Remote Sensing Image Segmentation Using Super-Pixel and Dot Product Representation of Graphs

Daming Zhang; Xueyong Zhang; Huayong Liu; Lu Li

doi:10.3788/LOP202259.1210015

Laser & Optoelectronics Progress, Volume. 59, Issue 12, 1210015(2022)

Remote Sensing Image Segmentation Using Super-Pixel and Dot Product Representation of Graphs

Daming Zhang^1,2、*, Xueyong Zhang^1,2, Huayong Liu¹, and Lu Li¹

Author Affiliations

¹School of Mathematics & Physics, Anhui Jianzhu University, Hefei 230022, Anhui , China

²Key Laboratory of Architectural Acoustic Environment of Anhui Higher Education Institutes, Hefei 230601, Anhui , China

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Abstract Get PDF(in Chinese)

Figures & Tables(15)

Fig. 1. Graph of function $\frac{2}{π} a r c t a n (l n {D_{I S}}_{N} / l n ε)$

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Fig. 2. Experimental results of Swiss Roll data. (a) Original data; (b) dimensionality reduction data before correction; (c) dimensionality reduction data after correction

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Fig. 3. Experimental results of UMIST Face Database. (a) Original data; (b) dimensionality reduction data before correction; (c) dimensionality reduction data after correction

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Fig. 4. Flow chart of the proposed multispectral remote sensing image segmentation algorithm

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Fig. 5. Experiment 1. (a) Original image; (b) Ground Truth

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Fig. 6. Segmentation results under parameter q in experiment 1. (a) q=5; (b) q=10; (c) q=20; (d) q=50; (e)‒(h) corresponding segmentation results

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Fig. 7. Segmentation results of experiment 2. (a) Original image; (b) Ground Truth; (c) segmentation result of SLIC; (d) segmentation result of proposed algorithm before correction; (e) segmentation result of proposed algorithm after correction

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Fig. 8. Segmentation results of experiment 3

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Fig. 9. Segmentation results of experiment 4

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Table 1. Flowchart of dot product representation of graphs

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Table 1. Flowchart of dot product representation of graphs

Input：data set $Y = [y_{1}, y_{2}, \dots, y_{n}] \in R^{p \times n}$ ；similarity matrix $S \in R^{n \times n}$ ；positive integer $d$ Output：matrix $X = [x_{1}, x_{2}, \dots, x_{n}] \in R^{d \times n}$
1. Initialize matrix $D$ to be $n \times n$ zero matrix
2. $S = S + D$
3. Compute the dth largest eigen-values $λ_{i}$ of matrix $S$ and the corresponding eigen-vectors $μ_{i}$ ， $i = 1, \dots, d$
4. Let $X = [x_{1}, x_{2}, \dots, x_{n}]$ ，where
$x_{j} = {(\sqrt[]{λ_{1}} μ_{1 j}, \dots, \sqrt[]{λ_{n}} μ_{n j})}^{T}$ ， $j = 1, \dots, n$
5. Let $D = I \circ X^{T} X$ ，where $I$ is identity matrix， $\circ$ is multiplication that elements of matrix multiplied by elements of matrix
6. Turn to step 2. until convergence
7. Output matrix $X$

Table 2. Similarity before modification versus similarity after modification

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Table 2. Similarity before modification versus similarity after modification

Parameter	Before modification	After modification
Distance	$D_{I S}$	${D_{I S}}_{N} = D_{I S} / T_{t h r e s h o l d}$
Range of similarity	$s_{i j} \in [0,1]$	$s_{i j}^{'} \in [- 1,1]$
Range of angular	$θ_{i j} \in [0, π / 2]$	$θ_{i j}^{'} \in [0, π]$
Calculation formula	$s_{i j} = e x p (- {‖y_{i} - y_{j}‖}^{2} / 2 σ^{2})$	$s_{i j}^{'} = \frac{2}{π} a r c t a n (l n {D_{I S}}_{N} / l n ε)$

Table 3. Evaluation results of experiment 1
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Table 3. Evaluation results of experiment 1
Parameter q= $5$ q= $10$ q= $20$ q= $50$
Precision 0.8729 0.8698 0.8236 0.7172
Recall 0.8763 0.8791 0.8367 0.7461

Table 4. Evaluation results of experiment 2
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Table 4. Evaluation results of experiment 2
Parameter Before correction After correction
Precision 0.7729 0.8651
Recall 0.8132 0.9264

Table 5. Evaluation results of experiment 3
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Table 5. Evaluation results of experiment 3
Parameter FNEA（100） FNEA（150） MCG Proposed algorithm（ $K = 7$ ） Proposed algorithm（ $K = 4$ ）
Precision 0.7729 0.7548 0.8498 0.8592 0.8636
Recall 0.8761 0.8827 0.9563 0.9681 0.9507

Table 6. Evaluation results of experiment 4
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Table 6. Evaluation results of experiment 4
Parameter FNEA（50） FNEA（100） MCG Proposed algorithm（ $K = 7$ ） Proposed algorithm（ $K = 4$ ）
Precision 0.7149 0.7283 0.8559 0.8337 0.8472
Recall 0.8132 0.8362 0.9317 0.9119 0.9326

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Daming Zhang, Xueyong Zhang, Huayong Liu, Lu Li. Remote Sensing Image Segmentation Using Super-Pixel and Dot Product Representation of Graphs[J]. Laser & Optoelectronics Progress, 2022, 59(12): 1210015

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