Suppression of stray light based on energy information mining

Ting Sun; Fei Xing; Jingyu Bao; Songsong Ji; Jin Li

doi:10.1364/AO.57.009239

1. INTRODUCTION

An attitude determination system is crucial for a spacecraft to perform precise space missions [1–5]. Nowadays, requirements for star trackers, especially miniaturized ones with high accuracy and high dynamic performance are increasing [6–11]. Since the star image is the only data source for the star tracker, the presence of stray light is fatal for its performance. Therefore, researches on the suppression of stray light for the star image are urgent. Effective distinction among star spots, the background, and the noise can provide essential information for subsequent star identification and attitude determination.

The studies on the suppression of stray light of star trackers mainly include the following: (1) design and optimization of lens hood [12–15]—a well-designed lens hood that considers the working orbit and exact space task can help the star tracker overcome some stray light problems; (2) data fusion between a star tracker and other sensors such as a gyroscope, and thus the invalid star tracker data can be compensated [16,17]; (3) star image processing—this is an important approach because the star image is the only information source of the star tracker. However, threshold optimization and noise elimination in the processing of the star image with stray light still lack special study and are crucial issues.

This work mainly focuses on a star extraction method based on energy information mining. Effective extraction and accurate centroid determination of the star spots cannot be obtained without a well-optimized processing algorithm. Star images are initially classified based on the gray-level co-occurrence matrix (GLCM) and k-nearest neighbor algorithm, with which the parameters in the background estimation and the threshold setting operation can be optimized. Then the local differential encoding, combined with Levenshtein distance (L-Distance) filtering, is adopted to distinguish the interference noise. The entire flow chart of the proposed method is described in Fig. 1. Through night sky experiments and multiframe verification, the recognition results of the extracted star spots by the proposed method can be validated.

Fig. 1. Flow chart of the proposed method.

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2. CLASSIFICATION OF STAR IMAGE WITH COMPLICATED BACKGROUND

A. Description of General Star Image

A typical star image has dozens of bright star spots and a dark background. The signal-to-noise ratio (SNR) is generally between 20 dB and 50 dB. The star spot principally exists with a Gaussian distribution within a window between $3 pixels \times 3 pixels$ to $5 pixels \times 5 pixels$ , as shown in Fig. 2. The noise of an active pixel sensor (APS) CMOS image sensor mainly includes thermal noise, photon shot noise, $1 / f$ noise, fix pattern noise, dark current noise, nonuniformity noise, etc., which may bring the change in gray distribution of the star image and form interference speckles. Figure 3 shows the inevitable interference speckles in the star images from the real night sky observation experiments. There are salt and pepper noise, irregularly shaped speckle, and non-Gaussian distributed speckle, which may bring interference in the process of star extraction and star identification.

Fig. 2. Typical energy distribution of a star spot in the real night sky observation experiment.

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Fig. 3. Several types of interference speckles in real night sky observation experiment: (a) is noise in single pixel; (b) is noise in a small region; (c) is noise distributed in a number of pixels.

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B. Influence of Stray Light

This work analyzes the influence of sunlight (type I), large-area cloud-like stray light (type II), and the moonlight (type III), and conducts a classification. The sunlight brings the gray value increasing of the entire image. The cloud-like stray light is stray light reflected by the clouds, and introduces the large area and slowly varying background. Strictly speaking, this situation is a phenomenon that occurs in the troposphere. It may not happen for a spacecraft like a satellite. We take this situation into consideration because the space environment is complicated, and unknown stray light conditions may exist. This type of stray light is completely different compared with other two types. So, we name it as “cloud-like stray light” and use it to verify the processing capability of the proposed algorithm. The moonlight brings bright speckle influence. Figure 4 summarizes the main features of the stray light and shows the comparison of the SNR. The SNR is a ratio relation between the signal and the noise [10 lg (signal/noise)]. The value of noise is calculated by the variance of gray values of the whole star image. By comparison, the SNR value of a general star image is about 54.9 dB.

Fig. 4. Star images affected (a) by sunlight; (b) by cloud-like stray light; (c) by moonlight.

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From the above SNR results, it can be seen that in the general star image, the background is dark and the SNR is high. Type III star image has the lowest SNR, and this is brought by the bright speckle in the star image.

C. Classification of Star Images by GLCM Values

GLCM [18–20] is utilized to classify star images with different types of stray light by statistics analysis of the distribution of gray values. The results for different star image types have diverse features, which can be a good basis for classification. Compared with frequency analysis, GLCM is more intuitive. Equation (1) defines GLCM as follows:

C_{Δ x, Δ y} (i, j) = \sum_{x = 1}^{n} \sum_{y = 1}^{m} {\begin{matrix} 1, & if I (x, y) = i and I (x + Δ x, y + Δ y) = j \\ 0, & otherwise . \end{matrix}

i

and

j

are the discrete levels of pixel values of a star image

I

, and represent coordinate axes of the co-occurrence matrix

C

;

x

and

y

are the positions of the pixel; and

Δ x, Δ y

are the position operators for the entire star image.

D. Classification Results

GLCM in the experiments adopts 10 levels, so the gray values of the star image are scaled from 1 to 10 linearly. Tables 1–4 all have 10 by 10 elements and display the details of the GLCM results.

Table 1. GLCM Values for a General Star Image

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Table 2. GLCM Values for a Star Image with Sunlight

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Table 3. GLCM Values for a Star Image with Cloud-Like Stray Light

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Table 4. GLCM Values for a Star Image with Moonlight

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Tables 1–4 show that for a general star image, the elements are mainly in the top left and bottom right parts of the GLCM, which indicates that the signals in the star image can be divided into two parts, including dark background (top left part) and the star information (bottom right part). For a type I star image, the elements are mainly in the bottom right part of the GLCM, which indicates that the signals in the star image are slowly varying. Furthermore, elements in the GLCM will move to the bottom right part along with the increasing of intensity of the stray light (sunlight). For a type II star image, the elements are distributed in a small region in the top left part of the GLCM. It means that the signals are also slowly varying and primarily composed of the background and cloud-like stray light in the large area with low energy. For a type III star image, the elements are mainly distributed diagonally in the GLCM. Besides the background and star spots, there are intermediate values in the GLCM, which are caused by moonlight and its image reflected by the lens. In summary, the values in the GLCM can describe considerable information about the image. For example, if the elements appear close to the diagonal, it means the image is smooth; if the elements are away from the diagonal, it means there is high-frequency noise in the image.

Then, the k-nearest neighbor algorithm is used to conduct the classification with an acceptable calculation consumption [21,22]. The GLCM results are rearranged into rows for the classification operation. A number of typical star images with different types of stray light are selected to form a training data set $T (x) = {(x_{1}, t_{1}), (x_{2}, t_{2}), \dots (x_{i}, t_{i})}$ , $i = 1, 2, \dots, M \cdot x_{i}$ is the vector of the training data, whereas $c (x_{i}) = t_{i} \in {c_{1}, c_{2}, \dots, c_{p}}$ , $p = 1, 2, 3 \dots, N$ is the corresponding classification result for the training data. For new input data $y_{j}$ , distance judgement is initially conducted to find the closest $k$ vectors $k (y_{j})$ in the training data, and its neighborhood is denoted as $D_{k}$ . Euclidean distance is adopted to conduct the distance judgment.

Then, the classification result $c (y_{j})$ can be decided by majority voting in $D_{k}$ , as shown in Eq. (2),

c (y_{i}) = \arg \max \sum_{y_{j} \in D_{k}} I (k (y_{j}), c_{p}), p = 1, 2, 3 \dots, N,

where

I

is an indicating function, and when

k (y_{j}) = c_{p}

,

I

is 1; otherwise,

I

is 0. Finally, the classification result

c (y_{j})

can be obtained.

By using this method, it is easy to determine the type of stray light in a star image. Optimization and dynamic adjustment of parameters can then be conducted in processing.

3. NOISE ELIMINATION BASED ON ENERGY DISTRIBUTION

This section mainly discusses the dynamic threshold setting and noise elimination based on gray-level distribution.

A. Dynamic Threshold Setting

For a general star image, the threshold setting is not difficult because the gray value contrast between the star spot and the dark background is evident. A global threshold with fast processing speed is sufficient. However, when stray light exists, an adaptive threshold is required for the irregular background. Commonly used global threshold methods, such as Otsu’s method, may not be a good choice for the varying background. In fact, an appropriate threshold setting method remains a challenge due to the diverse background and limited on-orbit calculating capability. Though some researches have been conducted on this based on 1D/2D morphology operation [6,23], the determination of the size of a structural operator is still a critical problem, especially for the complicated background. The operator of a fixed size is not applicable, and how to combine the selection of the structural operator and the type of the background is a new issue.

$f (x, y)$ represents the gray value of the star image at point $(x, y)$ , $b (x, y)$ is the value of structural operator $b$ at point $(x, y)$ , $D_{b}$ is the domain of $b$ , and $D_{f}$ is the domain of $f$ . $f$ eroded by $b$ can be expressed as $f Θ b$ [23]. Dilation operation is the inverse operation of erosion, which can be expressed as $f \oplus b$ . We use flat structuring elements in the morphological operation, so the structural operator $b$ is

b (i, j) = {\begin{matrix} 1, & i, j \in D_{b} \\ 0, & otherwise . \end{matrix}

The value of “1” or “0” decides whether this element involves in the morphology operation.

The opening operation is given by Eq. (3),

t = f \circ b = (f Θ b) \oplus b, L_{b} = {\begin{matrix} L_{Label - 1} \\ L_{Label - 2} \\ L_{Label - 3} \end{matrix} .

The shape of

b

is critical in the process of morphology operation. The structural operator

b

is set as a horizontal line, and the length of the line

L_{b}

is in a certain range. The size of the structural operator should be larger than the radius of the star points and be smaller than the border of stray light image, so that the varying details of the background can be extracted. Hence, when the stray light is primarily sunlight, whose classification result in Section 2 is Label-1,

L_{b}

is set as 15 pixels; when the stray light is moonlight, whose classification result is Label-3,

L_{b}

is set as 9 pixels; and when the stray light is cloud-like light, whose classification result is Label-2,

L_{b}

is set as 12 pixels. The reason for the different values of

L_{b}

is that, the interference brought by the sunlight is slowly varying, while the influence brought by the moonlight generally has sharp edges. The influence of cloud-like stray light is between them.

Through the opening operation, the initial background of the star image can be acquired. The background contains the information of the stray light, as shown in Fig. 5. The background is deleted from the star image first, and then the averaging calculation of the gray value of local blocks is employed to determine the $t$ value.

Fig. 5. Background results of different star images (a) with sunlight, (b) with cloud-like stray light, and (c) with moonlight.

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After determining the threshold value, binarization and connected component analysis can be further conducted.

B. Non-Gaussian Distributed Noise Elimination Based on Gray-Level Distribution

After star extraction, we can obtain all the suspected spots on the star image. These spots have a few common features: they usually occupy several or dozens of pixels, and their shape is close to a circle. But there are still differences between the star spot and the noise. The star spot is generally in accordance with the Gaussian distribution or at least a convex distribution, and the gray values in the center pixels are usually higher than those of the surrounding pixels. However, the gray values of the noise are disordered and have no certain pattern, as shown in Figs. 2 and 3. The regular star image processing tends to analyze the area and sum of energy of the suspected star spot region. However, these two indicators cannot well distinguish the star spot from the noise. Hence, we propose a noise distinction method based on regional image coding and L-Distance calculating, which further considers the gray-level distribution information and eliminates the spots that are not in accordance with the distribution of a star spot.

After the threshold setting and binarization mentioned in Section A, we obtain a region of suspected star spots. We record the center pixel of each extracted region and conduct the differential encoding in a region of $5 pixels \times 5 pixels$ around the center. The differential encoding is along the $x$ axis of the image sensor, as shown in Eq. (4). The encoding result is then rearranged into a string for further comparison. The selection reason for the region size of $5 pixels \times 5 pixels$ is to avoid the computation difficulty brought by different region sizes:

D = {\begin{matrix} 1 & g_{i, j} - g_{i - 1, j} \geq 0, \\ 0 & g_{i, j} - g_{i - 1, j} < 0, \end{matrix} i, j \in W_{5 \times 5} .

The obtained encoded string is compared with that of an ideally distributed star spot. Then the L-Distance [24,25] is adopted to indicate the relevance of the two strings. In comparison with direct correlation calculation and other distance expression methods, such as hamming distance, the L-Distance has a better robustness with acceptable computing consumption.

The L-Distance between data strings $s 1$ and $s 2$ is expressed by ${lev}_{s 1, s 2}$ , as shown in Eq. (5).

{lev}_{s 1, s 2} (i, j) = {\begin{cases} \max (i, j) & if \min (i, j) = 0, \\ \min {\begin{matrix} {lev}_{s 1, s 2} (i - 1, j) + 1 \\ {lev}_{s 1, s 2} (i, j - 1) + 1 \\ {lev}_{s 1, s 2} (i - 1, j - 1) + 1_{(s 1 (i) \neq s 2 (j))} \end{matrix} & otherwise . \end{cases}

The indicator function

1_{(s 1 (i) \neq s 2 (j))}

is equal to 0 when

s 1 (i) = s 2 (j)

and equal to 1 otherwise.

{lev}_{s 1, s 2} (i - 1, j) + 1

represents a deletion operation from

s 1

to

s 2

;

{lev}_{s 1, s 2} (i, j - 1) + 1

means an insertion operation; and

{lev}_{s 1, s 2} (i - 1, j - 1) + 1_{(s 1 (i) \neq s 2 (j))}

means a replacement operation. Figure 6 and Table 5 elaborate the distribution of the spots and results of the differential encoding operation, respectively.

Fig. 6. Distribution of the extracted spots and the differential encoding operation: (a) is an ideal star spot, (b) is a general star spot, and (c) is noise; (d), (e) and (f) are three-dimensional displays of energy distribution for (a), (b) and (c), separately.

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Table 5. Results of L-Distance

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4. PROCESSING AND VALIDATION BY REAL NIGHT SKY EXPERIMENTS

The star tracker used in the experiment is shown in Fig. 7(b). The baffle of the star tracker has been designed elaborately for better exclusive angles of the Sun and the Earth.

Fig. 7. (a) Real night sky observation experiments and (b) the star tracker in the experiments.

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The real night sky observation experiments were conducted at the National Astronomical Observatories, Chinese Academy of Sciences. The observation targets were actual stars. The experiment environment was selected specially according to the weather conditions for validation of different types of star images. The experiment setup is shown in Fig. 7(a).

The extraction result is verified by multiframe star images. In Fig. 8(a), the black circles denote the star spots, whereas the red asterisks represent the noise spots. Through the results, it can be seen that the L-Distance between the extracted star spot and ideally distributed star spot is small and generally around 0–3. The L-Distance between the noise spot and ideally distributed star spot is larger, and approximately 5–13, or even larger. Figures 9 and 10 display frequently appeared star and noise spots and their L-Distance results by real night sky observation experiments. Figure 9 contains results of various types of star spots with different star magnitudes and stray light conditions. It can be seen that the L-Distance is an effective indicator to identify the noise. In addition, the noise spot can be eliminated with an appropriate threshold. The threshold value can be adjusted according to the application tasks of the spacecraft. Lower threshold means more rigid selection, and more rigid selection means less star spots but more accurate star extraction. Higher threshold means looser selection. For the spots with L-Distances between 3 and 5, assessing whether it is noise is difficult because stars with lower brightness may have slight differences compared with the ideal distribution. In the attitude determination algorithm, a low weighting coefficient is assigned for these spots to reduce their influence on the attitude determination accuracy. Thus, accurate attitude information can be acquired without the interference of noise.

Fig. 8. (a) L-Distance results of the star spot and the noise (the black color represents the recognized star spots, and the red color represents the interference spots) and (b) the occurrence frequency of different L-Distance values.

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Fig. 9. Results of various types of star spots with different star magnitudes and stray light conditions.

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Fig. 10. L-Distance results of several types of noise spots.

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The description of the probability of different L-Distance values is not sufficiently detailed. Hence, the occurrence frequency of different L-Distance values of the star spot and the noise spot is shown in Fig. 8(b). It can be seen from Fig. 8(b) that the star spot and the noise spot have different ranges of L-Distance values. The value of 4 is a good dividing line for our star tracker system.

The following Figs. 11–13 are star extraction and identification results for star images with three types of stray light. Figures 11(a), 12(a), and 13(a) are extraction results with a frequently used threshold segmentation algorithm. The algorithm cannot well adapt to the changes of the background, and the extraction results have hardly any real star spots. Therefore, the subsequent star identification cannot be performed.

Fig. 11. Star extraction and identification results for type I star images (with sunlight); (a) is the extraction result with the frequently used threshold segmentation algorithm, and (b)–(d) are extraction results with our method along with the changes of the background (see Visualization 1).

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Fig. 12. Star extraction and identification results for type II star images (with cloud-like stray light); (a) is the extraction result with the frequently used threshold segmentation algorithm and (b)–(d) are extraction results with our method along with the changes of the background.

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Fig. 13. Star extraction and identification results for type III star images (with moonlight); (a) is the extraction result with the frequently used threshold segmentation algorithm, and (b)–(d) are extraction results with our method along with the changes of the background.

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Figures 11(b)–11(d), 12(b)–12(d), and 13(b)–13(d) are the extraction and identification results by using the proposed method (the blue small circles represent the position of the star spot, the red alphabets represent the extraction results, and the green alphabets represent identified star numbers in the star catalog). Along with the increasing sunlight energy, the extracted and identified star numbers have a reduction trend. However, as long as the pixels in the image are not saturated simultaneously, the star spots can still be well extracted and identified. A video of this process is in Visualization 1. When cloud-like stray light exists, the background becomes complicated. But Fig. 12 shows that the working results are satisfying. The results for images with moonlight stray light have the similar situation.

5. CONCLUSION

To solve the stray light issue of the star tracker, a classification method is proposed for the types of stray light based on a statistical analysis of the GLCM results. The parameters are then optimized based on the classification results to conduct estimation for the complicated background and threshold setting. After spot extraction, a local differential encoding combined with L-Distance filtering is conducted to eliminate the interference noise. Algorithms in this study are closely related and can solve the stray light problems through different aspects, such as background in a large area and noise in a small area. The real night observation experiments reveal that the proposed method has great performance in the processing of images with a large area and slowly varying background, and bright speckle interference. The interference noise can be eliminated, and the accurate star spot position can be obtained. Thus, star identification speed and the attitude calculation accuracy can be enhanced.

Funding

Young Elite Scientists Sponsorship Program by CAST (2016QNRC001); National Natural Science Foundation of China (NSFC) (61605099, 51522505); Key Research and Development Program of China (2016YFB0501201).

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Situation	Encoding Result	L-Distance with Ideal Star Spot
Ideal star spot	11111111110000000000	/
General star spot	11111111110000000000	0
Noise	11111110110111000100	5

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Suppression of stray light based on energy information mining

Abstract

1. INTRODUCTION

2. CLASSIFICATION OF STAR IMAGE WITH COMPLICATED BACKGROUND

A. Description of General Star Image

B. Influence of Stray Light

C. Classification of Star Images by GLCM Values

D. Classification Results

3. NOISE ELIMINATION BASED ON ENERGY DISTRIBUTION

A. Dynamic Threshold Setting

B. Non-Gaussian Distributed Noise Elimination Based on Gray-Level Distribution

4. PROCESSING AND VALIDATION BY REAL NIGHT SKY EXPERIMENTS

5. CONCLUSION

Funding

REFERENCES

Supplementary Material (1)

Cited By

Figures (13)

Tables (5)

Equations (6)

Applied Optics

( $i$ , $j$ )	1	2	3	4	5	6	7	8	9	10
1	1045120	102	7	2	0	0	0	0	0	0
2	103	162	0	0	0	0	0	0	0	0
3	6	1	1	0	0	0	0	0	0	0
4	2	0	0	0	0	0	0	0	0	0
5	0	0	0	0	0	0	0	0	0	0
6	0	0	0	0	0	183	56	0	0	0
7	0	0	0	0	0	55	176	36	0	0
8	0	0	0	0	0	0	35	233	35	0
9	0	0	0	0	0	0	0	34	115	51
10	0	0	0	0	0	0	0	0	50	987