A method of marking a space ruling target

Abstract

The application relates to the technical field of image processing, and specifically provides a marking method for a space scribe target, which comprises the following steps: acquiring a scientific image containing stars, acquiring the time stamp of each pixel in the scientific image, selecting a plurality of reference stars in the scientific image, performing two-dimensional elliptical Gaussian function fitting on the plurality of reference stars, obtaining PSF information of each reference star and establishing a two-dimensional polynomial interpolation model, interpolating the state vector when the observation time is located between two ephemeris sampling epochs, obtaining the motion trajectory of the target in the image plane according to all ephemeris data, traversing the motion trajectory, generating a weight template after drawing a transverse Gaussian distribution on a supersampling canvas, creating a binary geometric mask image, and generating a rotating rectangular anchor frame, deducting the background of the target, calculating a weighted flow sum, and calculating the signal-to-noise ratio of an optimal matching filter. The marking method has high marking precision and can effectively eliminate domain differences.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and specifically provides a method for marking spatially drawn targets. Background Technology

[0002] With the rapid penetration of deep learning technology into the field of spatial object detection, object detection networks such as YOLO and Faster R-CNN have demonstrated significant advantages over traditional handcrafted feature methods such as Hough transform and inter-frame difference in the recognition of faintly lined objects, thanks to their powerful automatic feature extraction capabilities. However, the performance of deep learning models is highly dependent on the quantity, quality, and diversity of training data, and the construction of current spatial lined object image datasets is facing severe technical bottlenecks, which have become a core obstacle restricting further improvements in algorithm performance.

[0003] In low signal-to-noise ratio scenarios, spatially drawn targets appear as weak stripe signals in a single frame image, completely submerged in background noise and indistinguishable to the naked eye. Manual annotation is not only extremely inefficient but also suffers from severe label noise, including mislabeling, omissions, and boundary deviations, making it virtually impossible. Particularly when the target's trajectory overlaps with background stars (a phenomenon known as star-crossing), the target and stellar signals alias at the pixel level, making accurate separation by humans impossible. This results in severely distorted label boundaries and flow labeling deviations exceeding 50%, rendering a large amount of valuable observational data unusable. Even resorting to pure computer simulation to generate perfectly annotated synthetic samples avoids the annotation challenges but introduces a more fundamental "domain gap" problem. Existing simulation methods generally employ a constant Gaussian point spread function model across the entire field of view, which fails to characterize the spatial variation characteristics of the PSF caused by aberrations such as field curvature and astigmatism in optical systems. Motion blur modeling is simplified to uniform trailing, ignoring the time differences in line-by-line exposure during rolling shutter and changes in target velocity. Noise models are also approximated only with additive white Gaussian noise or Poisson noise, failing to realistically reflect complex noise statistical characteristics such as readout noise, dark current non-uniformity, and gradual changes in skylight and background. Models trained with such "overly idealized" synthetic data suffer from severe feature distribution mismatches and insufficient generalization ability when facing real observations, a problem that is widely acknowledged.

[0004] Meanwhile, high-precision annotation itself requires a precise spatiotemporal reference as support. The mapping of a target from celestial coordinates to pixel coordinates involves multiple steps, including precise ephemeris analysis, optical time correction, atmospheric refraction correction, Earth's rotation and polar motion, and WCS calibration. Existing technologies often simplify or ignore some correction terms, leading to the accumulation of motion trajectory prediction errors. For high-speed targets and rolling shutter sensors, positional deviations can reach several pixels, failing to provide reliable prior information for annotation. More importantly, existing technologies generally lack systematic quality control and verification mechanisms, cannot automatically identify and locate systematic deviations in annotation, and lack closed-loop feedback correction processes. Annotation quality relies entirely on human experience, making it uncontrollable and untraceable.

[0005] In summary, the current spatial line drawing target dataset has significant shortcomings in five dimensions: low signal-to-noise ratio annotation, star crossing processing, simulation physical realism, spatiotemporal reference accuracy, and quality verification. There is an urgent need for a systematic solution that takes a precise spatiotemporal reference as a constraint, spatial variation PSF modeling as the core, optimal matching filtering as a means, and multi-dimensional quality control as a guarantee. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method for marking spatially drawn targets. It utilizes known reference stars in scientific images to obtain the target's trajectory on the image plane. After drawing a horizontal Gaussian distribution on an oversampled canvas, it downsamples to generate a weighted template. After removing the background, the target is labeled. This method offers high accuracy and can resolve domain difference issues.

[0007] The present invention provides a method for marking spatially lined targets, comprising: S1: Obtain a scientific image containing stars and the timestamp of each pixel in it; S2: Establish the mapping relationship between the pixel coordinate system and the celestial coordinate system corresponding to stars in scientific images; S3: Select multiple reference stars in the scientific image and use the PSF information of the reference stars to establish a two-dimensional polynomial interpolation model: , ; in, Represents the fitting coefficient. Denotes the order of a polynomial. and Both represent polynomial exponent indices in non-negative integer form. and These represent the row index and column index of the covariance matrix, respectively. S4: Access the target ephemeris file based on the timestamp, and obtain the target's state vector by combining interpolation to generate the target's trajectory in the image plane; S5: Traverse the motion trajectory, obtain local PSF information using a two-dimensional polynomial interpolation model, draw a horizontal Gaussian distribution on the created oversampling canvas, and then downsample to generate a weight template. ; in, This indicates that after the oversampled canvas is restored to the original image resolution through downsampling, the coordinates are... The unnormalized weight values ​​obtained at that point This represents the summation of all pixel coordinates within the coverage area of ​​the downsampled weighted template; S6: Create a binary geometric mask image and use a weighted template to calculate the weighted centroid coordinates of the target; Generate a rotating rectangular anchor frame: ; in, Indicates the center coordinates of the rotated rectangular anchor frame. This represents the lateral width perpendicular to the direction of the motion trajectory. It represents the longitudinal length along the direction of the motion trajectory. Indicates the rotation angle; After removing the background of the target, calculate the weighted sum of flows: ; in, This represents the pixel value after background subtraction. The normalized weight template is represented at the th line, number Weight values ​​at column pixels; Calculate the signal-to-noise ratio of the optimal matched filter: ; in, Indicates noise level; When the motion trajectory overlaps with stars in the background, the source of pollution is identified using a star catalog, and the weights of the polluted pixels are reset to zero; or the fitted PSF model of the stars in the background is subtracted in advance.

[0008] Preferably, the labeling method further includes S7: performing quality verification on the labeling results, including residual analysis, position verification, and photometric quality assessment; The marking is considered valid when all of the following conditions are met: Firstly, the skewness of the residual region must meet the following requirements. Secondly, systematic error. satisfy Pixels; the third is the saturation index. To meet .

[0009] Preferably, when the marking is unqualified, the marking result is corrected according to different failure characteristics: When there are ephemeris errors or WCS zero-point deviations, the motion trajectory is corrected iteratively or the WCS is recalibrated; when there are PSF model scaling errors, the PSF parameters are adjusted or the model is remodeled; when there are background estimation biases, the background region is reselected to achieve correction.

[0010] Preferably, the original image containing the star is acquired, and the original image is radiometrically calibrated to obtain a scientific image; The expression for the radiometric calibration of the original image is: , in, This represents the corrected scientific image. Represents the original image. Indicates a dark frame. Indicates a normalized flat field. This represents the bad pixel mask.

[0011] Preferably, the weighted centroid coordinates of the target are calculated using a weighted template: ; in, Represents pixel coordinates, Represents the weight template value. Represents a geometric mask. This represents the summation of all pixels within the area covered by the binary geometric mask.

[0012] Preferably, the method for obtaining PSF information is as follows: Select multiple reference stars in the scientific image, and fit a two-dimensional elliptic Gaussian function to each reference star: , in, Indicates amplitude, Represents a pixel coordinate vector. Indicates the PSF center, The covariance matrix is ​​represented; the two-dimensional elliptic Gaussian function is used to describe the PSF information of the reference star in scientific images; A two-dimensional polynomial interpolation model is established using PSF information from all reference stars: , ; in, Represents the fitting coefficient. Denotes the order of a polynomial. and Both represent polynomial exponent indices in non-negative integer form. and These represent the row index and column index of the covariance matrix, respectively.

[0013] Preferably, the state vector includes a position vector and a velocity vector, wherein the position vector... and velocity vector The expression is: , , in, Indicates the target is in the first place. Position components along the three-dimensional coordinate axes at each star's epoch. Indicates the target is in the first place. The velocity components along the three-dimensional coordinate axes at each epoch of a star.

[0014] The preferred interpolation method is: , in, Represents the Lagrange basis functions. Indicates the most recent epoch index, Indicates the interpolation order. Indicates the relative epoch index participating in the interpolation calculation. Indicates index based on the most recent epoch. Centered on, the The target position vector at each star's epoch. This indicates the target obtained through interpolation at the observation time. The position vector.

[0015] Preferably, the oversampling canvas is: ; in, The lateral standard deviation is represented as The normalized Gaussian kernel, Represents the coordinates in the oversampled canvas The cumulative weight value at the location, Indicates the exposure time range The total number of motion trajectory sampling points generated within the system. Represents the photometric model. Indicates the step size.

[0016] Preferably, the horizontal full width of the binary geometric mask image Represented as: , in, This represents the full width at half maximum (FWHM) of the target stripe in the direction perpendicular to the motion trajectory. This represents the representative lateral dispersion at the target location. This represents the lateral standard deviation of the target stripe in the direction perpendicular to the motion trajectory; The longitudinal length is expressed as: , , in, Indicates positional error. and These represent the coordinates of the start and end points of the motion trajectory, respectively. Indicates time uncertainty, This represents the projection of the target angular velocity onto the image plane. Indicates WCS (World Coordinate System) error. This indicates ephemeris error.

[0017] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention, by constructing a complete technical chain of "precise modeling—intelligent annotation—physical realism—closed-loop verification," offers significant advantages over existing technologies. In PSF modeling, a two-dimensional polynomial interpolation model of covariance matrix elements is established, allowing querying PSF parameters at any pixel location. This accurately describes the spatial variation characteristics caused by aberrations such as field curvature and astigmatism, significantly improving the physical consistency between simulated fringes and real data compared to the full-field constant PSF model, effectively solving the domain difference problem. In metering, a super-resolution numerical convolution method is used to generate weighted templates that perfectly match the target fringes point-by-point along the motion trajectory. Combined with optimal matched filtering, the theoretically optimal signal-to-noise ratio is achieved, making reliable detection of faint targets possible. For annotation, weighted centroids and PCA rotating anchor frames are used to achieve sub-pixel-level automated annotation, reducing single-frame processing time from minutes to seconds, improving efficiency by orders of magnitude. In star-crossing scenarios, stellar signals are automatically identified and separated based on the Gaia star catalog, transforming a large amount of previously unusable data into valid samples. Regarding spatiotemporal reference, a high-precision UTC-TT conversion link and rolling shutter line-by-line time mapping are established, achieving sub-pixel-level accuracy in motion trajectory prediction. The quality control system constructs a three-dimensional verification framework encompassing residual diagnosis, cross-correlation verification, and growth curve analysis. Combined with a failure mode diagnosis table, closed-loop correction is achieved, significantly improving the data pass rate. Multi-station validation demonstrates that the detection network trained using the dataset of this invention significantly outperforms models trained on purely simulated data in terms of recall, localization accuracy, and cross-platform robustness. Attached Figure Description

[0018] Figure 1 This is a flowchart of a spatial line marking method for targets provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and do not constitute a limitation thereof. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined to form various implementations. Furthermore, the order of the steps or actions in the method description can be changed or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various orders in the specification and drawings are merely for the clear description of a particular embodiment and do not imply a mandatory order, unless otherwise stated that a particular order must be followed.

[0021] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0022] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0023] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0024] like Figure 1 As shown, this embodiment of the invention provides a method for marking spatially drawn targets, including the following steps: S1: Obtain the raw image containing the star, perform radiometric calibration on the raw image to obtain the scientific image, and obtain the timestamp of each pixel in the scientific image.

[0025] The imaging system acquires raw images containing celestial objects (such as stars), typically in RAW or FITSH format. These raw images undergo radiometric calibration to obtain linear scientific images measured in photon counts. The image processor receives the raw images and accompanying calibration frame data, including background frames, dark-field frames, normalized flat-field frames, and bad pixel mask files. The calibration frame data serves as auxiliary image or mask data for radiometric and pixel response correction of the raw images. Specifically, the background frame characterizes the electronic bias under unexposed conditions, the dark-field frame characterizes the dark current response, the normalized flat-field frame corrects pixel response non-uniformity, and the bad pixel mask removes bad pixels, hot pixels, or invalid pixels.

[0026] The expression for the radiometric calibration of the original image is: , in, This represents the corrected scientific image. Represents the original image. Indicates a dark frame. Indicates a normalized flat field. This represents the bad pixel mask.

[0027] After radiometric calibration, the output scientific image exhibits linear response characteristics, with pixel values ​​directly reflecting the received photon count, laying the foundation for subsequent precise labeling.

[0028] Imaging systems have various shutter types, including global shutter and rolling shutter. Different shutter types result in different timestamps for pixels in the acquired image. To ensure accurate position calculation, this embodiment of the invention performs precise calculation of the timestamps corresponding to pixels. First, the image processor receives the camera exposure synchronization signal and the high-precision time source (GPS / NTP) signal to establish a precise Earth time reference system corresponding to the scientific image. The time conversion link is expressed as follows:

[0029] in, Terrestrial Time (TT) is a uniform time scale commonly used in astronomical calculations. It represents Coordinated Universal Time (UTC), which is the original time recorded by the camera exposure synchronization signal and a high-precision time source. This represents the cumulative number of leap seconds between International Atomic Time and Coordinated Universal Time. The term represents the relativistic correction between International Atomic Time (UTC) and Earth Time, and 32.184 seconds represents the fixed time offset between UTC and Earth Time. Through the above expression, Coordinated Universal Time (UTC) is converted into Earth Time, the astronomical standard.

[0030] Furthermore, since different shutter types result in different pixel exposure times, this embodiment of the invention establishes a time model based on shutter type, including a global shutter model corresponding to a global shutter and a rolling shutter model corresponding to a rolling shutter. Under the global shutter model, the expression for the pixel exposure time is: , in, Indicates the effective exposure time. Indicates the end of the exposure. This indicates the start time of exposure. In images acquired using a global shutter, all pixels have the same exposure time. .

[0031] In the rolling shutter model, all pixels within the same row have the same exposure center time, while pixels in different rows have different exposure center times. A row-by-row time mapping function is established. The expression for the exposure center time of a pixel is:

[0032] in, Indicates the first The exposure center moment of the row pixels, The row number representing the pixel, with values ​​ranging from 0 to... , This indicates the total number of rows in the scientific image or detector. Indicates the start time of the first line of exposure. This indicates the row scan time interval, which is determined by the sensor's readout rate.

[0033] By using a time conversion link and calculating the exposure time or the center moment of the exposure time based on the shutter type, the precise timestamp of each pixel in the scientific image that belongs to Earth time can be obtained, so as to facilitate the subsequent accurate calculation of the position.

[0034] S2: Establish the mapping relationship between the pixel coordinate system and the celestial coordinate system corresponding to stars in scientific images.

[0035] When marking targets, it is necessary to obtain their positions within the image. Therefore, this embodiment of the invention uses known stars in the scientific image as references to establish a mapping relationship between celestial coordinates and pixel coordinates. The celestial coordinates of the stars in the scientific image are known parameters and can be obtained by querying star catalogs, such as the Gaia DR3 catalog (Gaia Data Release 3). Only the coordinates of the centroids of the stars in the scientific image need to be obtained. .

[0036] Perform source detection algorithms on scientific images to extract the centroid coordinates of stars. The model is then geometrically matched with the star catalog. Embodiments of this invention employ a triangle or quadrilateral invariant algorithm for blind matching, or utilize telescope pointing for initial matching. Subsequently, a WCS model containing higher-order distortion corrections is constructed using a standard projection (such as TAN projection) and a SIP distortion polynomial, representing the mapping relationship between celestial coordinates and pixel coordinates. , , in, This represents the intermediate coordinates after distortion correction. and Both represent the distortion coefficient matrix. This indicates the order of the polynomial, typically ranging from 3 to 5. and Both represent polynomial exponent indices in non-negative integer form, where, Represents the power of the pixel's x-coordinate. The power of the pixel's y-coordinate is represented by x, and y represents the coordinates of the point to be mapped in the pixel coordinate system. Represented by pixel coordinate x The power and the pixel coordinate y A two-dimensional polynomial monomial formed by multiplying powers.

[0037] An optimization objective function is constructed, and the parameters of the WCS model are obtained through iterative optimization. Specifically, the star positions are refined using PSF fitting. Outliers are truncated and removed, and the parameters of the WCS model are recalculated until the location residual RMS converges. The optimization objective function is: , in, This represents the objective function value, used to evaluate the fitting error of the WCS model. A smaller objective function value indicates a smaller residual in the matching between the star positions in the star catalog and the star positions in the scientific image. This indicates the number of stars involved in the optimization of WCS model parameters. Indicates star index, Indicates the first The right ascension residual of a star Indicates the first The declination residual of a star Indicates declination, This indicates the position measurement error.

[0038] When the position residual RMS converges to within 0.2 arcseconds or 0.2 pixels, the final WCS model parameters are output, obtaining a complete WCS model to characterize the mapping relationship between celestial coordinates and pixel coordinates in scientific images. This invention embodiment achieves this through iterative optimization and... By truncating and removing outliers, the accuracy of the WCS model can be controlled within 0.2 pixels, thereby improving the labeling accuracy.

[0039] S3: Select multiple reference stars in the scientific image, perform two-dimensional elliptic Gaussian function fitting on the multiple reference stars to obtain the PSF information of each reference star, and use the PSF information of all reference stars to establish a two-dimensional polynomial interpolation model.

[0040] Due to aberrations such as field curvature and astigmatism in optical systems, the point spread function (PSF) exhibits spatial variation characteristics within the field of view. This invention, in order to achieve high-precision target marking, acquires the PSF information of each pixel in a scientific image. The specific acquisition method is as follows: In this invention, multiple uniformly distributed and unsaturated stars are selected from scientific images as reference stars for PSF information acquisition. In this embodiment, 200-500 reference stars are selected. A two-dimensional elliptic Gaussian function is fitted to each reference star. , in, Indicates amplitude, Represents a pixel coordinate vector. Indicates the PSF center, The covariance matrix is ​​represented as: , in, and These represent the standard deviations in the two principal axis directions, This represents the correlation coefficient.

[0041] The two-dimensional elliptic Gaussian function describes the PSF information of the reference star in the scientific image, and then a two-dimensional polynomial interpolation model is established using the PSF information of all reference stars: , ; in, Represents the fitting coefficient. This indicates the order of the polynomial, typically ranging from 2nd to 3rd. and Both represent polynomial exponent indices in non-negative integer form, where, Represents the power of the pixel's x-coordinate. Represents the power of the pixel's y-coordinate. and These represent the row and column indices of the covariance matrix, respectively. and The values ​​are all 1 or 2.

[0042] In this embodiment of the invention, the two-dimensional polynomial interpolation model is stored as a function get_local_psf_cov(x, y). Based on any pixel coordinate, the PSF covariance matrix corresponding to that pixel position can be queried through the two-dimensional polynomial interpolation model, providing local PSF information for subsequent weight template generation. The PSF information includes at least one of the following: amplitude of the reference star, center position, PSF covariance matrix, standard deviation of the principal axis direction, and correlation coefficient. The PSF covariance matrix characterizes the local PSF morphology at the location of the reference star.

[0043] S4: Access the target ephemeris file based on the timestamp to obtain the target's position and velocity vectors at the ephemeris epochs. Then, use interpolation to obtain the position and velocity vectors corresponding to the target observation times that are not recorded in the ephemeris epochs. Use the mapping relationship to convert the position and velocity vectors into image plane coordinates to generate the target's trajectory in the image plane.

[0044] Before marking, the target's trajectory needs to be obtained. Access the target's ephemeris file based on the timestamp to obtain the target's state vector at the ephemeris epoch. The state vector includes the position vector and velocity vector. Then, based on the state vector, the observatory coordinates, the light travel time correction, the Earth orientation parameter correction, the atmospheric refraction correction, and the mapping relationship, the specific positions of multiple points on the image plane where the target's trajectory is located can be obtained. Multiple points form the trajectory.

[0045] This invention utilizes an image processor to access the target's precise ephemeris file via a network interface or local storage. For GNSS satellites, this invention uses the SP3 format precise ephemeris published by IGS. For other space targets, it uses the corresponding TLE or precise orbit data.

[0046] The SP3 file parsing process is as follows: Read the ephemeris file header information to obtain the epoch interval. The coordinate system identifier is typically IGS14 / ITRF. The target's position and velocity vectors are extracted in chronological order for each epoch, corresponding to the International Celestial Reference System (ICRF). Position vector. and velocity vector The expression is: , , in, Indicates the target is in the first place. Position components along the three-dimensional coordinate axes at each star's epoch. Indicates the target is in the first place. The velocity components along the three-dimensional coordinate axes at each epoch of a star. Indicates the target is in the first place. The position vector at each star's epoch; Indicates the target is in the first place. The velocity vector at each star epoch.

[0047] For observation times not recorded at the ephemeris point In this embodiment of the invention, the values ​​are obtained based on the adjacent points before and after the given values ​​using an interpolation method. Specifically, this embodiment of the invention uses Lagrange polynomials or Chebyshev polynomials for interpolation: , in, Represents the Lagrange basis functions. This represents the most recent epoch index, and the number of ephemeris epochs involved in the interpolation calculation is... The highest degree of the corresponding interpolation polynomial is The value is usually taken as 8th or 10th order. This represents the relative epoch index used in the interpolation calculation, with a value range of [value range missing]. , Indicates index based on the most recent epoch. Centered on, the The target position vector at each star's epoch. This indicates the target obtained through interpolation at the observation time. The position vector.

[0048] Both the ephemeris obtained from the query and the ephemeris obtained from interpolation are output as ephemeris data. A sequence of triples, where... This represents the epoch time under a unified time base. This represents the position vector of the target in the geocentric celestial reference frame. This represents the velocity vector of the target in the geocentric celestial reference frame. The time resolution of the ephemeris data is better than 1 second.

[0049] The locations corresponding to ephemeris data are "points," and all ephemeris data can form a motion trajectory. Based on the ephemeris data and the observatory coordinates, a complete coordinate transformation chain is performed to generate the target's motion trajectory on the image plane. The coordinate transformation process is as follows: First, optical travel time correction is performed to calculate the propagation time of a photon from the target to the observation station, and the solution is obtained iteratively. Propagation time Represented as: , in, This represents the position vector of the target at the moment of photon emission. This represents the position vector of the observatory at the moment of photon reception. It represents the speed of light.

[0050] Secondly, Earth Orientation Parameters (EOPs) are applied to perform polar migration, precession, and nutation corrections: , in, This represents the target's position vector within the International Terrestrial Reference Frame (ITRF). Represents the polar shift matrix. Represents the Earth's rotation matrix. This represents the transformation matrix from the celestial sphere to the intermediate reference frame, including precession and nutation.

[0051] Then, a geocentric to station-centric conversion is performed, converting the coordinates to station-centric horizontal coordinates: , in, This represents the target's position vector relative to the station's center. This represents the target's position vector in the international Earth reference system. This represents the position vector of the observation station in the International Geodetic Reference System. The azimuth of the target in the station-centered horizontal coordinate system can be further calculated using this station-centered position vector. and elevation angle ,in, This indicates the azimuth of the target relative to the observation station. This indicates the elevation angle of the target relative to the ground plane of the observation station.

[0052] Then, the atmospheric refraction is corrected using the Bennett refraction model, which is expressed as: , in, This represents the elevation angle correction caused by atmospheric refraction, used to correct the elevation angle of a target. Its unit is arcminutes. This indicates the target elevation angle before refraction correction.

[0053] Corrected atmospheric refraction Projected onto pixel coordinates via the inverse transform of the WCS model: , in, Indicates the first The apparent right ascension and apparent declination of the target at each sampling time are obtained after optical time correction, Earth orientation parameter correction, and atmospheric refraction correction. Indicates the first The apparent right ascension of the target at each sampling time. Indicates the first The apparent declination of the target at each sampling time; This represents the pixel coordinates obtained by projecting the apparent right ascension and apparent declination through the inverse transformation of the WCS model.

[0054] Exposure time Within the sampling interval Generate a dense sequence of trajectory points, i.e., the motion trajectory: , in, Indicates the target is in the first place. Trajectory point information at each sampling point Indicates the first The exposure time corresponding to each sampling point and These represent the horizontal and vertical pixel coordinates of the target projected onto the image plane at that exposure time, respectively. Indicates the exposure time range The total number of motion trajectory sampling points generated within the system. satisfy , This represents the projection of the target angular velocity onto the image plane. It represents the standard deviation of PSF along the direction of the motion trajectory.

[0055] S5: Create an oversampling canvas, traverse the motion trajectory in S4, use a two-dimensional polynomial interpolation model to obtain local PSF information, draw a horizontal Gaussian distribution on the oversampling canvas, and then downsample to generate a weight template.

[0056] Based on the motion trajectory and a two-dimensional polynomial interpolation model, a weight template that accurately matches the actual stripe shape is generated using a numerical convolution method. The specific process is as follows: Creating an oversampling canvas The oversampling canvas is 3 to 5 times the size of the scientific image, and the sampling factor is denoted as . With step size Traverse each time point along the motion trajectory Perform the following operations at each location: Get the current location and velocity vector Calculate the unit tangential vector and normal vector : , , in, Represents the unit tangential vector The components along the x and y axes of the pixel coordinate system. Use a two-dimensional polynomial interpolation model to query the covariance matrix corresponding to this location. Calculate the lateral and longitudinal dispersion of the stripes: , .

[0057] A horizontal Gaussian distribution is plotted on the oversampled canvas. For rolling shutter speeds, the exposure time corresponding to the current row number must be considered. If the target exhibits brightness modulation (such as satellite spin flicker), a photometric model can be used. Weight the infinitesimal element.

[0058] The contributions of all time steps are summed on the supersampling canvas: , in, The lateral standard deviation is represented as The normalized Gaussian kernel, Represents the coordinates in the oversampled canvas The cumulative weight value at each point is used to record the cumulative contribution of each time element of the target motion trajectory on a canvas with a resolution higher than that of the original image.

[0059] The oversampled canvas is restored to its original resolution using an area-preserving downsampling algorithm (such as region averaging) and then normalized to obtain the weighted template. : , in, This indicates that after the oversampled canvas is restored to the original image resolution through downsampling, the coordinates are... The unnormalized weight values ​​obtained at that point This represents the summation of all pixel coordinates within the coverage area of ​​the downsampled weighted template.

[0060] Output weight template It is a floating-point numerical matrix that fully describes the spatial distribution, brightness gradient, and blurring characteristics of the target stripes, providing an ideal template for optimal matched filtering.

[0061] S6: Create a binary geometric mask. In the binary geometric mask, use the weighted template to calculate the weighted centroid coordinates, weighted flux sum, rotated rectangular anchor frame, and signal-to-noise ratio of the optimal matched filter of the target to complete the marking.

[0062] To accurately label targets and separate them from the background, a binary geometric mask image is created. The horizontal width and vertical length of the binary geometric mask image are determined as follows: Based on representative lateral diffusion at the target location and expected energy coverage Calculate the lateral half-width. Lateral dispersion is taken as the average value at the midpoint of the motion trajectory or along the entire path, and energy coverage is typically taken as 98%. Lateral half-width Represented as: , in, This represents the inverse function of the error function, used to inversely calculate the standard deviation multiple of the Gaussian distribution based on the desired energy coverage. For a Gaussian distribution, when... When, the corresponding value is approximately Then the full width horizontally. Represented as: , in, This represents the full width at half maximum (FWHM) of the target stripe in the direction perpendicular to the motion trajectory. This represents the lateral standard deviation of the target stripe in the direction perpendicular to the motion trajectory.

[0063] The horizontal full width, or the horizontal width of the binary geometric mask, varies in thickness due to optical aberrations at different locations. A representative width value is chosen, and then, based on 98% energy coverage, the fringe half-width (horizontal half-width) is calculated to be approximately 4.7 times the fringe half-width. This value ensures that most of the target's energy is captured without including too much background.

[0064] Based on the start and end points of the motion trajectory and Based on this, with an additional error margin, the vertical length of the binary geometric mask image is expressed as: , , in, Indicates positional error. Indicates time uncertainty, This represents the projection of the target angular velocity onto the image plane. Indicates WCS (World Coordinate System) error. This indicates ephemeris error.

[0065] The longitudinal length is calculated based on the starting point, ending point, and position error of the motion trajectory. The position error includes time uncertainty, WCS error, and ephemeris error, ensuring that the target is not missed during marking due to these uncertainties.

[0066] When the target trajectory is approximately parallel to the image coordinate axes, the mask region can be an axis-aligned rectangular region; when the target trajectory has an angle of inclination relative to the image coordinate axes, the mask region is a rectangular region rotated along the direction of the trajectory; when the target trajectory is curved, the horizontal half-width is extended along the normal direction based on the center line of the trajectory to form a strip-shaped mask region. For curved trajectories, this embodiment of the invention uses piecewise polylines or spline curves for fitting. A binary geometric mask image containing the above-mentioned rectangular or rotated rectangular regions is constructed, with pixels within the region having a value of 1 and pixels outside the region having a value of 0. For curved trajectories, the center line of the target trajectory is fitted with piecewise polylines or spline curves, and the horizontal half-width is extended to both sides along the normal direction of the center line of the trajectory. The strip region formed after the extension is determined as the binary geometric mask region. The output binary geometric mask image. Used for subsequent background estimation and target labeling. Binary geometric mask image. This is a black and white image where the pixel value of the target area is 1 and the background value is 0. (Binary geometric mask image) It can characterize which pixels belong to the target and which belong to the background, so as to estimate the background accordingly. In addition, it can limit the marking range so that metering and centroid calculation are only performed within the target area, avoiding background noise from interfering with the results.

[0067] Based on binary geometric mask image and weight template This generates centroid coordinates and boundary anchor box markers for precise target localization and tracking. The weighted centroid coordinates of the target fringes are then calculated using a weighted template. , in, Represents pixel coordinates, Represents the weight template value. Represents a geometric mask. This represents the summation of all pixels within the area covered by the binary geometric mask. The centroid coordinates have sub-pixel precision and represent the energy center of the target stripes.

[0068] Generating a rotating rectangular anchor frame based on a binary geometric mask image: , in, Indicates the center coordinates of the rotated rectangular anchor frame. The lateral width is perpendicular to the direction of the motion trajectory. , It represents the longitudinal length along the direction of the motion trajectory, i.e. , This represents the rotation angle. The methods for calculating each parameter are as follows: For the mask region of a binary geometric mask image Pixel coordinate collection within Principal component analysis (PCA) is performed to obtain the eigenvectors of the covariance matrix, i.e., the principal direction vectors. These principal direction vectors characterize the main extension directions of the target fringes in the image plane. Using these principal direction vectors, the rotation angle of the rotating rectangular anchor frame can be determined. This process aligns the anchor frame direction with the target stripe direction. Furthermore, it transforms the pixel coordinates within the mask area to a principal axis coordinate system based on the target stripe direction, allowing for the calculation of the longitudinal length along the motion trajectory and the lateral width perpendicular to the motion trajectory. The resulting rotated rectangular anchor frame better matches the true shape of tilted stripes or obliquely moving targets, reducing background pixel inclusion and target pixel omission, thus improving the accuracy of spatial line marking. The rotation angle is calculated based on the first principal component direction (principal direction). : , in, This indicates the weight of the first principal component.

[0069] Extract the image plane coordinates corresponding to pixels with a value of 1 from the binary geometric mask image, and transform the image plane coordinates to the principal axis coordinate system, using the target weighted centroid as the origin. The principal axis coordinate system is a coordinate system with the direction of the first principal component as the vertical axis and the direction perpendicular to the first principal component as the horizontal axis. Based on the extreme values ​​of each pixel's coordinates in the principal axis coordinate system, determine the vertical length and horizontal width of the rotating rectangular anchor frame. , in, This indicates that the first element within the masked area will be... The coordinates obtained by rotating the pixel coordinates to the principal axis coordinate system; This represents the projected coordinates of the pixel on the horizontal axis of the principal coordinate system. This represents the projected coordinates of the pixel on the vertical axis of the principal coordinate system. (This is achieved through calculation.) and The difference between the maximum and minimum values ​​yields the width of the rotating rectangular anchor frame in the horizontal direction. and length in the longitudinal direction .

[0070] Record the starting point coordinates, ending point coordinates, and corresponding times of the motion trajectory: , in, Indicates the coordinates of the starting point of the motion trajectory. Indicates the coordinates of the endpoint of the motion trajectory. This indicates the time corresponding to the starting point of the motion trajectory. This indicates the time corresponding to the end of the trajectory.

[0071] The above-mentioned marking information is output in a standard format, supporting formats such as JSON, COCO, and VOC XML, facilitating data exchange, visualization, and deep learning training. The output marking information includes the target's precise location, morphology, and spatiotemporal attributes, providing structured data for subsequent target tracking, trajectory association, and database storage. Precise location includes the weighted centroid coordinates of the target stripes, the coordinates of the starting and ending points of the motion trajectory, and the center coordinates of the rotating rectangular anchor frame; morphology includes a binary geometric mask, the horizontal width, vertical length, and rotation angle of the rotating rectangular anchor frame; spatiotemporal attributes include the time corresponding to the starting and ending points of the motion trajectory, the start and end times of exposure, and the line exposure time information under the rolling shutter model.

[0072] To ensure accurate metering, this embodiment subtracts the background. In the target mask... (i.e., binary geometric mask) Define the background strip area on both sides of ) and The width of the background stripe region is roughly the same as the width of the target mask, and there is a gap of 1-2 mask widths between the background stripe region and the target mask to avoid target contamination. Robust statistics are used to estimate the background level within the background stripe region. : .

[0073] Then use the median absolute deviation (MAD) to estimate the noise standard deviation. : , Where 1.4826 represents the conversion factor from MAD to standard deviation under a Gaussian distribution.

[0074] Execution background deduction: , in, This represents a scientific image after background subtraction. This indicates the scientific image after radiometric calibration in coordinates. The pixel value at that location. The scientific image after background removal contains only noise and the target signal.

[0075] Based on the scientific image after background subtraction, weighted template, and noise level The target signal is extracted using optimal matched filtering. First, the weighted flow sum is calculated: , in, This represents the pixel value after background subtraction. The normalized weight template is represented at the th line, number Weight values ​​at column pixels.

[0076] Assuming the noise is spatially uncorrelated and has uniform variance, the signal-to-noise ratio of the optimal matched filter is expressed as: , Calculate the standard deviation of the flow rate label obtained from error propagation, i.e., the flow rate uncertainty: .

[0077] When the target's trajectory overlaps with stars in the background, the source of contamination is identified using a star catalog (e.g., Gaia), and one of the following operations is performed on the contaminated pixels: the corresponding weights are reset to zero, i.e. The star's fitted PSF model is not included in the calculation; or the star's light is pre-subtracted from the data to avoid stellar light contamination of the target labeling. The output labeling results include weighted flux sum, flux uncertainty, and signal-to-noise ratio.

[0078] S7: Perform quality verification on the labeling results. Quality verification includes residual analysis, position verification, and photometric quality assessment.

[0079] To ensure the reliability of the labeling results, this embodiment of the invention performs multi-dimensional quality verification, including residual analysis, position verification, and photometric quality assessment. Details are as follows: Residual analysis: First, examine whether there are any problems with the residuals. Subtract the estimated signal model from the data to generate a residual image. .

[0080] The type of systematic error is then diagnosed through the spatial distribution characteristics of the residual image, including normal pattern, dipole structure, ring structure, and global offset. In the normal pattern, the residual image exhibits a zero-mean random noise distribution in the target region, with the standard deviation approaching the noise level. When the error type is a dipole structure, i.e., one side shows a positive residual and the other side shows a negative residual, it indicates that there is a sub-pixel position offset between the target signal model represented by the weight template and the actual target signal. When the error type is a ring structure, i.e., the residual image shows a structure with a negative center and a positive periphery, or vice versa, it indicates that there is a systematic bias in the PSF scale parameters. When the error type is an overall offset, the residual image shows a non-zero mean distribution in the target region, indicating inaccurate background subtraction.

[0081] Then, the skewness and kurtosis of the residual region are calculated: , in, This represents the residual pixel value within the residual region that participated in the statistical calculation. This represents the mathematical expectation operation, which in a discrete image corresponds to averaging the pixel values ​​within the residual region. This represents the mean value of the residual pixels within the residual region. This represents the standard deviation of the residual pixel values ​​within the residual region. Ideally, the skewness should be close to 0, the kurtosis should be close to 0, and it should conform to a Gaussian distribution.

[0082] Position Verification: The accuracy of the target position is verified through cross-correlation. A two-dimensional cross-correlation is performed between the background-subtracted local image of the target and the weighted template. This involves translating the weighted template across the background-subtracted local image of the target, calculating the dot product at each location, and finding the location with the largest dot product. The expression for the two-dimensional cross-correlation function between the background-subtracted local image of the target and the weighted template is as follows: , in, This represents the translational offset of the weighted template relative to the target local image after background subtraction in the x-axis and y-axis directions of the pixel coordinate system. This indicates the target local image after background subtraction at the th... Line 1 The pixel value at the column pixel.

[0083] A two-dimensional parabolic fit is performed near the location of the maximum dot product to obtain the sub-pixel accuracy offset of the actual motion trajectory relative to the predicted motion trajectory: .

[0084] This offset directly reflects the positional deviation of the actual trajectory relative to the predicted trajectory, and can be used to evaluate systematic errors or iteratively correct trajectory parameters. The systematic error is calculated based on this offset: .

[0085] Metering quality assessment: Generate a series of geometric masks with increasing lateral width. Then the first The horizontal half-width of each geometric mask is: , , in, This represents the step size, which is typically set to a value of [value to be filled in]. The half-width coverage area is to , This indicates the number of geometric masks generated during horizontal width scanning, which is the total number of different horizontal half-width templates.

[0086] Without relying on weighted templates, perform simple aperture metering for each geometric mask: .

[0087] Plotting the aperture photometric results as a curve with the horizontal width as the horizontal axis and the cumulative flow rate as the vertical axis, ideally, this curve should be... The nearby area quickly reaches the platform value, which corresponds to the target's actual total traffic.

[0088] Calculate the saturation index: , in, This represents the traffic of the maximum mask. This represents the throughput of the standard mask. A small saturation index indicates convergence, while a large index suggests that light from the target may be missing.

[0089] A mark is considered valid if all of the following conditions are met: Firstly, the skewness of the residual region must meet the following requirements. Secondly, systematic error. satisfy Pixels; the third is the saturation index. To meet .

[0090] If the marking is unqualified, targeted corrective measures are implemented based on different failure characteristics. This embodiment of the invention classifies three failure modes according to different failure characteristics: Mode A, Mode B, and Mode C. Correspondingly, when there is ephemeris error or WCS zero-point deviation, the failure mode is Mode A, with failure characteristics of dipole residuals + large positional offset, which can be corrected by iterative trajectory correction or recalibration of the WCS. When there is PSF model scaling error, the failure mode is Mode B, with failure characteristics of circular residuals + normal position, which can be corrected by adjusting PSF parameters or remodeling. When there is background estimation bias, the failure mode is Mode C, with failure characteristics of normal residuals + high saturation, which can be corrected by reselecting the background region.

[0091] Once verification is successful, a tagging report will be output containing the following: Photometric results: weighted flow rate and Signal-to-noise ratio ; Location information: centroid coordinates Anchor frame parameters endpoints of the motion trajectory; Time tags: Exposure start and end times (TT time system), rolling shutter speed time mapping; Quality indicators: residual statistics, position offset, saturation index, and validation pass criteria; Metadata: WCS model parameters, PSF model parameters, ephemeris source, processing software version.

[0092] Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0093] The specific embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any other corresponding changes and modifications made in accordance with the technical concept of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A method for marking spatially lined targets, characterized in that, include: S1: Obtain a scientific image containing stars and the timestamp of each pixel in it; S2: Establish the mapping relationship between the pixel coordinate system and the celestial coordinate system corresponding to the stars in the scientific image; S3: Select multiple reference stars in the scientific image and establish a two-dimensional polynomial interpolation model using the PSF information of the reference stars: ， ； in, Represents the fitting coefficient. Denotes the order of a polynomial. and Both represent polynomial exponent indices in non-negative integer form. and These represent the row index and column index of the covariance matrix, respectively. S4: Access the target ephemeris file based on the timestamp, and obtain the target's state vector by combining interpolation to generate the target's motion trajectory in the image plane; S5: Traverse the motion trajectory, obtain local PSF information using the two-dimensional polynomial interpolation model, draw a horizontal Gaussian distribution on the created oversampling canvas, and then downsample to generate a weight template. ； in, This indicates that after the oversampled canvas is restored to the original image resolution through downsampling, the coordinates are... The unnormalized weight values ​​obtained at that point This represents the summation of all pixel coordinates within the coverage area of ​​the downsampled weighted template; S6: Create a binary geometric mask image and use the weighted template to calculate the weighted centroid coordinates of the target; Generate a rotating rectangular anchor frame: ； in, Indicates the center coordinates of the rotated rectangular anchor frame. This represents the lateral width perpendicular to the direction of the motion trajectory. It represents the longitudinal length along the direction of the motion trajectory. Indicates the rotation angle; After removing the background of the target, calculate the weighted sum of flows: ； in, This represents the pixel value after background subtraction. The normalized weight template is represented at the th line, number Weight values ​​at column pixels; Calculate the signal-to-noise ratio of the optimal matched filter: ； in, Indicates noise level; When the motion trajectory overlaps with stars in the background, the source of pollution is identified using a star catalog, and the weights of the polluted pixels are reset to zero; or the fitted PSF model of the stars in the background is subtracted in advance.

2. The marking method for spatially lined targets as described in claim 1, characterized in that, The labeling method also includes S7: quality verification of the labeling results, which includes residual analysis, position verification, and photometric quality assessment; The marking is considered valid when all of the following conditions are met: Firstly, the skewness of the residual region must meet the following requirements. Secondly, systematic error. satisfy Pixels; the third is the saturation index. To meet .

3. The marking method for spatially lined targets as described in claim 2, characterized in that, When the marking is unqualified, the marking result is corrected according to different failure characteristics: When there are ephemeris errors or WCS zero-point deviations, the motion trajectory is corrected iteratively or the WCS is recalibrated; when there are PSF model scaling errors, the PSF parameters are adjusted or the model is remodeled; when there are background estimation biases, the background region is reselected to achieve correction.

4. The marking method for spatially lined targets as described in claim 1, characterized in that, Acquire a raw image containing stars and perform radiometric calibration on the raw image to obtain the scientific image; The radiometric calibration expression for the original image is as follows: ， in, This represents the corrected scientific image. Represents the original image. Indicates a dark frame. Indicates a normalized flat field. This represents the bad pixel mask.

5. The marking method for spatially lined targets as described in claim 1, characterized in that, Calculate the weighted centroid coordinates of the target using the weight template: ； in, Represents pixel coordinates, Represents the weight template value. Represents a geometric mask. This represents the summation of all pixels within the area covered by the binary geometric mask.

6. The marking method for spatially lined targets as described in claim 1, characterized in that, The method for obtaining the PSF information is as follows: Multiple reference stars are selected in the scientific image, and a two-dimensional elliptic Gaussian function is fitted to each reference star: ， in, Indicates amplitude, Represents a pixel coordinate vector. Indicates the PSF center, The covariance matrix is ​​represented; the two-dimensional elliptic Gaussian function is used to describe the PSF information of the reference star on the scientific image.

7. The marking method for spatially lined targets as described in claim 1, characterized in that, The state vector includes a position vector and a velocity vector, the position vector... and velocity vector The expression is: ， ， in, Indicates the target is in the first place. Position components along the three-dimensional coordinate axes at each star's epoch. Indicates the target is in the first place. The velocity components along the three-dimensional coordinate axes at each epoch of a star.

8. The marking method for spatially lined targets as described in claim 1, characterized in that, The interpolation method is as follows: ， in, Represents the Lagrange basis functions. Indicates the most recent epoch index, Indicates the interpolation order. Indicates the relative epoch index participating in the interpolation calculation. Indicates index based on the most recent epoch. Centered on, the The target position vector at each star's epoch. This indicates the target obtained through interpolation at the observation time. The position vector.

9. The marking method for spatially lined targets as described in claim 1, characterized in that, The oversampling canvas is: ； in, The lateral standard deviation is represented as The normalized Gaussian kernel, Represents the coordinates in the oversampled canvas The cumulative weight value at the location, Indicates the exposure time range The total number of motion trajectory sampling points generated within the system. Represents the photometric model. Indicates the step size.

10. The marking method for spatially lined targets as described in claim 1, characterized in that, The full width of the binary geometric mask image in the horizontal direction Represented as: ， in, This represents the full width at half maximum (FWHM) of the target stripe in the direction perpendicular to the motion trajectory. This represents the representative lateral dispersion at the target location. This represents the lateral standard deviation of the target stripe in the direction perpendicular to the motion trajectory; The longitudinal length is expressed as: ， ， in, Indicates positional error. and These represent the coordinates of the start and end points of the motion trajectory, respectively. Indicates time uncertainty, This represents the projection of the target angular velocity onto the image plane. Indicates the error of the WCS world coordinate system. This indicates ephemeris error.

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