A highly robust image segmentation algorithm based on trade-off factors and multidimensional spatial metrics

doi:10.11996/JG.j.2095-302X.2024030482

Abstract

Abstract:

Image segmentation is an important research direction in computer vision. Clustering algorithms, serving as an unsupervised method, have always been a powerful tool for image segmentation. However, in scenarios where image possess high-intensity noise and complex structures, the segmentation effect of clustering algorithms might prove unsatisfactory. To address this problem, a highly robust image segmentation algorithm was proposed based on trade-off factors and multi-dimensional space metrics. Firstly, a trade-off factor was introduced to effectively reduce the influence of noise on the segmentation result by adjusting the factor. Secondly, the algorithm integrated both low-dimensional and high-dimensional space metrics, enabling the capture of linear and nonlinear features in the image. In this way, the algorithm facilitated a more comprehensive understanding of the complex structure and texture in the image, thereby enhancing the accuracy and robustness of segmentation. Finally, the algorithm achieved image segmentation through the application of an enhanced fuzzy clustering algorithm. To verify the performance of the algorithm, extensive experiments were conducted on synthetic, natural, and medical images, and the results demonstrated that the proposed method significantly outperformed other algorithms in terms of segmentation.

Key words: image segmentation, clustering, unsupervised, trade-off factor, multidimensional spatial metric

CLC Number:

TP391

LIU Yi, QIU Junhai, ZHANG Jiaxing, ZHANG Xiaofeng, WANG Hua, ZHANG Caiming. A highly robust image segmentation algorithm based on trade-off factors and multidimensional spatial metrics[J]. Journal of Graphics, 2024, 45(3): 482-494.

Figures/Tables 15

Fig. 1 Algorithmic framework based on trade-off factors and multidimensional spatial metric

Fig. 2 Pixel correlation model

Fig. 3 The trade-off factors at point A of the image contaminated by mixed noise

Table 1 Relevant parameters involved in each type of algorithm

算法	参数	窗口大小
FCM	-	-
FCMS1	α=2	3×3
FCMS2	α=2	3×3
ENFCM	α=2	3×3
FGFCM	λ_s=3，λ_g=3	3×3
FLICM	-	3×3
LMKLFCM	β=3	3×3
KWFLICM	-	5×5
FRFCM	se=3	5×5
FCM_SICM	σ_d=5，σ_r=2	-
Proposed	β=0.7，γ₁=0.8	5×5

Fig. 4 Segmentation results of the first synthetic image ((a) Original image; (b) Noisy image corrupted by salt & pepper noise of 50% density; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

Fig. 5 Different evaluation indicators under different intensity noise of the first synthetic image ((a) SA; (b) Sen; (c) Jaccard; (d) Mpa; (e) PSNR)

Fig. 6 Segmentation results of the swan ((a) Original image; (b) Noisy image corrupted by Gaussian noise of 40% variance; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

Fig. 7 Segmentation results of the church ((a) Original image; (b) Noisy image corrupted by salt & pepper noise of 40% density; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

Fig. 8 Segmentation results of the airplane ((a) Original image; (b) Noisy image corrupted by mixed noise; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

Table 2 Vpc and Vpe on natural images

Indicators	Picture	FCM	FCMS1	FCMS2	ENFCM	FGFCM	FLICM	LMKLFCM	KWFLICM	FRFCM	FCM_SICM	Ours
V_pc	图8	0.622 8	0.724 7	0.730 0	0.817 0	0.818 2	0.872 0	0.775 3	0.691 3	0.661 6	0.791 1	0.898 3
	图9	0.830 8	0.604 9	0.732 1	0.799 0	0.825 2	0.517 5	0.725 5	0.730 6	0.756 1	0.757 5	0.911 2
	图10	0.578 5	0.571 7	0.606 0	0.772 1	0.779 2	0.501 9	0.624 2	0.483 0	0.632 9	0.633 3	0.926 6
V_pe	图8	0.961 8	0.669 4	0.655 8	0.461 5	0.456 4	0.357 4	0.549 5	0.790 3	0.865 5	0.565 2	0.317 6
	图9	0.317 6	0.979 6	0.666 4	0.528 2	0.463 0	1.174 2	0.694 7	0.717 5	0.656 6	0.635 1	0.258 6
	图10	1.052 8	1.047 4	0.954 6	0.587 2	0.556 0	1.179 3	0.919 6	1.249 7	0.926 0	0.845 2	0.252 4

Fig. 9 Segmentation results of the brain ((a) Original image; (b) Noisy image corrupted by Rician noise of 30% density; (c) Ground truth (d) FCM; (e) FCMS1; (f) FCMS2; (g) EnFCM; (h) FGFCM; (i) FLICM; (j) LMKLFCM; (k) KWFLICM; (l) FRFCM; (m) FCM_SICM; (n) Ours)

Fig. 10 Segmentation results of the skin ((a) Original image; (b) Ground truth; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKLFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) Ours)

Table 3 SA on medical images

Picture	FCM	FCMS1	FCMS2	ENFCM	FGFCM	FLICM	LMKLFCM	KWFLICM	FRFCM	FCM_SICM	Ours
图9	0.561 2	0.642 0	0.645 1	0.695 7	0.731 9	0.723 5	0.652 9	0.796 9	0.579 2	0.773 1	0.796 1
图10	0.912 6	0.921 3	0.921 9	0.920 4	0.920 2	0.912 4	0.912 4	0.900 4	0.922 3	0.916 4	0.925 1

Fig. 11 Partial segmentation results of Skyataset ((a) Noise-contaminated Skyataset_001; (b) Ground truth_001; (c) Results of the proposed algorithm; (d) Noise-contaminated Skyataset_045; (e) Ground truth_045; (f) Ours)

Table 4 Average results of the correlation algorithm on the Skyataset dataset

Indicators	FCM	FCMS1	FCMS2	ENFCM	FGFCM	FLICM	LMKLFCM	KWFLICM	FRFCM	FCM_SICM	Ours
SA	0.740 6	0.808 6	0.812 3	0.810 0	0.821 5	0.833 2	0.824 6	0.814 1	0.811 8	0.870 7	0.872 0
Sen	0.789 0	0.843 8	0.848 1	0.843 5	0.850 6	0.856 7	0.861 6	0.850 4	0.849 0	0.808 3	0.800 4
Jaccard	0.566 6	0.670 4	0.676 9	0.672 1	0.689 6	0.700 4	0.696 1	0.696 0	0.677 5	0.701 8	0.703 7
Mpa	0.789 0	0.843 8	0.848 1	0.843 5	0.850 6	0.856 7	0.861 6	0.850 4	0.849 0	0.808 3	0.800 4
PSNR	6.149 7	8.727 4	8.932 0	8.785 5	9.283 8	9.957 0	9.529 1	10.000 3	8.964 9	10.452 8	10.675 7

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