Fast 2D cumulative residual Tsallis entropy threshold segmentation method

Cong HUANG; Yao-bin ZOU

doi:10.37188/CJLCD.2022-0427

Chinese Journal of Liquid Crystals and Displays, Volume. 38, Issue 11, 1600(2023)

Fast 2D cumulative residual Tsallis entropy threshold segmentation method

Cong HUANG^1,2 and Yao-bin ZOU^1,2、*

¹Hubei Key Laboratory of Intelligent Vision Based Monitoring for Hydroelectric Engineering，China Three Gorges University，Yichang 443002，China

²College of Computer and Information Technology，China Three Gorges University，Yichang 443002，China

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Fig. 1. Two-dimensional histograms of different modes and their corresponding two-dimensional survival function surfaces

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Fig. 2. Two-dimensional survival function region division

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Fig. 3. Fast 2D-CRTE method for calculating total 2D-CRTE with different threshold vectors $(s, t)$ .

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Fig. 4. Calculation thought of auxiliary amount $B (s, t)$ （ $B (s, t)$ equals the total amount of information minus the corresponding $T (s, t)$ under the threshold vector $(s, t)$ ）.

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Fig. 5. Flow chart of the proposed fast 2D-CRTE method

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Fig. 6. 4 synthetic test images and their two-dimensional histograms（（a）~（d）corresponding to test images numbered 1，4，18，and 26，respectively）.

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Fig. 7. Segmentation results of 6 methods on 4 synthetic images in Fig.6（a）~（d）

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Fig. 8. 4 real-world images and their two-dimensional histograms（（a）~（d）corresponding to test images numbered 4，13，46，and 59，respectively）.

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Fig. 9. Visualization results of two-dimensional survival function， $R (s, t)$ ， $B (s, t)$ and 2D-CRTE on 4 real-world images in Fig.8.

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Fig. 10. Segmentation results of 6 methods on 4 histogram patterns of Fig.8 are nonpeak，unimodal，bimodal and multimodal.

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Fig. 11. ME value scatter maps of 6 segmentation methods on 76 real-world images

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Fig. 12. Survival function and total 2D-CRTE entropy change for entropy parameter $α$ at 0.001，0.1，0.5，0.99，1.1 and 1.5.

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Fig. 13. 10 Radar test images and their two-dimensional histograms（number 1~10 from left to right，top to bottom）.

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Fig. 14. Visualization results of two-dimensional survival function， $R (s, t)$ ， $B (s, t)$ and 2D-CRTE on test images numbered 1 and 6 in Fig.13.

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Fig. 15. Segmentation results of Fast 2D-CRTE method on 10 radar test images

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Table 0. [in Chinese]

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Table 0. [in Chinese]

算法1 Fast 2D-CRTE算法
输入.灰度图像I
输出.分割结果图像Y
步骤1.对输入的灰度图像I，应用式（1）、（2）计算得到二维直方图 $p (i, j)$ 。
步骤2.基于二维直方图 $p (i, j)$ 应用式（3）得到二维生存函数 $\bar{F} (i, j)$ 。
步骤3.在二维生存函数 $\bar{F} (i, j)$ 的基础上，按式（13）、（14）计算得出辅助计算量 $R (s, t)$ 。
步骤4.按式（15）、（16）计算得出辅助计算量 $T (s, t)$ ，然后按式（17）计算得出 $B (s, t)$ 。
步骤5.基于 $R (s, t)$ 和 $B (s, t)$ ，按式（12）计算得到阈值向量 $(s, t)$ 处的2D-CRTE。最后，通过式（9）选取2D-CRTE最大时的阈值向量 $(s^{}, t^{})$ 作为最终阈值向量。
步骤6.通过阈值向量 $(s^{}, t^{})$ 将灰度图像I的像素划分为目标和背景，得到相应的分割结果图像Y。

Table 1. ME value of 26 synthetic images by six segment methods and entropy parameter $α$ values and segmentation thresholds of Fast 2D-CRTE method

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Table 1. ME value of 26 synthetic images by six segment methods and entropy parameter $α$ values and segmentation thresholds of Fast 2D-CRTE method

图像编号	Fast 2D-CRTE	Fast 2D-OTSU	Fast 2D-Tsallis	SFFCM	AFCF	GLFIF	熵参数 $α$	分割阈值 $(s, t)$
1	0.002 9	0.000 4	0.004 6	0.029 6	0.670 2	0.066 9	0.001	（121，121）
2	0.006 6	0.006 8	0.008 3	0.030 2	0.285 5	0.049 1	0.001	（114，114）
3	0.052 6	0.007 6	0.036 6	0.031 1	0.137 4	0.306 5	0.001	（125，125）
4	0.000 0	0.436 6	0.381 3	0.097 2	0.059 3	0.430 5	0.001	（124，124）
5	0.000 5	0.181 2	0.352 5	0.001 5	0.484 8	0.001 5	0.001	（127，127）
6	0.000 0	0.000 0	0.049 5	0.980 7	0.000 9	0.578 4	0.1	（102，104）
7	0.000 4	0.332 1	0.108 8	0.105 8	0.031 0	0.682 5	0.001	（103，103）
8	0.002 1	0.460 9	0.366 9	0.633 1	0.994 4	0.493 7	0.001	（117，117）
9	0.000 6	0.433 1	0.228 2	0.826 7	0.001 1	0.457 1	0.001	（117，117）
10	0.010 0	0.000 5	0.003 0	0.030 5	0.178 9	0.040 0	0.001	（124，124）
11	0.056 6	0.002 7	0.008 2	0.029 4	0.040 6	0.046 2	0.5	（103，101）
12	0.006 3	0.003 4	0.009 2	0.031 7	0.278 1	0.063 2	0.01	（124，124）
13	0.004 8	0.004 6	0.012 1	0.031 1	0.062 9	0.049 1	0.1	（100，100）
14	0.011 4	0.005 4	0.004 8	0.030 3	0.201 6	0.047 1	0.001	（112，112）
15	0.001 6	0.001 5	0.003 7	0.030 1	0.314 6	0.262 0	0.1	（105，106）
16	0.012 7	0.002 8	0.004 3	0.031 0	0.084 1	0.054 4	0.1	（85，86）
17	0.010 6	0.014 1	0.005 1	0.029 8	0.269 8	0.278 7	0.001	（124，124）
18	0.009 9	0.011 1	0.006 7	0.029 8	0.098 6	0.051 1	0.1	（100，100）
19	0.037 2	0.000 1	0.005 1	0.030 6	0.065 5	0.055 8	0.001	（125，125）
20	0.019 8	0.005 2	0.006 0	0.030 0	0.325 2	0.045 7	0.001	（121，121）
21	0.011 1	0.000 1	0.003 2	0.031 2	0.076 6	0.053 6	0.001	（125，125）
22	0.013 7	0.005 9	0.005 5	0.031 0	0.296 6	0.045 8	0.001	（117，117）
23	0.006 1	0.000 2	0.003 1	0.030 0	0.210 7	0.057 6	0.001	（124，124）
24	0.010 1	0.005 4	0.007 0	0.028 6	0.283 8	0.047 4	0.1	（108，108）
25	0.019 4	0.008 4	0.008 7	0.031 4	0.165 5	0.047 2	0.001	（122，122）
26	0.002 7	0.003 2	0.004 1	0.031 1	0.196 4	0.043 5	0.001	（121，121）

Table 2. Average CPU runtime and mean ME value of 26 synthetic images by six segment methods
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Table 2. Average CPU runtime and mean ME value of 26 synthetic images by six segment methods
评价指标 Fast 2D-CRTE Fast 2D-OTSU Fast 2D-Tsallis SFFCM AFCF GLFIF
Time/s 0.042 2 0.054 5 0.065 2 0.174 6 1.151 9 0.539 2
ME 0.011 9 0.074 4 0.062 9 0.125 1 0.223 6 0.167 5

Table 3. Average CPU runtime and mean ME value of 6 segmentation methods on 76 real-world image
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Table 3. Average CPU runtime and mean ME value of 6 segmentation methods on 76 real-world image
评价指标 Fast 2D-CRTE Fast 2D-OTSU Fast 2D-Tsallis SFFCM AFCF GLFIF
Time（s） 0.183 2 0.184 0 0.419 0 0.184 5 1.360 2 0.990 7
ME 0.013 7 0.103 4 0.139 6 0.499 4 0.540 7 0.366 8

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Cong HUANG, Yao-bin ZOU. Fast 2D cumulative residual Tsallis entropy threshold segmentation method[J]. Chinese Journal of Liquid Crystals and Displays, 2023, 38(11): 1600

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Paper Information

Category: Research Articles

Received: Dec. 22, 2022

Accepted: --

Published Online: Nov. 29, 2023

The Author Email: Yao-bin ZOU (zyb@ctgu.edu.cn)

DOI:10.37188/CJLCD.2022-0427

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Table 0. [in Chinese]

Table 0. [in Chinese]

Table 1. ME value of 26 synthetic images by six segment methods and entropy parameter α values and segmentation thresholds of Fast 2D-CRTE method

Table 1. ME value of 26 synthetic images by six segment methods and entropy parameter α values and segmentation thresholds of Fast 2D-CRTE method

Table 2. Average CPU runtime and mean ME value of 26 synthetic images by six segment methods

Table 2. Average CPU runtime and mean ME value of 26 synthetic images by six segment methods

Table 3. Average CPU runtime and mean ME value of 6 segmentation methods on 76 real-world image

Table 3. Average CPU runtime and mean ME value of 6 segmentation methods on 76 real-world image

Table 1. ME value of 26 synthetic images by six segment methods and entropy parameter $α$ values and segmentation thresholds of Fast 2D-CRTE method

Table 1. ME value of 26 synthetic images by six segment methods and entropy parameter $α$ values and segmentation thresholds of Fast 2D-CRTE method