitives and iteratively partitions all superpixels using a bi-level segmentation operator, which combines fuzzy correlation and graph cut. By using this scheme, the proposed method can effectively handle color images and provide an important reference for the application of the maximum fuzzy correlation algorithm in the field of unsupervised color image segmentation. The limitation of the proposed approach is that it only segments images by using color information, which leads to suboptimal results when the objects and background have similar colors. Utilizing high-level cues in the proposed hierarchical segmentation framework while maintaining it as an unsupervised approach is a non-trivial task. We plan to study this issue as part of our future work.

# Key words

color image segmentation; unsupervised segmentation; superpixel; fuzzy correlation; graph cut

# 1 基本思路

1) 基于SLIC的超像素分割。由于层次化彩色图像分割算法是通过迭代实施单步的最大模糊相关图割2-划分操作完成。为此，在预处理阶段，采用计算耗时小，参数设置简单的SLIC(simple linear iterative clustering)算法[8]将彩色图像分割为若干超像素，减少图像基元的数目，提高后续算法的效率。

2) 快速最大模糊相关计算。实验表明最大模糊相关2-划分相比于常用的最大模糊熵分割具有更高的精度，但最优阈值的搜索耗时较长，采用Tang等人[7]提出的快速递推策略能有效去除冗余计算，提高效率。

3) 模糊相关图割2-划分。直接实施模糊相关2-划分操作，并没有考虑像素的空间相关性，分割结果仍存在孤立噪声，为此利用最大模糊相关来引导图割实施，构建模糊相关图割2-划分算子。

4) 非监督层次化彩色图像分割。利用单步模糊相关图割2-划分算子对彩色图像实施非监督的层次化分割，直到算法收敛为止。

# 2.1 基于SLIC的超像素分割

 $D = {d_{{\rm{lab}}}} + \frac{m}{s}{d_{xy}}$ (1)

 $\begin{array}{l} C\left( {g, c} \right) =- \ln \left[{{{\sum\limits_{k = 0}^{255} {\left( {\frac{{{u_{\rm{o}}}\left( k \right)p\left( k \right)}}{{{P_{\rm{o}}}}}} \right)} }^2}} \right] - \\ \;\;\;\;\;\;\;\;\ln \left[{\sum\limits_{k = 0}^{255} {{{\left( {\frac{{{u_{\rm{b}}}\left( k \right)p\left( k \right)}}{{{P_{\rm{b}}}}}} \right)}^2}} } \right] \end{array}$ (4)

# 2.3 模糊相关图割2-划分

 ${E_{{\rm{data}}}} = \left\{ \begin{array}{l} -\log \sum\limits_{k = 0}^{255} {{h_R}\left( k \right){\mu _{\rm{o}}}\left( k \right)} \;\;\;\;{l_R}为目标\\ -\log \sum\limits_{k = 0}^{255} {{h_R}\left( k \right){\mu _{\rm{b}}}\left( k \right)} \;\;\;\;{l_R}为背景 \end{array} \right.$ (5)

 ${E_{{\rm{smooth}}}} = {10^{\frac{{{I_{{\rm{Rmax}}}} - {I_{{\rm{Rmin}}}}}}{{255}}\alpha }}\exp \left( { - \frac{{{{\left( {{I_p} - {I_q}} \right)}^2}}}{{2{\sigma ^2}}}} \right)$ (6)

# 2.4 非监督层次化彩色图像分割

 $\begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{\rm{MSE = }}\\ \frac{1}{{3N}}\sum\limits_H {\sum\limits_{i = 1}^R {{N_i}} \left( {{\omega _i}-2{m_i}f\left( {{h_i}} \right) + f{{\left( {{h_i}} \right)}^2}} \right)} \end{array}$ (7)

 $\begin{array}{l} \Delta {\rm{MSE}}\left( h \right) = \frac{1}{{3N}}\sum\limits_D {\sum\limits_{k \in {{\bf{\Omega }} _h}} {{N_k}} (-2{\mu _k}(f\left( {{y_k}} \right)-} \\ \;\;\;\;\;\;\;\;f\left( {y{'_k}} \right)) + f{\left( {{y_k}} \right)^2}-f{\left( {y{'_k}} \right)^2}) \end{array}$ (8)

# 3.2 与其他彩色图像分割算法的结果对比

Table 1 Performance evaluation of different methods

 算法 PRI VOI GCE BDE JSEG 0.776 2.322 0.199 14.40 SAS 0.831 1.685 0.178 11.29 Ncut 0.724 2.906 0.223 17.15 本文 0.781 2.212 0.198 9.11

# 3.4 SLIC算法参数分析

SLIC的超像素分割算法是非监督层次化模糊相关图割算法的预处理步骤，SLIC中种子点个数e的设置将影响分割精度。图 9(a)分别显示了e为300，500，800时的超像素结果，图 9(b)显示了相应的最终分割结果。可见，当e值为800时，超像素的面积较小，图像细分程度较高，在相同阈值T的约束下，产生过分割结果。而当e值为300时，超像素面积较大，相同T时，产生欠分割的结果。e值为500时，目标和背景能较完整地提取。大量的实验也表明，e值为500时，算法的分割精度最高。

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