Universal ultra-large field-of-view image celestial body position measurement and analysis method

Abstract

The invention discloses a universal ultra-large field-of-view image celestial body position measurement and analysis method. The method comprises the following steps: S1, acquiring pixel coordinates of a celestial body and an initial optical center of a single image; s2, establishing a multi-objective optimization function based on the initial solution of the single image to obtain the initial solution of the single image; and S3, based on the initial solution of the single image, obtaining an accurate image optical center, zenith position parameters and distortion terms, establishing the universal ultra-large field-of-view image celestial body position measurement and analysis model, and using the model to realize ultra-large field-of-view image celestial body position measurement and analysis of all the equipment. According to the method, only one image is needed, and all images under the same equipment can be rapidly and automatically solved. The derivation of the formula of the method is based on rigorous coordinate conversion and parameters with physical significance, a model does not need to be trained, and the method has higher universality and can be suitable for all all-day cameras.

Description

Technical Field

[0001] The present application relates to a method for determining the position of a celestial body, and in particular to a universal method for analyzing the position of a celestial body using an ultra-large field of view image. Background Art

[0002] In optical astronomical observations, astronomers need to accurately locate the position of celestial bodies in astronomical images, that is, they need to obtain the right ascension and declination (RA, Dec) of the celestial body captured at a specific pixel position (x, y) in the image. In most cases, astronomical measurements can be made by solving the world coordinate system (WCS) method, comparing the observed position of the celestial body with the known reference star catalog, and then solving the coordinate transformation relationship through polynomial fitting. This method requires that the image projection is linear and works better for telescopes with a smaller field of view. However, for telescope images with a very large field of view (usually images with a field of view of more than 20°), the projection relationship is usually nonlinear, and it is difficult to directly use polynomial solutions.

[0003] Since the celestial sphere is hemispherical, its projection on the tangent plane is more suitable for description using polar coordinates. Therefore, Ceplecha (1987) proposed a method of using polar coordinates to describe a specific pixel position (x, y) as polar coordinates (θ, r). When the center of the polar coordinates is the zenith, the altitude and azimuth (Alt, Az) can be obtained by simply changing the reference axis of the polar coordinates, and then converted to right ascension and declination (RA, Dec) according to the observation time and geographic latitude.

[0004] The polar coordinate conversion method requires that the zenith position completely coincides with the optical center of the image, and cannot be applied to all images with a very large field of view. et al. (1995) proposed an improved solution for the polar coordinate method. Considering the deviation between the zenith position and the optical center of the image, two different coordinate systems are established, and the conversion relationship between the two coordinate systems is solved by spherical trigonometry to obtain (Alt, Az). This method comprehensively considers the camera distortion, lens distortion, zenith position and optical center deviation of the ultra-large field of view image observation equipment, and can accurately solve the position of celestial bodies in ultra-large field of view images. At the same time, because this method comprehensively considers more problems, the number of parameters that need to be solved has reached as many as 13, and the nonlinearity of the formula is high, so it is more difficult to solve.

[0005] To facilitate the solution, Barghini et al. (2019) et al. (1995) improved the technical solution by replacing the distortion term of the camera and lens with the known lens projection relationship, reducing the nonlinearity and the number of parameters, making the solution easier. However, this method does not take into account the error caused by the distortion term, so the error in the altitude and azimuth angle can reach more than 2°, which is poor in accuracy for celestial position measurement.

[0006] Tian et al. (2022) proposed that the distortion term problem in Barghini's technical solution can be corrected through machine learning methods. However, machine learning methods require a large number of preliminary samples, and the machine learning model is not universal and cannot be applied to other observation equipment.

[0007] Currently, there is no universal and high-precision method to solve the position of celestial bodies in ultra-large field of view images. Summary of the invention

[0008] In order to solve the above technical problems, the purpose of this application is to provide a universal method for analyzing the position of celestial bodies in ultra-large field of view images.

[0009] The technical solution adopted in this application is: a universal ultra-large field of view image celestial body position measurement and analysis method, comprising the following steps:

[0010] S1, obtaining the pixel coordinates of the celestial body and the initial optical center of a single image;

[0011] S2. Based on the pixel coordinates, establish an initial mapping from the pixel coordinates to the horizon coordinates; based on the initial mapping, establish a multi-objective optimization function based on the initial solution of the single image, and iteratively solve the multi-objective optimization function; convert the horizon coordinates to celestial coordinates to obtain the initial solution of the single image;

[0012] S3. Based on the initial solution of the single image, a preliminary cross-match is performed with the reference star catalog to obtain mapping points; based on the mapping points, the multi-objective optimization function is iteratively solved to obtain accurate zenith position parameters and distortion term parameters; using the amplitude of the sinusoidal waveform as an indicator, the pixel points near the initial optical center of the single image are iteratively solved to obtain the accurate image optical center; based on the accurate image optical center, zenith position parameters and distortion terms, the universal ultra-large field of view image celestial body position measurement and analysis model is obtained, and the trained model is used to realize the celestial body position measurement and analysis of all ultra-large field of view images taken by the device, and the pixel coordinates of the celestial body are converted into celestial coordinates.

[0013] Preferably, the multi-objective optimization function established in step S2 is expressed as:

[0014]

[0015] Wherein, (x, y) represents the position of the pixel coordinates of the celestial body, (x0, y0) represents the initial optical center of the image, r represents the distance from the coordinate point to the initial optical center of the image; (b, u) represents the projection polar coordinates with the initial optical center of the image (x0, y0) as the pole; (E, a0, ε) represents the zenith position parameters, a0 is the deviation of the projection coordinate azimuth from true north, E is the deviation of the zenith and the optical center in azimuth, and ε is the deviation of the zenith and the optical center in altitude; (a, z) represents the horizontal coordinates; (k1, k2, k3, k4) are the distortion term parameters.

[0016] Preferably, the acquisition of pixel coordinates of celestial bodies in step S1 is completed in batches by photometry software Source Extractor; the initial optical center of the image is determined manually or by an OpenCV software package using a circle center determination method.

[0017] Preferably, step S2 of obtaining an initial solution for a single image comprises the following steps:

[0018] S21, establishing an initial mapping from pixel coordinates to horizon coordinates;

[0019] S22, based on the initial mapping, establishing a multi-objective optimization function based on the initial solution of a single image, replacing the distortion term of formula (4) of the multi-objective optimization function with a known projection relationship, solving the initial zenith position parameters by fitting; solving the distortion term parameters (k1, k2, k3, k4) in formula (4) by iteration;

[0020] S23. Based on the observation time and geographic coordinates of the image, the observed horizontal coordinates (a, z) are converted to celestial coordinates (RA, Dec) to obtain an initial solution for a single image.

[0021] Preferably, for a fisheye lens, the projection relationship is u=F·arcsin(r / R), where F and R are derived from the known camera pixel size and film scale.

[0022] Preferably, solving the distortion term parameters comprises the following steps:

[0023] S221, based on the pixel coordinates of the celestial body and the initial optical center of the single image, the projection relationship u=F·arcsin(r / R) is used to replace the formula (4) of the multi-objective optimization function to obtain the initial projection polar coordinates u with the initial optical center of the image as the pole;

[0024] S222, obtaining initial zenith position parameters based on the initial mapping and initial projection polar coordinates u;

[0025] S223, based on the initial zenith position parameters, obtaining the projection polar coordinates (u, b) and the distance r from the coordinate point to the initial optical center of the image;

[0026] S224. Obtain distortion term parameters based on the obtained projection polar coordinates u and the distance r from the coordinate point to the initial optical center of the image. Repeat the above steps for multiple iterations to obtain accurate zenith position parameters and distortion term parameters.

[0027] Preferably, step S3 performs preliminary cross-matching with a reference star catalog based on the initial solution of the single image to obtain mapping points, including the following steps: based on the initial solution of the single image, solving the pixel position (x, y) of the celestial body in the image to obtain initial horizontal coordinates (a, z), then converting them into celestial coordinates (RA_cal, Dec_cal) according to the geographical location and observation time, and cross-matching with the reference celestial coordinates (RA_ref, Dec_ref) of the celestial body in the standard reference star catalog. , Establish a mapping from (x, y) → (RA_ref, Dec_ref) to obtain a mapping point.

[0028] Preferably, when the optical center is not accurate, there will be an additional sinusoidal signal in the residual in the azimuth direction when compared with the standard star catalog. Therefore, the amplitude of the sinusoidal waveform can be used as an indicator to iteratively solve the pixel points near the optical center, and the point with the minimum amplitude is the accurate optical center.

[0029] Preferably, the model obtained by solving the above three steps can be directly applied to all images taken by the device, and all parameters in the model have physical meanings. Therefore, if there are changes in the camera, only the parameters of the changed part need to be re-solved to continue using the model.

[0030] Beneficial effects of this application:

[0031] By integrating existing methods and introducing distortion terms, the method provided in this application can easily solve the position of celestial bodies in ultra-large field of view images while meeting accuracy requirements, solving the problem that there is currently no universal and accurate method for astronomical measurement of ultra-large field of view images. This method is highly versatile and can be applied to any image with an all-sky field of view. This method has extremely strong scalability and is not only applicable to all-sky cameras, but also to all ultra-large field of view images with nonlinear central symmetric projections. This method only requires one image to complete the solution of the position of celestial bodies, and after completing the initial preparations, all images under the same device can be automatically solved very quickly. It has great application prospects in application scenarios that require automation, such as unattended automated site measurement.

[0032] The derivation of the formula in this method is based on rigorous coordinate transformation and physically meaningful parameters. The method is generalizable. Compared with existing solutions, it is not limited to all-sky cameras and can be applied to all images with ultra-large fields of view, which is helpful for studying the optical properties of the device itself.

[0033] The coordinate transformation and distortion terms of this method are universal and do not require model training. Compared with machine learning methods, this method has stronger universality and can be applied to all all-sky cameras.

[0034] This scheme proposes a specific method to confirm the initial parameters and provides steps to more accurately find the optical center and zenith position of the image, which greatly improves the practicality and operability. BRIEF DESCRIPTION OF THE DRAWINGS DETAILED DESCRIPTION

[0035] In order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the main purpose of the present disclosure.

[0036] A general method for analyzing the position of celestial bodies in ultra-large field of view images comprises the following steps:

[0037] S1, obtaining the pixel coordinates of the celestial body and the initial optical center of a single image;

[0038] S2. Based on the pixel coordinates, establish an initial mapping from the pixel coordinates to the horizon coordinates; based on the initial mapping, establish a multi-objective optimization function based on the initial solution of the single image, and iteratively solve the multi-objective optimization function; convert the horizon coordinates to celestial coordinates to obtain the initial solution of the single image;

[0039] S3. Based on the initial solution of the single image, a preliminary cross-match is performed with the reference star catalog to obtain mapping points; based on the mapping points, the multi-objective optimization function is iteratively solved to obtain accurate zenith position parameters and distortion term parameters; using the amplitude of the sinusoidal waveform as an indicator, the pixel points near the initial optical center of the single image are iteratively solved to obtain the accurate image optical center; based on the accurate image optical center, zenith position parameters and distortion terms, the universal ultra-large field of view image celestial body position measurement and analysis model is obtained, and the trained model is used to realize the celestial body position measurement and analysis of all ultra-large field of view images taken by the device, and the pixel coordinates of the celestial body are converted into celestial coordinates.

[0040] In one embodiment, the multi-objective optimization function established in step S2 is expressed as:

[0041]

[0042] Wherein, (x, y) represents the position of the pixel coordinates of the celestial body, (x0, y0) represents the initial optical center of the image, r represents the distance from the coordinate point to the initial optical center of the image; (b, u) represents the projection polar coordinates with the initial optical center of the image (x0, y0) as the pole; (E, a0, ε) represents the zenith position parameters, a0 is the deviation of the projection coordinate azimuth from true north, E is the deviation of the zenith and the optical center in azimuth, and ε is the deviation of the zenith and the optical center in altitude; (a, z) represents the horizontal coordinates; (k1, k2, k3, k4) are the distortion term parameters.

[0043] In one embodiment, the acquisition of pixel coordinates of celestial bodies described in step S1 is completed in batches by photometry software SourceExtractor; the initial optical center of the image is determined manually or by the OpenCV software package using a method for determining the center of a circle.

[0044] In one embodiment, step S2 of obtaining an initial solution for a single image comprises the following steps:

[0045] S21, establishing an initial mapping from pixel coordinates to horizon coordinates;

[0046] The initial mapping from pixel coordinates to horizon coordinates is established in the following steps:

[0047] S211. Select bright stars with relatively uniform distribution and their pixel coordinates from the ultra-wide field of view image, and obtain their celestial coordinates from the standard reference star catalog. Usually, more than 20 bright stars are selected.

[0048] S212, converting the celestial coordinates into horizontal coordinates according to the observation time and the geographical location, thereby establishing an initial mapping from the pixel coordinates to the horizontal coordinates.

[0049] In one implementation, for all-sky camera images, since the number of bright stars in the sky is small and their features are obvious, the identity of each selected celestial body is confirmed by manual recognition.

[0050] In one implementation, for other large-field images with smaller fields of view, a combination of manual and automatic methods is used to roughly calculate the celestial coordinates of the celestial body using software such as astrometry.net, or the large-field image is cut into pieces to solve the celestial coordinates of the celestial body. Since the automatic software has a poor effect on large-field images, it is also necessary to manually correct the celestial coordinates of the selected celestial body.

[0051] S22, based on the initial mapping, the distortion term of formula (4) of the multi-objective optimization function is replaced by a known projection relationship, and the initial zenith position parameters are solved by fitting; the distortion term parameters (k1, k2, k3, k4) in formula (4) are solved by iteration;

[0052] In one embodiment, solving the distortion term parameters includes the following steps:

[0053] S221, based on the pixel coordinates of the celestial body and the initial optical center of the single image, the projection relationship u=F·arcsin(r / R) is used to replace the formula (4) of the multi-objective optimization function to obtain the initial projection polar coordinates u with the initial optical center of the image as the pole;

[0054] S222, obtaining initial zenith position parameters based on the initial mapping and initial projection polar coordinates u;

[0055] S223, based on the initial zenith position parameters, obtaining the projection polar coordinates (u, b) and the distance r from the coordinate point to the initial optical center of the image;

[0056] S224. Obtain distortion term parameters (k1, k2, k3, k4) based on the obtained projection polar coordinates u and the distance from the coordinate point to the initial optical center of the image.

[0057] In one embodiment, since the initial zenith position parameters obtained in step S222 are obtained based on the projection relationship, steps S221 to S224 are repeated for multiple iterations using the distortion term parameters and formula (4) of the multi-objective optimization function to obtain accurate zenith position parameters and distortion term parameters (k1, k2, k3, k4).

[0058] In one embodiment, the iteration parameters are selected as the horizon coordinates (a, z), and the convergence condition of the iteration is that the error change between the iteration parameters (a, z) and the reference horizon coordinates (a_ref, z_ref) is less than 0.3%.

[0059] S23. Based on the observation time and geographic coordinates of the image, the observed horizontal coordinates (a, z) are converted into celestial coordinates (RA, Dec).

[0060] In one embodiment, for a fisheye lens, the projection relationship is u=F·arcsin(r / R), where F and R are derived from the known camera pixel size and film scale.

[0061] In one embodiment, based on the initial solution of the single image, a preliminary cross-matching is performed with a reference star catalog to obtain mapping points, including the following steps:

[0062] Based on the initial solution of the single image, the pixel position (x, y) of the celestial body in the image is solved to obtain the initial horizontal coordinates (a, z), which are then converted into celestial coordinates (RA_cal, Dec_cal) according to the geographical location and observation time. After cross-matching with the reference celestial coordinates (RA_ref, Dec_ref) of the celestial body in the standard reference star catalog, a mapping from (x, y) → (RA_ref, Dec_ref) can be established.

[0063] The principle of crossmatch is to calculate the celestial coordinate distance of two celestial bodies. If the distance is less than a threshold, the two celestial bodies can be considered to be the same target. The threshold is usually related to the observation accuracy and can usually be taken as 3σ.

[0064] In one embodiment, cross matching can be performed using a variety of methods. For example, AstroPy provides a KDTree-based crossmatch software package for fast cross matching. Software calculation can also be written based on the principle.

[0065] In one embodiment, based on the mapping point (x, y)→(RA_ref, Dec_ref), when the multi-objective optimization function is iteratively solved, (RA_ref, Dec_ref) is first converted into reference horizon coordinates (a_ref, z_ref) according to the observation time and geographic coordinates, and then (x, y) and (a, z) are substituted into the principle formula to fit and iterate to solve various parameters.

[0066] In one embodiment, when the optical center is not accurate, there will be an additional sinusoidal signal in the residual in the azimuth direction when compared with the standard star catalog. Therefore, the amplitude of the sinusoidal waveform can be used as an indicator to iteratively solve the pixel points near the optical center, and the point with the minimum amplitude is the accurate optical center.

[0067] In one embodiment, based on the precise image optical center, zenith position parameters and distortion terms, a universal ultra-large field of view image celestial body position measurement and analysis model is obtained, and the trained model is used to implement the celestial body position measurement and analysis of all ultra-large field of view images taken by the device, and the pixel coordinates of the celestial body are converted into celestial sphere coordinates.

[0068] In one embodiment, the model obtained by solving the above three steps can be directly applied to all images taken by the device, and all parameters in the model have physical meanings. Therefore, if there are changes in the camera, only the parameters of the changed part need to be re-solved to continue using the model.

[0069] The above is a description of the preferred implementation of the present application, which is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or improvements to the technology in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A general method for analyzing the position of celestial bodies in ultra-large field of view images, characterized in that: The steps include: S1, obtaining the pixel coordinates of the celestial body and the initial optical center of a single image; S2. Based on the pixel coordinates, establish an initial mapping from the pixel coordinates to the horizon coordinates; Based on the initial mapping, a multi-objective optimization function based on an initial solution of a single image is established, and the multi-objective optimization function is iteratively solved; the horizontal coordinates are converted into celestial coordinates to obtain an initial solution of the single image; S3. Based on the initial solution of the single image, a preliminary cross-match is performed with the reference star catalog to obtain mapping points; based on the mapping points, the multi-objective optimization function is iteratively solved to obtain accurate zenith position parameters and distortion term parameters; using the amplitude of the sinusoidal waveform as an indicator, the pixel points near the initial optical center of the single image are iteratively solved to obtain the accurate image optical center; based on the accurate image optical center, zenith position parameters and distortion terms, a universal ultra-large field of view image celestial body position measurement and analysis model is obtained, and the model is used to implement the celestial body position measurement and analysis of all ultra-large field of view images taken by the device, and the pixel coordinates of the celestial body are converted into celestial coordinates.

2. The method according to claim 1, characterized in that The multi-objective optimization function established in step S2 is expressed as: Wherein, (x, y) represents the pixel coordinates of the celestial body, (x0, y0) represents the initial optical center of the image, r represents the distance from the coordinate point to the initial optical center of the image; (b, u) represents the projection polar coordinates with the initial optical center of the image (x0, y0) as the pole; (E, a0, ε) represents the zenith position parameters, a0 is the deviation of the projection coordinate azimuth from true north, E is the deviation of the zenith and the optical center in azimuth, and ε is the deviation of the zenith and the optical center in altitude; (a, z) represents the horizontal coordinates; (k1, k2, k3, k4) are the distortion term parameters.

3. The method according to claim 2, characterized in that The pixel coordinates of the celestial body described in step S1 are completed in batches by the photometric software Source Extractor; the initial optical center of the image is determined manually or by the OpenCV software package using the method of determining the center of a circle.

4. The method according to claim 2, characterized in that: Step S2: finding the initial solution for a single image includes the following steps: S21, establishing an initial mapping from pixel coordinates to horizon coordinates; S22, based on the initial mapping, establishing a multi-objective optimization function based on the initial solution of a single image, replacing the distortion term of formula (4) of the multi-objective optimization function with a known projection relationship, solving the initial zenith position parameters by fitting; solving the distortion term parameters (k1, k2, k3, k4) in formula (4) by iteration; S23. Based on the observation time and geographic coordinates of the image, the observed horizontal coordinates (a, z) are converted to celestial coordinates (RA, Dec) to obtain an initial solution for a single image.

5. The method according to claim 4, characterized in that For a fisheye lens, the projection relationship is u=F·arcsin(r / R), where F and R are derived from the known camera pixel size and film scale.

6. The method according to claim 5, characterized in that In step S22, solving the distortion term parameters includes the following steps: S221, based on the pixel coordinates of the celestial body and the initial optical center of the single image, the projection relationship u=F·arcsin(r / R) is used to replace the formula (4) of the multi-objective optimization function to obtain the initial projection polar coordinates u with the initial optical center of the image as the pole; S222, obtaining initial zenith position parameters based on the initial mapping and initial projection polar coordinates u; S223, based on the initial zenith position parameters, obtaining the projection polar coordinates (u, b) and the distance r from the coordinate point to the initial optical center of the image; S224. Obtain distortion term parameters based on the projection polar coordinate u and the distance r from the coordinate point to the initial optical center of the image. Repeat the above steps for multiple iterations to obtain accurate zenith position parameters and distortion term parameters.

7. The method according to claim 6, characterized in that Step S3 performs preliminary cross-matching with the reference star catalog based on the initial solution of the single image to obtain mapping points, including the following steps: based on the initial solution of the single image, the pixel position (x, y) of the celestial body in the image is solved to obtain the initial horizontal coordinates (a, z), and then converted into celestial coordinates (RA_cal, Dec_cal) according to the geographical location and observation time, and cross-matched with the reference celestial coordinates (RA_ref, Dec_ref) of the celestial body in the standard reference star catalog to establish a mapping point from (x, y) → Mapping of (RA_ref, Dec_ref) to obtain the mapping point.

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