Star map matching method for optical circular rotation imaging based on graph neural networks

Tingting Xu; Tingting Xu; Tingting Xu; Xiubin Yang; Xiubin Yang; Zongqiang Fu; Zongqiang Fu; Ge Jin; Ge Jin; Wei Chen; Wei Chen; Miaoran Huang; Guoyu Lu

doi:10.1364/JOSAA.486401

Journal of the Optical Society of America A
Vol. 40,
Issue 6,
pp. 1191-1200
(2023)
•https://doi.org/10.1364/JOSAA.486401

Star map matching method for optical circular rotation imaging based on graph neural networks

Tingting Xu, Xiubin Yang, Zongqiang Fu, Ge Jin, Wei Chen, Miaoran Huang, and Guoyu Lu

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Tingting Xu, Xiubin Yang, Zongqiang Fu, Ge Jin, Wei Chen, Miaoran Huang, and Guoyu Lu, "Star map matching method for optical circular rotation imaging based on graph neural networks," J. Opt. Soc. Am. A 40, 1191-1200 (2023)

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Abstract

This paper focuses on a dynamic star image acquisition and matching method for space situational awareness, which can quickly search for widely distributed resident space objects. First, the optical circular rotation imaging method performed by a single space camera is proposed to obtain a series of star images. And then, the image matching method based on graph neural networks is proposed for generating a wide observation star image. Experiment results show that compared with baseline matching algorithms, the matching accuracy and matching precision of the proposed algorithm are improved significantly.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Item	Parameter	Unit
Magnitude threshold of camera	8	Mv
Field of view	$12 \times 12$	Deg(°)
Focal length	22	mm
Image dimensions	$1024 \times 1024$	Pixel
Pixel size	$0.012 \times 0.012$	Mm
Exposure time	50	ms
Radius of the point spread function	3	Pixel
Right ascension	−180 to 180	Deg(°)
Declination	−180 to 180	Deg(°)
Angular velocity $ω_{z} (ω_{o})$	2	Deg/s(°/s)
Angular velocity $ω_{y} (ω_{s})$	2	Deg/s(°/s)

Method	Matching Precision	Matching Score
SIFT $+$ NN	0.6174	0.1018
SIFT $+$ MSG	0.8193	0.1365
SP $+$ SG	0.8964	0.1894
SP $+$ MSG (ours)	0.9288	0.2073

Item	Parameter	Unit
Magnitude threshold of camera	8	Mv
Field of view	$12 \times 12$	Deg(°)
Focal length	22	mm
Image dimensions	$1024 \times 1024$	Pixel
Pixel size	$0.012 \times 0.012$	Mm
Exposure time	50	ms
Radius of the point spread function	3	Pixel
Right ascension	−180 to 180	Deg(°)
Declination	−180 to 180	Deg(°)
Angular velocity $ω_{z} (ω_{o})$	2	Deg/s(°/s)
Angular velocity $ω_{y} (ω_{s})$	2	Deg/s(°/s)

Method	Matching Precision	Matching Score
SIFT $+$ NN	0.6174	0.1018
SIFT $+$ MSG	0.8193	0.1365
SP $+$ SG	0.8964	0.1894
SP $+$ MSG (ours)	0.9288	0.2073

Algorithm 1: Topology Graph Data Building
Input: A pair of star images (A, B)
1. features and positions of star points extraction Eq. (11)
2. build undirected full connected weighted graphs $G_{A}$ from $i, j \forall i \in V_{A}, \forall j \in V_{A}$ by Eq. (12)
3. generate the MST ${G_{A}}_{(mst)}, {G_{B}}_{(mst)}$ of $G_{A}, G_{B}$ by Kruskal algorithm
Output: Topology Graph Data of star images $G_{A} = {^{(0)} h_{i}^{A}, E_{A (mst)}}, i \in V_{A}$ , $G_{B} = {^{(0)} h_{j}^{B}, E_{B (mst)}}, j \in V_{B}$

Algorithm 2: Multiplex Graph Node Embedding
Input: lst layer graph data $G_{A} = {^{(0)} h_{i}^{A}, E_{A (mst)}}, i \in V_{A}$ , $G_{B} = {^{(0)} h_{j}^{B}, E_{B (mst)}}, j \in V_{B}$
1. single graph node embedding $(^{(l)} h_{i}^{A},^{(l)} h_{j}^{B}), \forall i \in V_{A}, \forall j \in V_{B}$ by Eq. (14)
2. cross-graph attention $a_{i \to j}$ between two graphs by Eq. (18)
3. cross-graph aggregation $Δ h_{i}^{A}$ , $Δ h_{j}^{B}$ by Eq. (16)
4. multiplex graph node features $^{(l + 1)} h_{i}^{A},^{(l + 1)} h_{j}^{B} \forall i \in V_{A}, \forall j \in V_{B}$ by Eq. (13)
Output: (l $+$ 1)-th layer $G_{A} = {^{(l + 1)} h_{i}^{A}, E_{A (mst)}}, i \in V_{A}$ , $G_{B} = {^{(l + 1)} h_{j}^{B}, E_{B (mst)}}, j \in V_{B}$

Algorithm 1: Topology Graph Data Building
Input: A pair of star images (A, B)
1. features and positions of star points extraction Eq. (11)
2. build undirected full connected weighted graphs $G_{A}$ from $i, j \forall i \in V_{A}, \forall j \in V_{A}$ by Eq. (12)
3. generate the MST ${G_{A}}_{(mst)}, {G_{B}}_{(mst)}$ of $G_{A}, G_{B}$ by Kruskal algorithm
Output: Topology Graph Data of star images $G_{A} = {^{(0)} h_{i}^{A}, E_{A (mst)}}, i \in V_{A}$ , $G_{B} = {^{(0)} h_{j}^{B}, E_{B (mst)}}, j \in V_{B}$

Algorithm 2: Multiplex Graph Node Embedding
Input: lst layer graph data $G_{A} = {^{(0)} h_{i}^{A}, E_{A (mst)}}, i \in V_{A}$ , $G_{B} = {^{(0)} h_{j}^{B}, E_{B (mst)}}, j \in V_{B}$
1. single graph node embedding $(^{(l)} h_{i}^{A},^{(l)} h_{j}^{B}), \forall i \in V_{A}, \forall j \in V_{B}$ by Eq. (14)
2. cross-graph attention $a_{i \to j}$ between two graphs by Eq. (18)
3. cross-graph aggregation $Δ h_{i}^{A}$ , $Δ h_{j}^{B}$ by Eq. (16)
4. multiplex graph node features $^{(l + 1)} h_{i}^{A},^{(l + 1)} h_{j}^{B} \forall i \in V_{A}, \forall j \in V_{B}$ by Eq. (13)
Output: (l $+$ 1)-th layer $G_{A} = {^{(l + 1)} h_{i}^{A}, E_{A (mst)}}, i \in V_{A}$ , $G_{B} = {^{(l + 1)} h_{j}^{B}, E_{B (mst)}}, j \in V_{B}$

Abstract

Data availability

Cited By

Figures (13)

Tables (4)

Equations (21)

Journal of the Optical Society of America A