A Robust Image Segmentation Algorithm Based on Weighted Filtering and Kernel Metric

Yi Liu; Xiaofeng Zhang; Yujuan Sun; Hua Wang; Caiming Zhang

doi:10.3788/LOP231545

Laser & Optoelectronics Progress, Volume. 61, Issue 8, 0837005(2024)

A Robust Image Segmentation Algorithm Based on Weighted Filtering and Kernel Metric

Yi Liu¹, Xiaofeng Zhang^1,2、*, Yujuan Sun¹, Hua Wang¹, and Caiming Zhang³

Author Affiliations

¹School of Information and Electrical Engineering, Ludong University, Yantai 264025, Shandong , China

²School of Information Engineering, Yantai Institute of Technology, Yantai 264003, Shandong , China

³School of Software, Shandong University, Jinan 250014, Shandong , China

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Figures & Tables(19)

Fig. 1. Weighted filter

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Fig. 2. Recovery results of natural image corrupted by 30% salt & pepper noise by different filters. (a) Orginal image; (b) image corrupted by 30% salt & pepper noise; (c) recovery result by inverse gradient weighted filter; (d) recovery result by mean filter; (e) recovery result by median filter; (f) recovery result by weighted filter

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Fig. 3. Pixel correlation model

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Fig. 4. Framework of the proposed algorithm

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Fig. 5. Iterative process of the proposed algorithm

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Fig. 6. Segmentation results of different algorithms on the first synthetic image. (a) Original image; (b) noisy image corrupted by 30% Gaussian noise; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) proposed algorithm

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Fig. 7. Segmentation results of different algorithms on the second synthetic image. (a) Original image; (b) noisy image corrupted by 30% salt & pepper noise; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) proposed algorithm

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Fig. 8. Segmentation results of different algorithms on natural image. (a) Original image; (b) FCM; (c) FCMS1; (d) FCMS2; (e) EnFCM; (f) FGFCM; (g) FLICM; (h) LMKFCM; (i) KWFLICM; (j) FRFCM; (k) FCM_SICM; (l) proposed algorithm

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Fig. 9. Segmentation results of different algorithms on the first remote sensing image. (a) Original image; (b) groundtruth; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) proposed algorithm

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Fig. 10. Segmentation results of different algorithms on the second remote sensing image. (a) Original image; (b) groundtruth; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) proposed algorithm

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Fig. 11. Segmentation results of different algorithms on the medical image. (a) Original image; (b) groundtruth; (c) FCM; (d) FCMS1; (e) FCMS2; (f) EnFCM; (g) FGFCM; (h) FLICM; (i) LMKFCM; (j) KWFLICM; (k) FRFCM; (l) FCM_SICM; (m) DeepLabV3+; (n) U-net; (o) proposed algorithm

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Fig. 12. Results of the proposed algorithm for different size windows

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Fig. 13. Segmentation results for different class numbers. (a) Original image; (b) class number is 2; (c) class number is 3; (d) class number is 4; (e) class number is 5

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Table 1. Algorithm details

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Table 1. Algorithm details

Algorithm： A robust image segmentation algorithm based on weighted filtering
Input：Iteration termination condition $ε$ ，fuzzy factor $m$ ，number of clusters C，local window size $N_{R}$ ，maximum number of iterations T
Output： Segmented image
Step 1. Calculate $w_{i r}$ and $s (i, r)$ according to formulas（5）and（7）.
Step 2. Obtain the filtered image according to formula（6）.
Step 3. Randomly initialize the fuzzy membership degree and cluster center.
Step 4. Set the iteration counter $b = 0$ .
Step 5. Update the fuzzy membership degree $u_{_{i j}}^{(b)}$ according to formula（12）.
Step 6. Update the cluster center $v_{_{i j}}^{(b)}$ according to formula（13）.
Step 7. $b = b + 1$ ，if $m a x \{u_{_{i j}}^{(b)} - u_{_{i j}}^{(b + 1)}\} < ε$ or $b > T$ ，go to Step 8，otherwise go to Step 5. Step 8. According to $C_{i} = a r g_{j} [m a x (u_{i j})]$ ，assign each pixel to the class $C_{i}$ with the largest membership degree to obtain the final segmented image.

Table 2. Relevant parameters involved in each type of algorithm

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Table 2. Relevant parameters involved in each type of algorithm

Algorithm	Parameter	Window size
FCM^［13］	—	—
FCMS1^［32］	$α = 2$	3×3
FCMS2^［32］	$α = 2$	3×3
EnFCM^［19］	$α = 2$	3×3
FGFCM^［18］	$λ_{s} = 3$ ， $λ_{g} = 3$	3×3
FLICM^［17］	—	3×3
LMKFCM^［20］	$β = 3$	3×3
KWFLICM^［21］	—	5×5
FRFCM^［22］	$s_{e} = 3$	5×5
FCM_SICM^［23］	$σ_{d} = 5, σ_{r} = 2$	—
Proposed method	—	5×5

Table 3. Segmentation indicators of related algorithms on synthetic images

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Table 3. Segmentation indicators of related algorithms on synthetic images

Picture	Indicator	FCM	FCMS1	FCMS2	EnFCM	FGFCM	FLICM	LMK- FCM	KW- FLICM	FR- FCM	FCM_SICM	Proposed
1	$S_{A}$	0.5974	0.3537	0.9530	0.9620	0.9644	0.3519	0.3456	0.3492	0.3734	0.9438	0.9848
	P	0.6689	0.3818	0.9627	0.9708	0.9726	0.6250	0.4014	0.2632	0.3927	0.9455	0.9870
	R	0.6632	0.3792	0.9670	0.9735	0.9751	0.6280	0.3796	0.3754	0.3815	0.9434	0.9877
	$F_{1}$	0.6335	0.3388	0.9635	0.9714	0.9732	0.5856	0.3564	0.1890	0.3496	0.9443	0.9873
2	$S_{A}$	0.8442	0.7954	0.8399	0.7673	0.9256	0.9419	0.8414	0.9432	0.9839	0.9710	0.9934
	P	0.8019	0.7164	0.8634	0.8164	0.9305	0.6575	0.7545	0.7199	0.7090	0.8997	0.9509
	R	0.7390	0.5034	0.6595	0.6506	0.7663	0.5997	0.5595	0.8677	0.7709	0.8917	0.9785
	$F_{1}$	0.7035	0.5335	0.7009	0.6548	0.8147	0.4692	0.6078	0.7747	0.7139	0.8896	0.9639

Table 4. Segmentation indicators $V_{p c}$ and $V_{p e}$ of the related algorithms on the natural image
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Table 4. Segmentation indicators $V_{p c}$ and $V_{p e}$ of the related algorithms on the natural image
Indicator FCM FCMS1 FCMS2 EnFCM FGFCM FLICM LMKFCM KWFLICM FRFCM FCM_SICM Proposed
$V_{p c}$ 0.540 0.814 0.815 0.857 0.864 0.891 0.840 0.824 0.562 0.819 0.945
$V_{p e}$ 1.293 1.099 0.926 0.629 0.580 1.179 0.833 1.024 0.655 0.448 0.119

Table 5. Segmentation indicators of related algorithms on remote sensing images

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Table 5. Segmentation indicators of related algorithms on remote sensing images

Picture	Indicator	FCM	FCMS1	FCMS2	EnFCM	FGFCM	FLICM	LMK- FCM	KW- FLICM	FR- FCM	FCM_SICM	Proposed
1	$S_{A}$	0.9266	0.9475	0.9537	0.9470	0.9502	0.9787	0.9814	0.9788	0.9645	0.9753	0.9938
	$P$	0.9359	0.9513	0.9554	0.9517	0.9488	0.9791	0.9835	0.9660	0.9531	0.9741	0.9867
	$R$	0.9606	0.9022	0.9151	0.9005	0.9118	0.9611	0.9644	0.9742	0.9470	0.9565	0.9960
	$F_{1}$	0.9481	0.9261	0.9348	0.9254	0.9300	0.9700	0.9739	0.9701	0.9501	0.9652	0.9913
2	$S_{A}$	0.8526	0.9530	0.9522	0.9529	0.9566	0.9675	0.9712	0.9758	0.9444	0.9559	0.9864
	$P$	0.8807	0.9493	0.9466	0.9494	0.9506	0.9573	0.9716	0.9688	0.9352	0.9534	0.9838
	$R$	0.7629	0.9171	0.9162	0.9174	0.9217	0.9503	0.9502	0.9540	0.9136	0.9273	0.9720
	$F_{1}$	0.8031	0.9322	0.9305	0.9324	0.9353	0.9536	0.9605	0.9611	0.9240	0.9398	0.9778

Table 6. Indicator $S_{A}$ of related algorithms on medical image
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Table 6. Indicator $S_{A}$ of related algorithms on medical image
FCM FCMS1 FCMS2 EnFCM FGFCM FLICM LMFCM KWFLICM FRFCM FCM_SICM DeepLabV3+ U-net Proposed
0.9072 0.9075 0.9055 0.9044 0.9046 0.9070 0.9077 0.9106 0.9210 0.9171 0.5678 0.6662 0.9216

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Yi Liu, Xiaofeng Zhang, Yujuan Sun, Hua Wang, Caiming Zhang. A Robust Image Segmentation Algorithm Based on Weighted Filtering and Kernel Metric[J]. Laser & Optoelectronics Progress, 2024, 61(8): 0837005

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