Preamble

Astronomical Techniques and Instruments, Vol. 2, July 2025, 265–273

Article

Open Access

Research on the Accurate Calculation Method of Crater Position in Lunar Surface Images Based on Feature Matching

Yanning Zheng¹,², Xue Dong¹,², Zhipeng Liang¹,², Jian Gao¹, Bowen Guan¹, Liyan Sun¹, Xingwei Han¹,², He Dong³

¹Changchun Observatory, National Astronomical Observatories, Chinese Academy of Sciences, Jilin 130117, China
²University of Chinese Academy of Sciences, Beijing 100049, China
³College of Information Technology, Jilin Normal University, Jilin 136000, China

*Correspondences: dongx@cho.ac.cn; donghe@jlnu.edu.cn

Received: March 4, 2025; Accepted: March 13, 2025; Published Online: April 29, 2025
https://doi.org/10.61977/ati2025026; https://cstr.cn/32083.14.ati2025026

© 2025 Editorial Office of Astronomical Techniques and Instruments, Yunnan Observatories, Chinese Academy of Sciences. This is an open access article under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/)

Citation: Zheng, Y. N., Dong, X., Liang, Z. P., et al. 2025. Research on the accurate calculation method of crater position in lunar surface images based on feature matching. Astronomical Techniques and Instruments, 2(4): 265−273. https://doi.org/10.61977/ati2025026.

Abstract

Lunar Laser Ranging (LLR) imposes extremely high requirements on telescope pointing accuracy. To improve pointing accuracy and address the limitation that telescope pointing correction via all-sky star tracking yields insufficient precision, we propose a processing scheme that selects larger lunar craters near the Lunar Corner Cube Retroreflector (LCCR) as reference features for computing telescope pointing bias. Accurately determining crater positions in images is crucial for calculating this pointing bias; therefore, we propose a method for accurately calculating crater positions based on lunar surface feature matching. This method utilizes matched feature points obtained from image feature matching, employing a deep learning approach to solve for the image transformation matrix. The known position of a crater in a reference image is then mapped using this matrix to calculate the crater's position in the target image. We validate this method using craters near the Lunar Corner Cube Retroreflectors of Apollo 15 and Luna 17, finding that the calculated crater position in the target image falls at the center of the crater, even for image features with large distortion near the lunar limb. The maximum image matching error is approximately 1″, and the minimum is only 0.47″, which meets the pointing requirements of Lunar Laser Ranging. This method provides a new technical means for high-precision pointing bias calculation in LLR systems.

Keywords: Lunar Laser Ranging system; High-precision pointing correction; Lunar surface features; Image feature matching; Deep learning; Crater position calculation

1. Introduction

Lunar exploration is essential for studying the Moon and utilizing its resources, and it lays important groundwork for establishing lunar bases and conducting further deep space exploration. Robotic probes undertaking lunar exploration require core scientific support, such as accurate lunar orbital parameters and lunar reference frames, to ensure optimal execution of exploration missions. Although China's lunar exploration has achieved world-renowned results, there are still areas requiring more work to match other international agencies in technical fields such as Lunar Laser Ranging (LLR).

LLR is a technology for precisely measuring the Earth-Moon distance that, especially with the application of next-generation single solid Lunar Corner Cube Retroreflectors (LCCRs)—optical devices installed on the Moon's surface to reflect Earth-based laser beams—is expected to reach millimeter-level observation accuracy [1–3]. LLR data play a crucial role in astronomical geodynamics, lunar physics, general relativity, and studies on the Earth-Moon reference frame, providing a strong scientific basis for exploring the Earth-Moon system and the Moon's internal structure [4–6].

Laser ranging systems inevitably yield pointing errors due to mechanical processing, installation, gravity, and temperature changes [7]. The distance between Earth and the Moon is approximately 380,000 km, and a pointing bias of 1″ from the ground toward the Moon corresponds to a distance error of 1.86 km on the lunar surface. The Luna 17 LCCR, because of its uncertain location, acquired only a small amount of valid data in the early stages of its placement and was then "lost" until 2010, when high-resolution images taken by the Lunar Reconnaissance Orbiter Camera (LROC) helped reposition Lunokhod 1 and regain valid observational data from Luna 17. Notably, the new estimated coordinates of Luna 17 differ from the original estimated coordinates by approximately 5 km [8], which corresponds to a pointing bias of only about 3″ from the ground station. In addition, the number of laser ranging echo photons is inversely proportional to the fourth power of the distance, and the number of effective echo photons that can be received is very limited for LLR systems [9,10]. Consequently, telescope pointing accuracy is even more important for LLR [11], making it a key factor affecting the success of observations.

Telescope pointing error correction is usually achieved by tracking dozens of stars in the all-sky region, obtaining the stellar pointing bias and modeling the pointing error, thereby achieving pointing bias correction for the telescope [12,13]. Although this method improves the integrated pointing accuracy of the telescope across the all-sky region, the bias for a specific pointing may still be too large, negatively impacting LLR observations. Meanwhile, with accumulated telescope operation time and seasonal changes, a previously devised pointing model may no longer be applicable, leading to a further decrease in pointing accuracy that would seriously compromise the performance of the LLR system.

To meet the pointing accuracy requirements for LLR, we devise a processing scheme to calculate and correct the current pointing bias of the telescope in real time. Given the small size of the LCCR and the large Earth-Moon distance, it is difficult for ground-based cameras to accurately capture its shape. To alleviate this, we suggest using a larger crater near the LCCR as a reference feature to calculate pointing bias. Because telescope pointing bias varies very little over a small range of azimuth and altitude changes, the pointing deviation calculated based on the crater can be directly applied to the corresponding LCCR. Accurately obtaining the position of craters in the image is key to determining pointing bias. Crater images on the lunar surface can be distorted due to observation angle, lunar surface topography, lighting conditions, and other factors. Traditional crater recognition techniques rely on edge detection to extract features [14–17], but they do not currently show satisfactory performance.

Deep learning techniques have shown continuous progress, prompting their application to crater recognition [18–22]; however, these methods mainly focus on recognizing craters in orthographic projection view, determining whether a region in the image is a crater and its approximate contour, rather than pinpointing the positional coordinates of the crater in the image. To solve this problem, our proposed method for accurately calculating lunar crater positions uses lunar surface feature matching. The method solves the transformation matrix between feature points by matching common feature points between the reference image and the target image. It then accurately calculates the exact location of the crater in the target image using the transformation matrix and known crater location information in the reference image. The effectiveness and accuracy of feature matching are ensured by the uniqueness of lunar craters and their surrounding geomorphological features such as mountain ranges, hills, and rift valleys.

2. Materials and Methods

Image matching is a technique that can identify and establish corresponding relationships between similar structures in two or more images. Feature-based image matching algorithms are fast, stable, and computationally efficient, typically including three stages: feature point detection, feature point description, and matching [23,24]. Early image matching techniques relied primarily on manually determined features, acquired using bespoke algorithms that extract local or global characteristics from images to represent their key information. These algorithms include Scale Invariant Feature Transform (SIFT) [25], Speeded Up Robust Features (SURF) [26], and Oriented FAST and Rotated BRIEF (ORB) [27], which usually rely on pre-determined structures, meaning accuracy may be unreliable for complex scenery or under adverse lighting conditions.

With the rapid development of deep learning technology, the field of image matching has seen significant progress, and numerous advanced methods based on deep learning have emerged that outperform traditional methods for determining feature positions and other non-deep-learning methods on image matching datasets. Standout examples are SuperPoint [28] and SuperGlue [29], whose developers have performed comparative analyses with traditional methods to verify the superior performance of their algorithms. Here, we use the SuperPoint and SuperGlue algorithms for feature matching in lunar surface images.

2.1. SuperPoint and SuperGlue Algorithms

SuperPoint and SuperGlue are two important algorithms for feature point detection and matching, and their core processes are shown in Fig. 1 [FIGURE:1]. The SuperPoint algorithm uses a full convolutional neural network to achieve keypoint detection and description in a self-supervised learning framework. SuperGlue is a neural network that uses an attention mechanism to jointly search for correspondences, eliminating non-matching points by aggregating contextual information between two sets of local features to achieve efficient matching.

As shown in Fig. 2 [FIGURE:2] [28], the SuperPoint architecture is a full convolutional neural network that operates on full-size images, using descriptors for interest point detection. The model consists of an input, shared encoder, interest point detection decoder, interest point description decoder, and output. The shared encoder processes and reduces the dimensionality from H × W to H/8 × W/8 of the input image. The interest point detection decoder finds interest points based on task weights, computed by the interest point detector head. After passing through Softmax and Reshape, a tensor sized H × W is output. Another decoder performs description of the interest points, and a tensor sized H × W × D is output after passing through Bi-Cubic Interpolation and L2 Norm. For detection and description of interest points, traditional methods follow a processing order in which detection is followed by description, whereas SuperPoint network parameters enable sharing between detection and description tasks to generate interest points and descriptors simultaneously.

SuperGlue comprises two main parts: the Attention Graph Neural Network and the Optimal Match Layer (shown in Fig. 3 [FIGURE:3] [29]). The Attention Graph Neural Network takes feature points p and their descriptors d as inputs, which are processed into a single vector by the Keypoint Encoder module. Subsequently, the attention intersection network layer carries out multiple iterations to generate richer matching descriptors f. The Optimal Matching Layer finds optimal allocation using the Sinkhorn Algorithm for T iterations.

SuperPoint and SuperGlue are robust to external factors such as shape change and light change. Through self-supervised learning, SuperPoint is able to stably detect keypoints in different visual environments, while SuperGlue uses its attention mechanism and contextual information to improve matching quality and maintains high accuracy even under challenging conditions, meeting the stringent requirements of lunar surface feature matching.

2.2. Creation of a Reference Image Library

The image field of view used in this paper has a size of 3′, and based on the mean Earth-Moon distance and lunar diameter, the distance range of the lunar surface covered by the 3′ field of view corresponds to approximately 10% of the lunar diameter. The lunar surface images used in the study were taken from the NASA SVS (Scientific Visualization Studio) website [30]. SVS has modeled lunar phase changes and libration effects on the Moon at hourly intervals using LROC images, with corresponding atlases available for download. The reference image of the lunar surface used in this paper was taken from this atlas, and the 3′ field of view corresponds to an image size of 282 × 282 pixels, with each pixel corresponding to 0.6383″. The theoretical locations of the craters in the reference image are acquired from Lunar QuickMap [31], a powerful web application for data exploration and analysis that provides detailed lunar surface information such as crater names and coordinates.

Lunar QuickMap uses imagery from LROC [32], which has an image resolution of up to 0.5 m/pixel [33]. Meanwhile, the Lunar QuickMap tool can provide a scale with a maximum resolution of 10 m [31], which is equivalent to a pointing deviation of 1/180″ (shown in Fig. 4 [FIGURE:4]). For these reasons, the Lunar QuickMap data best meet the LLR requirements.

Lunar surface features and the visual integrity of craters can change significantly due to varying lighting conditions, and this must be taken into account when constructing a reference image set. In this study, we classify the Moon's terminator line into seven cases according to its position relative to the selected craters (shown in Fig. 5 [FIGURE:5]): Near Evening Line (NEL), Small Area in the Night Region (SANR), Large Area in the Night Region (LANR), Small Area in the Light Region (SALR), Large Area in the Light Region (LALR), Near Morning Line (NML), and Moon Daytime (MDT). The details of the cases are shown in Table 1 [TABLE:1].

2.3. Image Transformation and Crater Position Calculation

A homography is a mapping between any two images of the same planar surface acquired separately [34], and it can handle geometric transformations in images such as rotation, scaling, translation, and perspective. As discussed in Section 2.1, we can match feature points between the reference image (Ref_Img) and the target image (Target_Img), and then use these points to solve for the corresponding homography transformation matrix [35].

The homography transformation is represented by a 3 × 3 matrix H for mapping a point X in one image plane to a point X′ in another image plane, as shown in Fig. 6 [FIGURE:6]. This transformation can be expressed as

$$
\begin{pmatrix}
x' \
y' \
\omega'
\end{pmatrix}
= H X,
\quad
\begin{pmatrix}
x' \
y' \
\omega'
\end{pmatrix}
=
\begin{pmatrix}
h_{11} & h_{12} & h_{13} \
h_{21} & h_{22} & h_{23} \
h_{31} & h_{32} & h_{33}
\end{pmatrix}
\begin{pmatrix}
x \
y \
\omega
\end{pmatrix};
\tag{1}
$$

where $h_{11}, h_{12}, \ldots, h_{33}$ are matrix elements, $X$ and $X′$ are homogeneous coordinates, and in general $\omega′ = \omega = 1$.

Using the homography transformation matrix H, it is possible to achieve transformation of the reference image, including the craters within the image. The transformed reference image is denoted as Ref_Img_1.

The reference image library mentioned in Section 2.2 contains 7 images, and the target image needs to be feature-matched with these reference images one by one. The number of matching points is an important indicator to measure the similarity between two images. A higher number of matching points indicates that the features of the two images are more coincident, suggesting a higher degree of similarity and more reliable matching.

The accuracy and validity of matching results can be quantified by matching precision; with higher precision, the accuracy of the match becomes more secure. We adopt the Root Mean Square Error (RMSE) of the matching point coordinates as an evaluation metric for the precision of matching points, given by

$$
\text{RMSE} = \sqrt{\frac{1}{m} \sum_{j=1}^{m} \left[ (x'_j - \hat{x}_j)^2 + (y'_j - \hat{y}_j)^2 \right]};
\tag{2}
$$

where $m$ is the number of matched points, $j$ is the index of the matched point, $(x'_j, y'_j)$ are the coordinates of the $j$-th matching point on Ref_Img_1, and $(\hat{x}_j, \hat{y}_j)$ are the coordinates of the $j$-th matching point on Target_Img.

To screen out the reference image that best fits the target image, we construct a scoring mechanism based on the number of matching points and matching accuracy, as shown in Equation (3). In this mechanism, the level of the score directly reflects the confidence of the match between the reference image and the target image, with higher scores indicating higher confidence. The matching score of the $i$-th reference image, $\text{Score}_i$, is calculated as

$$
\text{Score}_i = \frac{\min(\text{RMSE}_1, \text{RMSE}_2, \ldots, \text{RMSE}_n)}{\text{RMSE}_i} + \frac{m_i}{\max(m_1, m_2, \ldots, m_n)};
\tag{3}
$$

where $n$ is the number of images in the reference image set, $i$ is the reference image index, $m_i$ is the number of matching points between the $i$-th reference image and the target image, and $\text{RMSE}_i$ is the matching accuracy obtained from the $i$-th reference image and the target image.

The index $k$, corresponding to the maximum value of the score, is

$$
k = \arg\max(\text{Score}_i), \quad 1 \leq i \leq n.
\tag{4}
$$

The steps for solving the crater coordinate in the target image are as follows:

1. Feature matching. The Ref_Img and Target_Img are input into SuperPoint, and the output feature points and descriptors are used as input for SuperGlue to output the matched points.

2. Image transformation. The matched points are used to solve for the homography transformation matrix $H$ between Ref_Img and Target_Img. Matrix $H$ is applied to transform Ref_Img and obtain Ref_Img_1. At the same time, matrix $H$ is applied to convert the coordinates of the craters in the reference image and record the transformed coordinates.

3. Secondary feature matching. The SuperPoint and SuperGlue algorithms perform feature detection and matching on Ref_Img_1 and Target_Img, the transformation matrix $H$ is calculated, the number of matched points $m$ is recorded, and the RMSE of the matched point coordinates is calculated.

4. Calculate scores and select the best reference image. All reference images are analyzed iteratively, repeating steps 1 to 3, and the score of each matching is calculated according to Equation (3). The reference image with the highest score is then determined.

5. Determine the coordinates of the craters in the target image. After selecting the best reference image, to improve matching accuracy, multiple iterations of matching and transformation are performed based on the results of step 3 until the RMSE converges. The coordinates of the crater obtained from the last transformation correspond to the position of the crater in the target image.

3. Results and Discussion

To verify the validity and general applicability of our proposed method, we select images of the crater Aristillus near the Apollo 15 reflector and the crater Bianchini near the Luna 17 reflector under different lighting conditions and carry out validation experiments. Bianchini, being close to the lunar limb, shows significant variation in visible lunar surface features, while Aristillus, located in a more central region of the Moon, has more regular shapes. The matching of image features and determination of crater locations for Aristillus and Bianchini are shown in Fig. 7 [FIGURE:7] and Fig. 8 [FIGURE:8], respectively. There are significant differences between the reference and target images in terms of location, angle, and lighting conditions before feature matching. After feature matching and transformation of the reference image through translation, rotation, scaling, and other transformations via the transformation matrix, the obtained images are highly compatible with the target images, and the calculated crater positions fall precisely on the center of the corresponding crater positions in the target images, proving the validity of the crater position coordinates.

The accuracy of image feature matching points for Aristillus and Bianchini under different lighting conditions is given in Table 2 [TABLE:2]. As discussed in Section 2.2, one pixel in the image corresponds to 0.6383″, and the maximum RMSE value is 1.583 pixels, equivalent to approximately 1″, while the minimum value is only 0.735 pixels, equivalent to 0.47″. The RMSE is the integrated error of pixel coordinates, and its correlation with the telescope's integrated pointing accuracy can be analyzed in terms of the effect on the telescope's azimuth axis and elevation axis. When the matching error comes only from the image height direction, it only affects the telescope's elevation axis, and the pointing accuracy of the elevation axis equals the matching error. When the matching error comes only from the image width direction, it only affects the telescope's azimuth axis, and the pointing accuracy of the azimuth axis equals the matching error divided by the cosine of the current elevation angle. Considering a telescope with an elevation axis of 60° as an example, the integrated pointing accuracy results are shown in Table 3 [TABLE:3]. When lighting conditions are poor and lunar surface feature distortions are severe, the calculation accuracy of the telescope's pointing error is at its worst at 2″ (see Table 2 and Table 3). With good image conditions, the calculation accuracy of the telescope's pointing error is less than 1″, with a minimum value of approximately 0.5″, which meets the pointing requirement for LLR and further confirms the validity of the calculated crater positions. It also demonstrates the robustness and accuracy of the image feature matching method, which maintains good computational accuracy even in the presence of large distortion of image features at the lunar limb.

Each target image is matched with all reference images, the best match is filtered, and the crater position is calculated. The runtime of the program is shown in Table 4 [TABLE:4]. The basic process of pointing correction for the telescope is to stop tracking the current LCCR, switch to the target crater, wait for the telescope tracking to stabilize, take a photo of the lunar surface feature, calculate the position of the crater in the image, calculate the telescope pointing bias, stop tracking the crater, and continue to track the original LCCR and carry out the observation based on the correction of the pointing bias. The whole pointing correction process is time-consuming, and the time taken by the lunar surface feature matching program is acceptable for it. The program can be further optimized to enhance its operational efficiency.

The matching points do not appear in the dark areas of the lunar surface images (see Fig. 7 and Fig. 8), and feature matching points exist only in the light areas. Combined with the accuracy data in Table 2, when dark areas of a lunar surface image account for a large proportion, the matching process becomes a local matching rather than whole-image matching, resulting in a decrease in matching accuracy. Therefore, when selecting lunar surface features near the LCCR, it is advisable to choose areas with the largest possible illuminated area to increase the distribution ratio of feature points, thereby improving matching accuracy. In addition, using the classification method in Section 2.2, the accuracy of classification can be further refined according to light conditions, especially for the three categories of NEL, NML, and MDT. This refinement aims to expand the sample size of the reference image library, ensuring that the target image can be matched with a more appropriate reference image, thereby improving the accuracy of calculated lunar crater coordinates in the target image.

Another point we would like to discuss is an overall scheme for applying our proposed methodology to LLR systems. During the LLR process, factors such as environmental temperature and telescope altitude angle change over time, causing temperature, gravity, and other factors to affect telescope pointing. To ensure pointing accuracy, pointing corrections need to be performed periodically (at intervals typically in the range of 15–20 min) when no valid data are captured. The LLR system is driven locally by the software used for our proposed method. When telescope pointing correction is needed, the LLR control system guides the telescope to track a given crater on the lunar surface. When telescope tracking is stable, a camera is used to take an image of the lunar surface, and the position of the crater in the image is calculated. Then, the off-target amount of the crater coordinates is calculated based on the crater position in the image and the theoretical position. Finally, based on this off-target amount, the telescope pointing bias is calculated and sent to the LLR control system for pointing correction.

4. Conclusion

Here, we conceptualize a processing scheme for calculating the pointing bias of an LLR system based on lunar craters. To accurately calculate the position of craters in lunar surface images, we propose a precise method for crater position calculation based on lunar feature matching. This method detects and matches common feature points between reference and target images using the deep learning algorithms SuperPoint and SuperGlue to solve for the transformation matrix between these feature points. It then uses this matrix to calculate the position of craters in the target image. We also design a scoring mechanism to select the best-matching reference image from a reference image library.

Experiments conducted with craters near the Apollo 15 and Luna 17 reflectors show that the crater coordinates calculated by the proposed method fall at the center of the craters in the target image, with the maximum image matching error being about 1″ and the minimum as low as 0.47″. This demonstrates good computational accuracy. Theoretically, the integrated pointing error of the telescope after correction by this method is approximately 1″, meeting the pointing requirements for LLR.

We also find that selecting lunar surface features with larger illuminated areas near the LCCR can increase the distribution proportion of feature points in the image, which is expected to improve matching accuracy. Additionally, the computational accuracy of lunar crater coordinates in the target image may be further enhanced by refining the classification of reference images and expanding the sample size of the reference image library to match the target image with more suitable reference images. To verify these speculations, future research will require more in-depth analytical demonstrations and experiments.

Acknowledgments

This research was funded by the Natural Science Foundation of Jilin Province (20220101125JC) and the National Natural Science Foundation of China (12273079).

Author Contributions

Yanning Zheng conceived the ideas, implemented the study, and wrote the paper. Xue Dong, Xingwei Han, and He Dong performed manuscript review, editing, and mentoring. Zhipeng Liang and Jian Gao made suggestions for the optimization of the methodology. Bowen Guan and Liyan Sun conducted the screening and categorization of the experimental data. All authors read and approved the final manuscript.

Declaration of Interests

The authors declare no competing interests.

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