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

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 12 >Page 1210015 > Article

Laser & Optoelectronics Progress
Vol. 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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DOI: 10.3788/LOP202259.1210015 Cite this Article Set citation alerts

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 Copy Citation Text

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

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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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 1. Flowchart of dot product representation of graphs

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 2. Similarity before modification versus similarity after modification

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 3. Evaluation results of experiment 1

Parameter	Before correction	After correction
Precision	0.7729	0.8651
Recall	0.8132	0.9264

Table 4. Evaluation results of experiment 2

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 5. Evaluation results of experiment 3

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

Table 6. Evaluation results of experiment 4

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