基于多尺度多方向Gabor变换的Tsallis熵阈值分割方法

邹耀斌; 张进玉; 周欢; 孙水发; 夏平

doi:10.11999/JEIT211306

基于多尺度多方向Gabor变换的Tsallis熵阈值分割方法

doi: 10.11999/JEIT211306

邹耀斌^{1, 2, 3},
张进玉^{1, 3},
周欢^{1, 3, ,},
孙水发^{2, 3},
夏平^{2, 3}

1.
三峡大学大数据研究中心宜昌 443002
2.
湖北省水电工程智能视觉监测重点实验室(三峡大学) 宜昌 443002
3.
三峡大学计算机与信息学院宜昌 443002

基金项目: 国家自然科学基金(62172255, 61871258)

详细信息

作者简介:
邹耀斌：男，副教授，主要研究方向为数字图像处理、大数据分析、机器学习

张进玉：女，硕士生，研究方向为数字图像处理

周欢：男，教授，主要研究方向为移动社交网络、智能信息处理、车联网以及无线传感器网络

孙水发：男，教授，主要研究方向为智能信息处理、计算机视觉、多媒体信息处理、3维处理及可视化

夏平：男，教授，主要研究方向为机器学习、智能信息处理、多尺度几何分析及其应用

通讯作者:
周欢　zhouhuan117@163.com

中图分类号: TN911.73
计量
- 文章访问数: 754
- HTML全文浏览量: 384
- PDF下载量: 101
- 被引次数: 0
出版历程
- 收稿日期: 2021-11-22
- 修回日期: 2022-05-04
- 录用日期: 2022-05-17
- 网络出版日期: 2022-05-25
- 刊出日期: 2023-02-07

Tsallis Entropy Thresholding Based on Multi-scale and Multi-direction Gabor Transform

ZOU Yaobin^{1, 2, 3},
ZHANG Jinyu^{1, 3},
ZHOU Huan^{1, 3
, ,},
SUN Shuifa^{2, 3},
XIA Ping^{2, 3}

1.
Center for Big Data, China Three Gorges University, Yichang 443002, China
2.
Hubei Key Laboratory of Intelligent Vision Based Monitoring for Hydroelectric Engineering, China Three Gorges University, Yichang 443002, China
3.
College of Computer and Information Technology, China Three Gorges University, Yichang 443002, China

Funds: The National Natural Science Foundation of China (62172255, 61871258)

摘要

摘要: 为了能在统一框架内处理无模态、单模态、双模态或者多模态直方图情形下的自动阈值选取问题，该文提出一种基于多尺度多方向Gabor变换的Tsallis熵阈值分割方法(MGTE)。该方法先通过Gabor变换得到多尺度乘积图像，然后利用内外轮廓图像从多尺度乘积图像中重构1维直方图，并在重构1维直方图上采用Tsallis熵计算模型来选取4个方向Tsallis熵取最大值时对应的阈值，最后对4个方向的阈值进行加权求和作为最终分割阈值。将提出的方法和5个分割方法在4幅合成图像和40幅真实世界图像上进行了实验。结果表明提出的方法虽然计算效率不占优势，但它的分割适应性和分割精度有明显的提高。
- 阈值分割 /
- Gabor变换 /
- Tsallis熵差 /
- 多尺度乘积
Abstract: To deal with automatic threshold selection issue in non-modal, unimodal, bimodal or multimodal situations within a unified framework, a Tsallis Entropy thresholding segmentation method based on Multi-scale and multi-direction Gabor transform (MGTE) is proposed. The multi-scale product image is first obtained by the Gabor transform and then the inner and outer contour images are used to reconstruct the one-dimensional histogram from the multi-scale product image. Based on the reconstruction of the one-dimensional histogram, the Tsallis entropy calculation model is utilized to select 4 thresholds by maximizing Tsallis entropy in 4 different directions, and finally the weighted sum of the 4 thresholds is used as the final threshold. The proposed method is compared with 5 segmentation methods on 4 synthetic images and 40 real-world images. The results show that the proposed method has no advantage in computational efficiency, but its adaptability and segmentation accuracy are significantly improved.
- Thresholding segmentation /
- Gabor transform /
- Tsallis entropy difference /
- Multi-scale product

HTML全文

图 1 灰度直方图的左右划分示意图

下载: 全尺寸图片幻灯片

图 2 分割实验

下载: 全尺寸图片幻灯片

图 3 4个模态合成图像的灰度直方图及不同方法所得阈值比较

下载: 全尺寸图片幻灯片

图 4 不同分割方法在4个模态合成图像上的分割比较

下载: 全尺寸图片幻灯片

图 5 4个不同编号真实世界图像的灰度直方图及不同方法所得阈值比较

下载: 全尺寸图片幻灯片

图 6 不同分割方法在4个编号真实世界图像上的分割结果比较

下载: 全尺寸图片幻灯片

图 7 6个分割方法在40幅测试图像上的ME值比较

下载: 全尺寸图片幻灯片

表 1 6个分割方法在4幅合成图像上的分割阈值$ t $和ME值(%)

分割方法	无模态	单模态	双模态	多模态
分割方法	t, ME	t, ME	t, ME	t, ME
IT	201, 0.00	214, 0.00	129, 0.01	209, 0.00
MGTE	201, 0.00	212, 0.01	129, 0.01	214, 0.01
ITT	133, 22.22	162, 28.80	128, 0.01	146, 17.40
TET	126, 24.00	151, 48.57	73, 21.70	98, 28.16
FRFCM	*, 1.17	*, 39.43	*, 0.17	*, 0.87
ICAC	*, 19.58	*, 0.02	*, 0.00	*, 2.95

下载: 导出CSV

表 2 5个分割方法的计算效率比较(s)

分割方法	合成图像上CPU耗时		真实世界图像上CPU耗时
分割方法	均值	标准偏差	均值	标准偏差
MGTE	0.453	0.075	0.651	0.312
ITT	0.003	0.002	0.003	0.002
TET	0.010	0.002	0.011	0.003
FRFCM	0.065	0.064	0.030	0.027
ICAC	0.027	0.019	0.194	0.206

下载: 导出CSV

参考文献(26)

[1]	吴一全, 孟天亮, 吴诗婳. 图像阈值分割方法研究进展20年(1994–2014)[J]. 数据采集与处理, 2015, 30(1): 1–23. doi: 10.16337/j.1004-9037.2015.01.001 WU Yiquan, MENG Tianliang, and WU Shihua. Research progress of image thresholding methods in recent 20 years (1994–2014)[J]. Journal of Data Acquisition and Processing, 2015, 30(1): 1–23. doi: 10.16337/j.1004-9037.2015.01.001
[2]	范九伦, 雷博. 倒数粗糙熵图像阈值化分割算法[J]. 电子与信息学报, 2020, 42(1): 214–221. doi: 10.11999/JEIT190559 FAN Jiulun and LEI Bo. Image thresholding segmentation method based on reciprocal rough entropy[J]. Journal of Electronics &Information Technology, 2020, 42(1): 214–221. doi: 10.11999/JEIT190559
[3]	SEZGIN M and SANKUR B. Survey over image thresholding techniques and quantitative performance evaluation[J]. Journal of Electronic Imaging, 2004, 13(1): 146–168. doi: 10.1117/1.1631315
[4]	KAPUR J N, SAHOO P K, and WONG A K C. A new method for gray-level picture thresholding using the entropy of the histogram[J]. Computer Vision, Graphics, and Image Processing, 1985, 29(3): 273–285. doi: 10.1016/0734-189X(85)90125-2
[5]	吴一全, 张金矿. 二维直方图θ划分最大Shannon熵图像阈值分割[J]. 物理学报, 2010, 59(8): 5487–5495. doi: 10.7498/aps.59.5487 WU Yiquan and ZHANG Jinkuang. Image thresholding based on θ-division of 2-D histogram and maximum Shannon entropy[J]. Acta Physica Sinica, 2010, 59(8): 5487–5495. doi: 10.7498/aps.59.5487
[6]	SAHOO P, WILKINS C, and YEAGER J. Threshold selection using Rényi's entropy[J]. Pattern Recognition, 1997, 30(1): 71–84. doi: 10.1016/S0031-3203(96)00065-9
[7]	WEI Wei. Gray image thresholding based on three-dimensional Rényi entropy[C]. The 6th International Congress on Image and Signal Processing, Hangzhou, China, 2013: 599–603.
[8]	龙建武, 申铉京, 魏巍, 等. 一种结合纹理信息的三维Rényi熵阈值分割算法[J]. 小型微型计算机系统, 2011, 32(5): 948–952. LONG Jianwu, SHEN Xuanjing, WEI Wei, et al. 3-D Rényi entropy thresholding algorithm combining with the texture[J]. Journal of Chinese Computer Systems, 2011, 32(5): 948–952.
[9]	DE ALBUQUERQUE M P, ESQUEF I A, MELLO A R G, et al. Image thresholding using Tsallis entropy[J]. Pattern Recognition Letters, 2004, 25(9): 1059–1065. doi: 10.1016/j.patrec.2004.03.003
[10]	吴一全, 张金矿. 二维直方图θ-划分Tsallis熵阈值分割算法[J]. 信号处理, 2010, 26(8): 1162–1168. doi: 10.3969/j.issn.1003-0530.2010.08.008 WU Yiquan and ZHANG Jinkuang. Image thresholding based on 2-D histogram θ-division and Tsallis entropy[J]. Signal Processing, 2010, 26(8): 1162–1168. doi: 10.3969/j.issn.1003-0530.2010.08.008
[11]	YE Zhiwei, YANG Juan, WANG Mingwei, et al. 2D Tsallis entropy for image segmentation based on modified chaotic bat algorithm[J]. Entropy, 2018, 20(4): 239. doi: 10.3390/e20040239
[12]	ZHANG Hong. One-dimensional Arimoto entropy threshold segmentation method based on parameters optimization[C]. 2011 International Conference on Applied Informatics and Communication, Xi’an, China, 2011: 573–581.
[13]	卓问, 曹治国, 肖阳. 基于二维Arimoto熵的阈值分割方法[J]. 模式识别与人工智能, 2009, 22(2): 208–213. doi: 10.3969/j.issn.1003-6059.2009.02.007 ZHUO Wen, CAO Zhiguo, and XIAO Yang. Image thresholding based on two-dimensional Arimoto entropy[J]. Pattern Recognition and Artificial Intelligence, 2009, 22(2): 208–213. doi: 10.3969/j.issn.1003-6059.2009.02.007
[14]	NIE Fangyan, ZHANG Pingfeng, LI Jianqi, et al. A novel generalized entropy and its application in image thresholding[J]. Signal Processing, 2017, 134: 23–34. doi: 10.1016/j.sigpro.2016.11.004
[15]	SPARAVIGNA A C. Bi-level image thresholding obtained by means of Kaniadakis entropy[EB/OL]. https://arxiv.org/vc/arxiv/papers/1502/1502.04500v2.pdf, 2021.
[16]	LI C H and LEE C K. Minimum cross entropy thresholding[J]. Pattern Recognition, 1993, 26(4): 617–625. doi: 10.1016/0031-3203(93)90115-D
[17]	AL-OSAIMI G and EL-ZAART A. Minimum cross entropy thresholding for SAR images[C]. The 3rd International Conference on Information and Communication Technologies: From Theory to Applications, Damascus, Syria, 2008: 1245–1250.
[18]	ZHU Zhenfeng, LU Hanqing, and ZHAO Yao. Scale multiplication in odd Gabor transform domain for edge detection[J]. Journal of Visual Communication and Image Representation, 2007, 18(1): 68–80. doi: 10.1016/j.jvcir.2006.10.001
[19]	LINDEBERG T. Scale-space for discrete signals[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1990, 12(3): 234–254. doi: 10.1109/34.49051
[20]	SUYARI H and TSUKADA M. Law of error in Tsallis statistics[J]. IEEE Transactions on Information Theory, 2005, 51(2): 753–757. doi: 10.1109/TIT.2004.840862
[21]	闫海霞, 赵晓晖. 基于Tsallis熵差的遥感图像边缘检测方法[J]. 计算机应用研究, 2009, 26(9): 3598–3600. doi: 10.3969/j.issn.1001-3695.2009.09.117 YAN Haixia and ZHAO Xiaohui. Edge detection method based on Tsallis entropy difference of remote sensing image[J]. Application Research of Computers, 2009, 26(9): 3598–3600. doi: 10.3969/j.issn.1001-3695.2009.09.117
[22]	TSALLIS C. Possible generalization of Boltzmann-Gibbs statistics[J]. Journal of Statistical Physics, 1988, 52(1/2): 479–487. doi: 10.1007/BF01016429
[23]	BEMIS R. Thresholding tool[EB/OL]. http://cn.mathworks.com/matlabcentral/fileexchange/6770-thresholding-tool, 2022.
[24]	CAI Hongmin, YANG Zhong, CAO Xinhua, et al. A new iterative triclass thresholding technique in image segmentation[J]. IEEE Transactions on Image Processing, 2014, 23(3): 1038–1046. doi: 10.1109/TIP.2014.2298981
[25]	LEI Tao, JIA Xiaohong, ZHANG Yanning, et al. Significantly fast and robust fuzzy C-means clustering algorithm based on morphological reconstruction and membership filtering[J]. IEEE Transactions on Fuzzy Systems, 2018, 26(5): 3027–3041. doi: 10.1109/TFUZZ.2018.2796074
[26]	WANG Dong and WANG Xiaoping. The Iterative Convolution-Thresholding Method (ICTM) for image segmentation[EB/OL]. https://arxiv.org/pdf/1904.10917.pdf, 2021.