Universal super-wide field image celestial position measurement analysis method

Abstract

The application discloses a general super-large field of view image celestial body position measurement 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-target optimization function based on an initial solution of the single image, and obtaining the initial solution of the single image; S3, based on the initial solution of the single image, obtaining an accurate image optical center, zenith position parameters and distortion items, establishing the general super-large field of view image celestial body position measurement analysis model, and using the model to realize super-large field of view image celestial body position measurement analysis of all images taken by the device. The method can automatically solve all images under the same device extremely fast only by using one image. The derivation of the formula of the method is based on strict coordinate conversion and parameters with physical meaning, does not need to train a model, has stronger universality, and can be applied to all all-sky 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 captured celestial objects in astronomical images. In other words, they need to obtain the right ascension and declination (RA, Dec) of the celestial object captured at a specific pixel position (x, y) in the image. In most cases, astronomical measurements can be performed by solving the World Coordinate System (WCS) method, comparing the observed celestial position with a 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 an extremely large field of view (usually referring to images with a field of view exceeding 20°), the projection relationship is often nonlinear, making it difficult to directly use polynomial solutions.

[0003] Because the celestial sphere is hemispherical, its projection onto a tangent plane is more suited to polar coordinates. Therefore, Ceplecha (1987) proposed a method using polar coordinates, describing a specific pixel position (x, y) as polar coordinates (θ, r). When the center of the polar coordinates is the zenith, simply changing the polar coordinate reference axis yields the altitude and azimuth (Alt, Az). These can then be converted to right ascension and declination (RA, Dec) based on the observation time and geographic latitude.

[0004] Polar coordinate conversion requires that the zenith position and the image optical center completely coincide with each other, which cannot be applied to all ultra-large field of view images. et al. (1995) proposed an improved polar coordinate method. Taking into account the deviation between the zenith position and the image optical center, two different coordinate systems were established. Spherical trigonometry was used to solve the transformation relationship between the two coordinate systems to obtain (Alt, Az). This method comprehensively considers camera distortion, lens distortion, and the deviation between the zenith position and the optical center of ultra-wide field-of-view imaging equipment, and can accurately determine the position of celestial objects in ultra-wide field-of-view images. However, due to the comprehensive considerations of this method, as many as 13 parameters need to be solved, and the formula is highly nonlinear, making it difficult to solve.

[0005] To facilitate the solution, Barghini et al. (2019) et al. (1995) improved on the technical solution by replacing the camera and lens distortion terms with known lens projection relationships, reducing nonlinearity and the number of parameters, making the solution easier. However, this method does not account for the errors caused by the distortion terms, so the errors in the results in elevation and azimuth can reach more than 2°, making it less accurate for celestial position measurements.

[0006] Tian et al. (2022) proposed using machine learning to correct the distortion term in Barghini's technique. However, machine learning methods require a large number of initial samples, and the machine learning model is not universal and cannot be applied to other observation equipment.

[0007] At present, there is no universal and high-precision method to solve the position of celestial objects 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. Obtain the pixel coordinates of the celestial body and the initial optical center of a single image;

[0011] S2. Based on the pixel coordinates, establishing an initial mapping from the pixel coordinates to the horizontal coordinates; based on the initial mapping, establishing a multi-objective optimization function based on the initial solution of the single image, and iteratively solving the multi-objective optimization function; converting the horizontal 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] Where (x, y) represents the pixel coordinate position of the celestial body, (x0, y0) represents the initial optical center of the image, and r represents the distance from the coordinate point to the initial optical center of the image; (b, u) represents the projected 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 projected coordinate azimuth from true north, E is the deviation between the zenith and the optical center in azimuth, and ε is the deviation between the zenith and the optical center in altitude; (a, z) represents the horizontal coordinates; and (k1, k2, k3, k4) are the distortion term parameters.

[0016] Preferably, the pixel coordinates of the celestial body in step S1 are obtained 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 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 horizontal coordinates;

[0019] S22. Based on the initial mapping, a multi-objective optimization function based on the initial solution of a single image is established, the distortion term of equation (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 equation (4) are solved 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 the 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 includes 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 projected polar coordinate 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 projected polar coordinates u;

[0025] S223. Based on the initial zenith position parameters, obtain the projected 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 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.

[0027] Preferably, step S3 performs preliminary cross-matching with a reference star catalog based on the initial solution of the single image to obtain a mapping point, comprising 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 the 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 them with the reference celestial coordinates (RA_ref, Dec_ref) of the celestial body in the standard reference star catalog, and then establishing a mapping from (x, y)→(RA_ref, Dec_ref) to obtain a mapping point.

[0028] Preferably, when the optical center is inaccurate, an additional sinusoidal signal will be present in the azimuth residual when compared with the standard star catalog. Therefore, the amplitude of this sinusoidal waveform can be used as an indicator to iteratively solve the pixel points near the optical center. The point where the amplitude is minimized is the accurate optical center.

[0029] Preferably, the model obtained by the above three steps can be directly applied to all images taken by the device, and all parameters in the model have physical meaning. Therefore, if there is a change 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 extremely versatile and can be applied to any image with an all-sky field of view. This method is extremely scalable and can be applied not only 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 celestial body position, 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 unmanned automated site measurement.

[0032] The derivation of the formulas 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 an ultra-large field of view, which helps to study 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, it has stronger versatility and can be applied to all all-sky cameras.

[0034] This solution 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 its practicality and operability. BRIEF DESCRIPTION OF THE DRAWINGS DETAILED DESCRIPTION

[0035] To better illustrate the present disclosure, numerous specific details are provided in the following detailed description. Those skilled in the art will appreciate that the present disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art are not described in detail in order to highlight the main points of the present disclosure.

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

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

[0038] S2. Based on the pixel coordinates, establishing an initial mapping from the pixel coordinates to the horizontal coordinates; based on the initial mapping, establishing a multi-objective optimization function based on the initial solution of the single image, and iteratively solving the multi-objective optimization function; converting the horizontal 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] Where (x, y) represents the pixel coordinate position of the celestial body, (x0, y0) represents the initial optical center of the image, and r represents the distance from the coordinate point to the initial optical center of the image; (b, u) represents the projected 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 projected coordinate azimuth from true north, E is the deviation between the zenith and the optical center in azimuth, and ε is the deviation between the zenith and the optical center in altitude; (a, z) represents the horizontal coordinates; and (k1, k2, k3, k4) are the distortion term parameters.

[0043] In one embodiment, the pixel coordinates of the celestial body in step S1 are obtained in batches by the photometric software SourceExtractor; the initial optical center of the image is determined manually or by the OpenCV software package using a circle center determination method.

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

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

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

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

[0048] S212. Convert 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 object is confirmed by manual recognition.

[0050] In one implementation, for other, smaller, and extra-large field-of-view images, a combination of manual and automated methods is employed, using software such as astrometry.net to roughly calculate the celestial coordinates of celestial objects. Alternatively, the extra-large field-of-view images are sliced ​​and diced to determine the celestial coordinates. Because automated software performs poorly for extra-large field-of-view images, manual correction of the selected celestial coordinates is also required.

[0051] S22. Based on the initial mapping, the distortion term of the multi-objective optimization function (4) 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 the 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 projected polar coordinate 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 projected polar coordinates u;

[0055] S223. Based on the initial zenith position parameters, obtain the projected 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 coordinate 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 horizontal coordinates (a, z), and the convergence condition of the iteration is that the error change between the iteration parameters (a, z) and the reference horizontal coordinates (a_ref, z_ref) is less than 0.3%.

[0059] S23. Based on the observation time and geographic coordinates of the image, convert the observed horizontal coordinates (a, z) 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, a preliminary cross-matching is performed based on the initial solution of the single image and 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 object 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 geographic location and observation time. After cross-matching with the reference celestial coordinates (RA_ref, Dec_ref) of the celestial object in the standard reference star catalog, a mapping from (x, y) to (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. Alternatively, software calculation can be written based on the principle.

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

[0066] In one embodiment, when the optical center is inaccurate, an additional sinusoidal signal may be present in the azimuth residual when compared with a standard star catalog. Therefore, the amplitude of this sinusoidal waveform can be used as an indicator to iteratively calculate the value of the pixel points near the optical center. The point at which this amplitude is minimized is the precise 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 coordinates.

[0068] In one embodiment, the model obtained through the above three steps can be directly applied to all images captured by the device, and all parameters in the model have physical meaning. Therefore, if there is a change 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 embodiments of the present application. The above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, practical applications, or improvements to the technology in the market, or to enable other persons skilled in the art to understand the embodiments disclosed herein.

Claims

1. A general method for analyzing the position of celestial bodies using ultra-large field of view images, characterized in that: The steps include: S1. Obtain 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 horizontal coordinates; Establishing a multi-objective optimization function based on an initial solution of a single image based on the initial mapping, and iteratively solving the multi-objective optimization function; converting the horizontal coordinates to celestial coordinates to obtain an initial solution of the single image; 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 model is used to implement celestial body position measurement and analysis of all ultra-large field of view images captured 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: Where (x, y) represents the pixel coordinates of the celestial body, (x0, y0) represents the initial optical center of the image, and r represents the distance from the coordinate point to the initial optical center of the image; (b, u) represents the projected 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 projected coordinate azimuth from true north, E is the deviation between the zenith and the optical center in azimuth, and ε is the deviation between the zenith and the optical center in altitude; (a, z) represents the horizontal coordinates; and (k1, k2, k3, k4…) are 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 circle center determination method.

4. The method according to claim 2, characterized in that Step S2 of obtaining the initial solution for a single image includes the following steps: S21, establishing an initial mapping from pixel coordinates to horizontal coordinates; S22. Based on the initial mapping, a multi-objective optimization function based on the initial solution of a single image is established, the distortion term of equation (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 equation (4) are solved 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 the initial solution of the 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 a 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 coordinate 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 projected polar coordinates u; S223. Based on the initial zenith position parameters, obtain the projected 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 projected 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 S2 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 them with the reference celestial coordinates (RA_ref, Dec_ref) of the celestial body in the standard reference star catalog, establishing a mapping from (x, y) → (RA_ref, Dec_ref), and obtaining mapping points.

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