• Laser & Optoelectronics Progress
  • Vol. 60, Issue 16, 1610004 (2023)
Jing Liu*, Yue Tian, and Jiulun Fan
Author Affiliations
  • School of Communication and Information Engineering, Xi'an University of Post & Telecommunications, Xi'an 710121, Shaanxi, China
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    DOI: 10.3788/LOP222085 Cite this Article Set citation alerts
    Jing Liu, Yue Tian, Jiulun Fan. Image Threshold Segmentation Method Based on Cumulative Residual Information Energy[J]. Laser & Optoelectronics Progress, 2023, 60(16): 1610004 Copy Citation Text show less
    Probability distribution function
    Fig. 1. Probability distribution function
    Cumulative distribution function
    Fig. 2. Cumulative distribution function
    Cumulative residual distribution function
    Fig. 3. Cumulative residual distribution function
    Cumulative residual information energy function
    Fig. 4. Cumulative residual information energy function
    Color images of test images. (a) 368016; (b) 135069; (c) 12074; (d) 100007; (e) 238011
    Fig. 5. Color images of test images. (a) 368016; (b) 135069; (c) 12074; (d) 100007; (e) 238011
    Gray images of test images. (a) 368016; (b) 135069; (c) 12074; (d) 100007; (e) 238011
    Fig. 6. Gray images of test images. (a) 368016; (b) 135069; (c) 12074; (d) 100007; (e) 238011
    Gray histograms of test images. (a) 368016; (b) 135069; (c) 12074; (d) 100007; (e) 238011
    Fig. 7. Gray histograms of test images. (a) 368016; (b) 135069; (c) 12074; (d) 100007; (e) 238011
    Segmentation results of different methods (#368016). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 8. Segmentation results of different methods (#368016). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Segmentation results of different methods (#135069). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 9. Segmentation results of different methods (#135069). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Segmentation results of different methods (#12074). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 10. Segmentation results of different methods (#12074). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Segmentation results of different methods (#100007). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 11. Segmentation results of different methods (#100007). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Segmentation results of different methods (#238011). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 12. Segmentation results of different methods (#238011). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Comparison of segmentation accuracy of test images under different methods
    Fig. 13. Comparison of segmentation accuracy of test images under different methods
    Comparison of peak signal-to-noise ratio of test images under different methods
    Fig. 14. Comparison of peak signal-to-noise ratio of test images under different methods
    Color images of test images. (a) cell1; (b) cell2; (c) cell3
    Fig. 15. Color images of test images. (a) cell1; (b) cell2; (c) cell3
    Gray histograms of test images. (a) cell1; (b) cell 2; (c) cell 3
    Fig. 16. Gray histograms of test images. (a) cell1; (b) cell 2; (c) cell 3
    Segmentation results of different methods (#cell1). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 17. Segmentation results of different methods (#cell1). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Segmentation results of different methods (#cell 2). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 18. Segmentation results of different methods (#cell 2). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Segmentation results of different methods (#cell3). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Fig. 19. Segmentation results of different methods (#cell3). (a) Standard segmentation; (b) method 1; (c) method 2; (d) method 3; (e) method 4; (f) method 5; (g) method 6; (h) method 7
    Image numberBrute force(considering symmetry)Recursive algorithm
    Average value81.14180.1452
    36801690.94960.1471
    13506978.56730.1409
    1207478.08050.1407
    10000780.44770.1333
    23801177.66410.1638
    Table 1. Running time of brute force and recursive algorithm
    Image numberMethod 1Method 2Method 3Method 4Method 5Method 6Method 7
    Average value76.1946.0875.7368.3459.5984.1687.05
    36801640.6722.8336.4371.1227.3987.5089.16
    13506996.3845.4096.3993.3867.3496.4496.22
    1207476.6745.2775.5445.8565.9876.4476.90
    10000783.6244.3886.8666.4873.8176.5189.06
    23801183.6072.5083.4364.8663.4583.9183.92
    Table 2. Comparison of segmentation accuracy of test images under different methods
    Image numberMethod 1Method 2Method 3Method 4Method 5Method 6Method 7
    Average value45.472343.843545.429044.656044.071545.697245.8953
    36801644.192743.204743.909844.142843.274545.788445.9916
    13506949.379046.347149.386848.624846.114149.430549.3727
    1207444.571142.952244.503342.932543.699844.548444.5544
    10000746.339044.111846.534945.176845.519045.755746.5860
    23801142.879642.601742.810142.403241.750342.962842.9716
    Table 3. Comparison of peak signal-to-noise ratio of test images under different methods
    Image numberMethod 1Method 2Method 3Method 4Method 5Method 6Method 7
    Average value92.2548.5891.7051.3925.7179.1894.07
    cell191.8851.5291.4252.3614.0368.7998.67
    cell294.2140.8893.9548.0411.7693.8194.34
    cell390.6553.3489.7353.7851.3574.9489.21
    Table 4. Comparison of segmentation accuracy of test images under different methods
    Image numberMethod 1Method 2Method 3Method 4Method 5Method 6Method 7
    Average value40.214139.913540.121539.891138.544039.549740.2371
    cell136.556136.809036.638036.860036.174536.829436.8690
    cell235.744935.446735.703235.474034.791234.797935.7911
    cell348.341447.484848.023347.339544.666447.022048.0512
    Table 5. Comparison of peak signal-to-noise ratio of test images under different methods
    Jing Liu, Yue Tian, Jiulun Fan. Image Threshold Segmentation Method Based on Cumulative Residual Information Energy[J]. Laser & Optoelectronics Progress, 2023, 60(16): 1610004
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