A High-Accuracy Alignment Approach for Solar Images of Different Wavelengths

The sun emits electromagnetic radiation across various wavelengths, including infrared, visible light, ultraviolet, extreme ultraviolet, and X-rays. The observation of these different wavelengths provides insight into the physical processes occurring in the solar atmosphere at varying heights and temperatures. Therefore, multi-wavelength observations provide comprehensive and three-dimensional information for studying solar activity. Multi-wavelength observation is an important method for empirical solar physics research. Many solar activity phenomena exhibit different observational characteristics across different radiation wavelengths, with varying brightness and spatial forms. Image alignment at a single wavelength facilitates observation and study of the sun’s evolution at that specific wavelength. Conversely, performing image alignment across multiple wavelengths facilitates a comprehensive analysis of these activity phenomena, thereby helping to uncover the patterns of solar activity.

A telescope pointing and tracking system can be used for single-wavelength image stabilization (Staiger, 2013). This makes it possible to acquire information like heliocentric coordinates and align single-wavelength images. However, even if the telescope is designed to have sub-arcsecond pointing and tracking accuracy, problems such as bending of the optical support system due to its structure and thermal jitter can lead to inaccuracies during the observation process. Shimizu et al. (2007) utilized two Ultra Fine Sun Sensors (UFSS-A and UFSS-B) to detect satellite jitter. In fact, not only can jitter measurements be realized by hardware, but also various algorithms can be used to detect the jitter problem. Orange et al. (2014),for example, performed pointing jitter measurements on the Helioseismic and Magnetic Imager (HMI) and AIA on the Solar Dynamics Observatory (SDO) using a mutual correlation algorithm. In contrast to the alignment of single-wavelength images, multi-wavelength image alignment is the alignment of solar images from different wavelengths. These images usually originate from different wavelengths of the same observing instrument or from different wavelengths of different observing instruments. There may also be small offsets and pixel size differences between images taken at different wavelengths by the same instrument (Guglielmino et al., 2010). Shimizu et al. (2007) evaluated the internal offsets and size differences of the broadband filter imager of the Solar Optical Telescope (SOT). The alignment of images across different wavelengths poses a significant challenge due to the varied criteria associated with different wavelengths and instruments. This challenge is further compounded by the presence of scale, rotation, and translation differences, which can arise from instrument differences, wavelength differences, and disparities in image processing techniques. Therefore, various algorithms need to be developed to realize image alignment between different wavelengths.

Typically, image alignment involves the estimation of translation, rotation, and scaling. With the increasing demand for fine information in solar physics research, the accuracy requirements of image alignment have increased. At present, two primary classical methods are employed for solar image alignment. One is a region-based statistical method, which maximizes the correlation between images through the statistical information of image regions to achieve alignment. Cross-correlation (CC) and phase correlation (PC) are two common statistical alignment methods. Kuehner et al. (2010) achieved multi-wavelength alignment on HINODE/SOT by CC algorithm, and Berkebile-Stoiser et al. (2009) also used CC algorithm to achieve the image alignment of Dutch open telescope (DOT) and the transition region and coronal explorer (TRACE). However, CC performs well in sub-pixel accurate translation transformations but has difficulty in scale and rotation transformations. Conversely, the PC algorithm has been developed to achieve rotation and scale transformations between images using Fourier transform, Polar Coordinate transform, and Logarithmic transform (Reddy & Chatterji, 1996). Druckmüller (2009) achieved the alignment of coronal images during a total solar eclipse by measuring the translations, rotations, and scale factors between images with the PC algorithm. The IPC algorithm is an extension of the PC algorithm that utilizes the differential evolution algorithm to optimize the parameters and improve the effectiveness and accuracy of the algorithm (Hrazdíra et al., 2020). Another approach is the feature-based matching method, which utilizes salient regions, lines, or points in the image as distinct reference features. Lowe (1999, 2004) designed and developed the scale invariant feature transform (SIFT) method by combining the steps of feature point detection, vector generation, and matching search. In the solar photosphere, the spot features are obvious, thus prompting the application of the SIFT method in the field of astronomy (Yue et al., 2015). Yang et al. (2018) employed this method to align and localize the local solar magnetic field from the Huairou Solar Observatory (HSO) with full-disk solar magnetic field images from SDO/HMI. Later, Ji et al. (2019) employed SIFT to align HMI, GONG, and AIA 304 Å data with TiO and H$\alpha$ wavelength images acquired by NVST. In addition, SIFT was utilized to conduct a search for solar active regions (Jiang et al., 2022).

Optical flow (OF) represents a significant research direction within the domain of computer vision, with applications including target recognition and tracking. Recently, OF methods have also been applied to the alignment of solar images. Cai et al. (2022) utilized the OF algorithm to align the H$\alpha$ data of the NVST and evaluated its performance accuracy with raster images obtained from the Fast Imaging Solar Spectrometer (FISS) run by the GST. Moreover, the accuracy of the method is higher than the CC algorithm. Yang et al. (2022) used OF and SIFT algorithms to align the data from GST. However, both of them only utilized OF for translational direction. Also, the OF method can be used for high-resolution solar image reconstruction (Liu et al., 2022).

The distinct observational characteristics exhibited by different wavelengths are attributable to the varied solar atmospheres observed. To realize the alignment of different wavelengths of solar images, it is necessary to require similar structures between these wavelengths. However, in scenarios where the similarity between images is low, particularly when only a portion of the similar structure is present, achieving an accurate alignment between images can be a formidable challenge. Currently, the correlation algorithms are reliant on the similarity between images. If there are only partially similar structures between wavelengths, the accuracy of the correlation algorithm is decreases. For feature point matching algorithms, the higher the number of feature points, the higher the alignment accuracy usually is. In practical applications, the number of feature points in solar images is often small, and there is too much manual intervention, making it difficult to improve the alignment accuracy. When aligning images from the SDI 1216 Å and AIA 304 Å channels, the two datasets exhibit significant differences in spatial resolution, leading to inherently low global similarity. And regions and edge boundaries demonstrate limited structural correspondence (Figure 1). We use the Bhattacharyya (1943) coefficient to quantify the similarity between the images. A subsequent comparison of the intensity histograms of the solar images yielded a Bhattacharyya coefficient of 0.58 for SDI 1216 Å and AIA 304 Å and 0.79 for SUTRI 465 Å and AIA 304 Å. Therefore, the alignment effect of these two methods is not ideal.

In this paper, a novel solar image alignment approach based on dense OF and the RANSAC algorithm is proposed. It is able to realize region-based matching by using the partially similar structure between images on solar images where feature points are difficult to find. Then, it detects information such as translation, rotation, and scale. The paper is organized as follows: Section 2 describes the solar image data used for alignment; Section 3 details the alignment method using the example of SDI 1216 Å and AIA 304 Å alignment; Section 4 evaluates the alignment accuracy of the method and shows the results; and conclusions and discussions are given in Section 5.

Three data groups are selected for analysis: AIA 304 Å, SDI 1216 Å, and SUTRI 465 Å. And we can validate the proposed approach through these data. The three selected data groups are from neighboring regions of the solar atmosphere in adjacent time periods and have partially similar structural features. Among them, AIA 304 Å is primarily employed for the observation of the chromosphere and the transition region, SDI 1216 Å is utilized for the observation of the chromosphere-to-corona region of the Sun, and SUTRI 465 Å focuses on the upper transition region of the Sun. In this image alignment experiment, two groups of data are selected for the purpose of aligning different wavelengths: SUTRI 465 Å and AIA 304 Å data on November 14, 2022, and SDI 1216 Å and AIA 304 Å data on January 31, 2024.

The Atmospheric Imaging Assembly (AIA) was launched on February 11, 2010 from the Solar Dynamics Observatory (SDO) (Pesnell et al., 2012). The AIA is capable of observing ten different wavelengths, including seven extreme ultraviolet, two ultraviolet, and one visible wavelength. In in-orbit observations, AIA 304 Å has a spatial resolution of 1.5^′′ and a temporal resolution of 12 s, generating images of 4096$\times$4096 pixels². The image scale is 0.6^′′ pixel^-1 (Lemen et al., 2012).

The Lyman-alpha (Ly$\alpha$) Solar Telescope (LST) is one of the payloads on board the Advanced Space-based Solar Observatory (ASO-S), which was successfully launched on October 8, 2022 (Gan et al., 2023). The Solar Disk Imager (SDI) is an instrument onboard the LST with an operating spectrum of the Ly$\alpha$ line (1216 Å) (Chen et al., 2019). In the in-orbit observations, SDI has a spatial resolution of approximately 9.5^′′ (Chen et al., 2024) and a temporal resolution of 10 s, generating images of 4608$\times$4608 pixels². The image scale is 0.5^′′ pixel^-1 (Li et al., 2019).

The Solar Upper Transition Region Imager (SUTRI) was carried on board the SATech-01 satellite of the Chinese Academy of Sciences and was successfully launched on July 22, 2022, with an orbital period of 96 min (Zhang et al., 2024). SUTRI operates at the spectral line of Ne VII 465 Å and is mainly formed in the transition region in the solar atmosphere above 0.5 MK degrees. In the in-orbit observations, SUTRI has a spatial resolution of 8^′′ and a temporal resolution of 30 s, generating images of 2048$\times$2048 pixels². The image scale is 1.229^′′ pixel^-1 (Bai et al., 2023).

One image from each of the above three data groups is selected as a reference for the simulation of the alignment experiment. The generation of three test groups is achieved through the presetting of four parameters: scale, rotation angle, x-direction displacement, and y-direction displacement. Each test group contains 1000 randomly generated images that have undergone similarity transformation. The alignment evaluation of the single-wavelength simulated data is performed in Section 4 through three test groups.

Given the differences in the solar atmospheric regions observed by AIA 304 Å and SDI 1216 Å, we aim to align the two images by focusing on the similar regions that are common to both. It is evident that these two wavelengths contain similar structures within the quiet region of the sun. Utilizing the dense OF method facilitates the extraction of these similar structures. And due to the inherent limitations of the OF algorithm, its capacity to process a wide range of movement is constrained. Consequently, it is necessary to first perform a coarse alignment of the image prior to calculating the OF vectors. The utilization of the dense OF algorithm gives rise to mismatched OF vectors. These erroneous vectors are observed in active solar regions, such as flares, as well as in the sun’s limb, which are dissimilar regions. Therefore, it is necessary to eliminate these dissimilar regions with the help of the RANSAC algorithm and retain only the similar regions between images. Concurrently, the OF within these regions is employed as the acquired feature points to fit the similarity transformation model. Subsequently, the translation, rotation, and scale parameters between the images are derived.

In summary, the alignment method proposed in this paper consists of three main steps: First, the process of coarse alignment is executed by employing the FITS header file data of the two solar images; Second, the OF field of the two images is calculated following the coarse alignment; Lastly, the OF vectors within the OF field are used as feature points to fit the similarity transformation model using RANSAC. This process enables the derivation of the similarity transformation matrix and the realization of the fine alignment of the images. Figure 2 shows the specific registration process of AIA 304 Å and SDI 1216 Å.

We select two approaches for evaluation: Monte Carlo simulation and UABJM, to validate the alignment accuracy of our method. The three datasets in this experiment are obtained from different instruments with varying wavelengths. They inherently lack precise alignment relationships. So it becomes challenging to directly assess cross-band alignment accuracy. We therefore conduct preliminary evaluations using Monte Carlo simulation on single-wavelength data. Subsequently, we introduce the CC algorithm to compare alignment accuracy in translational dimensions. To demonstrate our method’s noise robustness, we perform additional validation by incorporating Gaussian noise into solar images. The UABJM method is employed for accuracy assessment for cross-wavelength alignment verification. The validity of UABJM for single-wavelength evaluation is first confirmed through comparison with Monte Carlo simulation results. Following this confirmation, we extend the UABJM methodology to evaluate different wavelength alignment accuracy.

The image alignment of different wavelengths of the sun has historically been a pivotal aspect in the research of the sun. In this paper, a solar image alignment approach is proposed. This approach is based on the dense OF and the RANSAC algorithm. It finds the feature points by extracting the OF fields on these similar structures. From there, it comes to fitting the similarity transformation model to realize the alignment. And the alignment test is performed employing two different groups of images, designated SUTRI 465 Å and AIA 304 Å, along with SDI 1216 Å and AIA 304 Å. Then, the accuracy of the alignment is evaluated based on the UABJM. The efficacy of the approach is demonstrated through its high degree of accuracy in performing single wavelength simulation alignment experiments, with scale errors $<$ 5$e^{-6}$, rotation errors $<$ 1^′′, and translation direction errors $<$ 0.01 pixels. This also indicates that the approach will exhibit high accuracy in the actual alignment work in a single wavelength. And it is expected to be applied in the future to measure the jitter problem of observation instruments. In the actual alignment work in different wavelengths, the accuracy will vary due to the similarity between the images. And the more similar structures, alignment has higher accuracy. We simply use the Bhattacharyya coefficient to quantify the similarity between the images. SUTRI 465 Å and AIA 304 Å exhibits higher similarity. The alignment of the SDI 1216 Å and AIA 304 Å images can be performed at the sub-pixel level. Furthermore, in the image alignment of SUTRI 465 Å with AIA 304 Å, which exhibits a higher degree of similarity, the pixel error is reduced even further. The rotated pixel errors for each of these alignments are observed to be larger. In fact, the rotated pixel error on the solar image is not as large as calculated. This is because the calculated error is the maximum rotation pixel error for the image, at the upper right corner of the image (by the lower left corner as the origin). And the fact that the sun is in the center of the image does not include that location.

The alignment approach proposed in this paper is not without its limitations in terms of practical application. Given the OF algorithm’s dependence on small motion, this approach is also constrained in its ability to measure large ranges (a significant image position discrepancy) and large motions (such as flares). In the specific code implementation, there exists a pixel window to detect motion. The dimensions of the window, therefore, must be carefully calibrated to ensure that the OF vectors do not exceed their boundaries and fail to identify similar regions. On the other hand, an large window can lead to a decline in the accuracy of the results. Therefore, determining the use of the appropriate window is also a problem, and the topic is not explored in this paper. At the same time, the approach also depends on the degree of similarity between images. When the degree of similarity between two solar images decreases, the accuracy of the approach will be reduced. For example, the degree of similarity between the SDI 1216 Å and AIA 304 Å images in the paper is lower than that between the SUTRI 465 Å and AIA 304 Å images, and the errors of the former are larger than those of the latter. Furthermore, when the degree of similarity between two solar images is minimal, the alignment approach is rendered ineffective. Therefore, the existence of similar structures between images and small image motion are important prerequisites for the method in this paper.

Our alignment approach is implemented in Python. And the AIA 304 Å and SDI 1216 Å alignment work is publicly available on GitHub: https://github.com/yushiweiliang/Alignment-Method.git.

We acknowledge the use of data from the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO), the Solar Disk Imager (SDI) of the Lyman-alpha (Ly$\alpha$) Solar Telescope (LST), and the Solar Upper Transition Region Imager (SUTRI). We also appreciate all the help from the colleagues in the laboratory team. This work is supported by the National Natural Science Foundation of China under grant 12373115, the Yunnan Key Laboratory of Solar Physics and Space Science under the number 202205AG070009, and the Yunnan Revitalization Talent Support Program under the numbers 202305AS350029 and 202305AT350005.