A method for extracting the centroid of targets in dim space based on morphological reconstruction

Abstract

A method for extracting the centroid of faint spatial targets based on morphological reconstruction is proposed. First, histogram statistics are performed on the optical spatial target image. Then, parameters of a two-class Gaussian mixture model are estimated from the histogram to obtain an estimated ideal histogram. The ideal histogram is matched with the original image histogram, and grayscale correction is performed on the original image. Adaptive two-parameter threshold segmentation is applied to the corrected image to obtain a binary image. Morphological erosion is used to iteratively process the binary image, reconstructing it for each pixel using the required number of iterations, resulting in a reconstructed grayscale image. Finally, the reconstructed grayscale image is interpolated and fitted with a Gaussian model to obtain a high-resolution image of the star and the target, from which the centroid position is determined. This method effectively solves the problems of low accuracy and poor noise resistance in existing techniques for locating the centroid of faint spatial targets with trailing characteristics.

Description

Technical Field

[0001] This invention relates to the field of space exploration technology, and in particular to a method for extracting the centroid of faint space targets based on morphological reconstruction. Background Technology

[0002] High-precision centroid extraction technology for space targets is a crucial step after target detection and tracking, but before generating astronomical positioning information. The accuracy of space target detection products, such as astronomical positioning and orbit determination information, largely depends on the accuracy of centroid extraction. Currently, the required accuracy for astronomical positioning of targets is generally at the arcsecond level, which necessitates centroid extraction accuracy at the sub-pixel level, or even above 0.1 pixels.

[0003] The accuracy of target centroid extraction is affected by sensor lens distortion, noise, overexposed pixels, and contamination from surrounding light sources. Additionally, stellar backgrounds and target trails in the scene can also reduce estimation accuracy. This is especially true for small, faint targets such as low-level stars, which often appear as only a few diffuse bright spots on the CCD pixel. The trails and edges of the target itself often fail to form regular, elliptical shapes, making it difficult to establish a standard Gaussian distribution in grayscale statistics. This makes it difficult to accurately evaluate targets using traditional methods such as ordinary centroids and square-weighted centroids. Improved threshold centroid methods and surface fitting methods can effectively estimate centroids in inertial frame-based staring scenes through interpolation, but the accuracy of centroid localization drops rapidly when the relative velocity between the observation platform and the stellar background is high.

[0004] Currently, high-precision centroid extraction methods for space targets typically include: preprocessing to reduce interference and contamination from background light sources around the camera or in specific sky areas, preventing high-brightness noise pixels from being detected as false alarms; improving the contrast between stars, target edges and surrounding noise; and improving the resolution of star and target pixels through fitting interpolation to enhance the accuracy of centroid calculation.

[0005] However, existing technologies suffer from problems such as low centroid positioning accuracy and poor noise resistance for dim targets in space with trailing patterns. Summary of the Invention

[0006] Based on the above, this disclosure provides a method for centroid extraction of faint spatial targets based on morphological reconstruction, so as to improve the centroid extraction accuracy of such targets.

[0007] The method for extracting the centroid of targets in dim space based on morphological reconstruction disclosed herein includes the following steps:

[0008] Step 1: Perform histogram statistics on the optical space target image, estimate the parameters of the histogram using a two-class Gaussian mixture model, and obtain the mean and variance of the noise distribution, as well as the mean and variance of the star and target distributions;

[0009] Step 2: The two Gaussian mixture model histograms obtained in Step 1 are used to match the histogram of the original image to obtain an approximate result of the model histogram, and the original image is then corrected for grayscale based on the approximate result;

[0010] Step 3: Perform adaptive two-parameter thresholding on the grayscale-corrected image to obtain a binary image;

[0011] Step 4: Iteratively process the binary image based on morphological erosion calculation, and restore each pixel by iterative erosion calculation until the results before and after processing are consistent, and obtain the reconstructed grayscale image of the binary image;

[0012] Step 5: Interpolate and Gaussian fit the reconstructed grayscale image to obtain a high-resolution image of the star and the target, and determine the centroid position using the centroid method.

[0013] Furthermore, step 1 is detailed as follows:

[0014] Given a spatial target grayscale image data x(i,j) (i,j∈[0,N-1],i,j∈Z), where N is the number of pixels in the image, perform histogram statistics on the image x(i,j) to obtain g(y):

[0015] g(y)=g1(y)+g2(y)+Δ(y) (1)

[0016] Where y∈[0,65535], y∈Z, and Δ(y) represents the histogram error function.

[0017] g1(y) and g2(y) represent the Gaussian statistical distribution histograms of background noise and stars and targets, respectively:

[0018]

[0019] Where μ1 and μ2 represent the mean, and σ1 and σ2 represent the variance.

[0020] In real-world space target images, background noise is often not significantly different from the brightness of faint stars and targets, with a small difference between μ1 and μ2. The two Gaussian distributions in the histogram overlap, making it easy for ordinary thresholding methods to reject faint targets as false alarms. Simultaneously, because the grayscale of stars and targets differs little from the noise, filtering methods easily reduce the signal-to-noise ratio of faint targets, and preprocessing methods such as ordinary histogram equalization can easily increase the grayscale value of bright spots in the noise, creating new false alarms. This method estimates the parameters of the two types of mixture Gaussian distribution histograms to form an ideal histogram, and then performs histogram matching on the original image to achieve correction calculations.

[0021] For the maximum value of g(y) M = max(g(y)), there exists a corresponding x-coordinate y of M. M∈[min{μ1,μ2},max{μ1,μ2}]; for the variance σ of g(y), there is σ∈[min{σ1,σ2},max{σ1,σ2}].

[0022] make Let y represent the area of ​​the total histogram. Thr,L and y Thr,R ,have and Then min{μ1,μ2}∈[y Thr,L ,y M ],max{μ1,μ2}∈[y M ,y Thr,R ]. β is the area ratio threshold.

[0023] The centers of the two types of Gaussian distribution histograms will not exist outside the boundaries of the effective gray-level pixel regions. Therefore, the estimation of μ1, μ2, σ1, and σ2 is equivalent to...

[0024]

[0025] Due to [y] Thr,L ,y M ] interval and [y M ,y Thr,R ], T(μ′1,σ′1,μ′2,σ′2) is a monotonic function, let σ′1=σ′2=var(x(i,j)).

[0026] First, let μ'2 = y M Search for y,μ′1∈[y Thr,L ,y M Within the range, when T(μ′1,var(x(i,j)),y M When var(x(i,j)) is true, the best estimate of the mean of g1(y) is obtained, μ1.

[0027] Then, let μ′1 = μ1, and search for y, μ′2 ∈ [y M ,y Thr,R Within the range, when T(μ1,var(x(i,j)),μ'2,var(x(i,j))) is minimized, the optimal estimate of the mean of g2(y) is obtained as μ2.

[0028] Finally, consider T(μ1,σ′1,μ2,σ′2) in y∈{[y Thr,L ,μ1],[μ2,y Thr,R Within the range of ]}, the function is monotonic. Searching within the range of σ′1∈(0,σ],σ′2∈[σ,+∞), the optimal parameter estimates μ1, μ2, σ1, and σ2 for the two types of Gaussian mixture models can be obtained when T(μ1,σ′1,μ2,σ′2) is minimized.

[0029] Thus, the histogram estimation result of the original data is obtained as g′(y)=g1(y)+g2(y).

[0030] Furthermore, step 2 is detailed below:

[0031] Calculate the cumulative distribution functions of g(y) and g′(y) respectively.

[0032]

[0033] Where, v∈[0,65535], v∈Z.

[0034] Find the set of coordinates F_index(v) that is closest to F(v) and F′(v):

[0035]

[0036] Among them, w∈[0,65535],w∈Z,τ(τ<10,τ∈Z + () represents the mean window.

[0037] The specific method can be as follows: calculate the mean of the cumulative distribution function F(v) of the original image histogram within the range of 2τ+1, and find the difference between it and the estimated cumulative distribution function F′(v) vector of the histogram to obtain the coordinates of the minimum difference, and store them in the coordinate set F_index(v).

[0038] The mapped and corrected image x′(i,j) after histogram matching is obtained based on the corresponding value of x(i,j) in the coordinate set F_index(v):

[0039] x′(i,j)=F_index(x(i,j)) (6)

[0040] Furthermore, step 3 is detailed below:

[0041] Adaptive two-parameter constant false alarm rate (CFAR) detection is performed on the corrected image data x′(i,j). The detection process includes statistical analysis of information from three windows: the target window T. a The radius parameters for the three types of windows—protection window P, background window B, and background window—are as follows: r P and r B The target window mainly includes the grayscale information of the target to be detected; the protection window mainly includes the grayscale information between the target and the background, which is used to protect the diffuse part of the target from being counted in the background window; the background window mainly covers the star noise information.

[0042] The criterion for determining whether a target has been detected within the target window is:

[0043]

[0044] in, μ is the mean of the target window. B σ is the mean of the background window. B T represents the standard deviation of the background window. Thr For comparison, a threshold between 1 and 2 is generally chosen.

[0045] The radius r of background window B B The size is determined by the camera angle and the number of CCD pixels, and is inversely proportional to the former and directly proportional to the latter. Once the camera design is fixed, r... B Fixed. Target window T a radius The size is determined by the brightness statistics within the background window B:

[0046]

[0047] Here, it is assumed that the brightness set inside the background window B is mainly composed of the target brightness. Therefore, the radius of the target window is determined based on the brightness statistics within the area for each slide, which can effectively increase the coverage of the target window's effective information.

[0048] The result of the binary image is:

[0049]

[0050] Furthermore, step 4 specifically includes:

[0051] Let x rt (i,j) represents x″ b (i,j)=x′ b (i,j)x(i,j) is the grayscale image restored after morphological erosion, x min =min(x″) b (i,j)) represents the minimum value of the original data under the binary image mask.

[0052] Let x rt (i,j)=0; Perform the operation on a single pixel of the entire image, if x″ b (i,j)=x min Then x rt (i,j)=x rt (i,j)+1; for x″ b (i,j) is subjected to erosion and iterated. B is the erosion template, z 2 Indicates the eroded image region, updates image x″ b =x″ b，next Repeat the previous step until x″b With x″ b，next They are equal. The resulting x rt (i,j) is the reconstructed grayscale image.

[0053] Furthermore, step 5 specifically includes:

[0054] For the reconstructed image x rt (i,j) are subjected to interpolation and Gaussian filtering fitting, and x′ is defined. rt (i′,j′)(i′,j′∈[0,DN-1],i′,j′∈Z), where D represents the multiple of the one-dimensional data after interpolation. Initialize x′ rt (i′,j′)=0,x′ rt The interpolation calculation process for (i′,j′) is x′ rt (0:D:DN-1,0:D:DN-1)=x rt (:,:); Gaussian filtering is applied to the interpolated result, and the result is: h represents a two-dimensional Gaussian filter. Considering engineering-level pipelined computation, a small order p (p∈Z) is generally chosen. + (p≥3); Repeat the iterations on the filtered fitting results, with the number of iterations generally chosen as p. 2 Next, that is:

[0055]

[0056] The final iterative result of formula (10) is the image data x″. rt Binarization:

[0057]

[0058] Connected component labeling of the binarization result yields star and target coverage information:

[0059]

[0060] The positions of each star and the target's center of mass are:

[0061]

[0062] Compared with the prior art, the beneficial effects of this disclosure are: (1) By using the parameter estimation of the two types of Gaussian mixture model of histogram, an ideal histogram is obtained, which avoids the problem of easily eliminating weak targets as false alarms or increasing the gray value of bright spots in noise in the prior art, causing new false alarms; (2) Matching the estimated histogram with the original image histogram and performing gray-level correction on the original image reduces the interference and pollution of background light sources around the camera or in specific sky areas, and prevents high-brightness noise pixels from being detected as false alarms; (3) Adaptive dual-parameter threshold segmentation is performed on the gray-level corrected image to obtain a binary image, which eliminates the problem that the previous threshold segmentation is not suitable for isolating larger or smaller targets from noise; (4) Interpolation and Gaussian fitting are performed on the binary reconstructed gray-level image to obtain high-resolution star and target images, which reduces the impact of overexposure and diffusion on the centroid and reduces the impact of noise and target deformation on the centroid calculation; (5) The method is easy to implement in engineering. Attached Figure Description

[0063] The above and other objects, features and advantages of this disclosure will become more apparent from the more detailed description of exemplary embodiments of this disclosure taken in conjunction with the accompanying drawings, in which the same reference numerals generally represent the same components.

[0064] Figure 1 A flowchart illustrating an exemplary embodiment of this disclosure;

[0065] Figure 2 Example of a normalized statistical histogram for the original image;

[0066] Figure 3 Comparison of the original image histogram, estimated histogram, and histograms of each component;

[0067] Figure 4 It is a histogram matching of the images before (a) and after (b);

[0068] Figure 5 These are the binary grayscale reconstructed image (a) and the magnified local image (b);

[0069] Figure 6 These are magnified comparison images of local areas before (a) and after (b) interpolation and Gaussian fitting. Detailed Implementation

[0070] Preferred embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While preferred embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art.

[0071] This disclosure provides a high-precision centroid extraction method for targets in dim space based on morphological reconstruction. An exemplary embodiment is shown in the attached diagram. Figure 1 As shown, the main steps include:

[0072] Step 1: Perform histogram statistics on the optical space target image, and estimate the parameters of the histogram using a two-class Gaussian mixture model to obtain the mean and variance of the noise distribution, as well as the mean and variance of the star and target distributions.

[0073] For a spatial target grayscale image data x(i,j) (i,j∈[0,4095],i,j∈Z), where N is the number of image pixels, perform histogram statistics on the image x(i,j) to obtain g(y), as follows: Figure 2 As shown:

[0074] g(y)=g1(y)+g2(y)+Δ(y) (1)

[0075] Where y∈[0,65535], y∈Z, and Δ(y) represents the histogram error function;

[0076] g1(y) and g2(y) represent the Gaussian statistical distribution histograms of background noise and stars and targets, respectively:

[0077]

[0078] Where μ1 and μ2 represent the mean, and σ1 and σ2 represent the variance;

[0079] The maximum value of g(y) is M = max(g(y)) = 1.335 * 10 6 There exists an x-coordinate y corresponding to M. M =104; For the variance σ of g(y), there exists σ = 99.59;

[0080] make To represent the area of ​​a histogram, define y Thr,L and y Thr,R ,have and Then min{μ1,μ2}∈[y Thr,L ,y M ],max{μ1,μ2}∈[yM,y Thr,R β is the area ratio threshold;

[0081] Considering that the centers of the two types of Gaussian distribution histograms will not exist outside the boundaries of the effective gray-level pixel region, when β = 0.1, y Thr,L =89, y Thr,R =129;

[0082] Therefore, the estimation of μ1, μ2, σ1, and σ2 is equivalent to:

[0083]

[0084] Due to [y] Thr,L ,y M ] interval and [y M ,y Thr,R Let T(μ′1,σ′1,μ′2,σ′2) be a monotonic function, and let σ′1=σ′2=var(x(i,j));

[0085] First, let μ'2 = y M Search for y,μ′1∈[y Thr,L ,y M Within the range, when T(μ′1,var(x(i,j)),y M When var(x(i,j)) is true, the best estimate of the mean of g1(y) is μ1 = 100.

[0086] Then, let μ′1 = μ1, and search for y, μ′2 ∈ [y M ,y Thr,R Within the range, when T(μ1,var(x(i,j)),μ'2,var(x(i,j))) is minimized, the optimal estimate of the mean of g2(y) is μ2=110;

[0087] Finally, consider T(μ1,σ′1,μ2,σ′2) in y∈{[y Thr,L ,μ1],[μ2,y Thr,R Within the range of ]}, the function is monotonic. Searching within the range σ′1∈(0,σ],σ′2∈[σ,+∞), the optimal parameter estimates for the two types of Gaussian mixture models are obtained when T(μ1,σ′1,μ2,σ′2) is minimized: μ1=100, μ2=110, σ1=30, and σ2=120. This yields the histogram estimation result for the original data: g′(y)=g1(y)+g2(y), as shown below. Figure 3 As shown.

[0088] Step 2: Match the histograms of the two types of Gaussian mixture models obtained in Step 1 with the histogram of the original image to obtain an approximate result of the model histogram, and perform grayscale correction on the original image based on the approximate result.

[0089] Calculate the cumulative distribution functions of g(y) and g′(y) respectively.

[0090]

[0091] Where, v∈[0,65535], v∈Z;

[0092] Find the set of coordinates F_index(v) that are closest to F(v) and F′(v).

[0093]

[0094] Where w∈[0,65535], w∈Z, and τ=5 is the mean window;

[0095] The mean of the cumulative distribution function F(v) of the original image histogram is calculated within the range of 2τ+1, and the difference between it and the estimated cumulative distribution function F′(v) vector is obtained to get the coordinates of the minimum difference, which are then stored in the coordinate set F_index(v).

[0096] The mapped and corrected image x′(i,j) after histogram matching is obtained based on the corresponding value of x(i,j) in the coordinate set F_index(v):

[0097] x′(i,j)=F_index(x(i,j)) (6)

[0098] like Figure 4 As shown, the image after histogram matching suppresses light source contamination and reduces the impact of noise on stars and targets.

[0099] Step 3: Perform adaptive two-parameter thresholding on the grayscale-corrected image to obtain a binary image.

[0100] Adaptive two-parameter constant false alarm rate (CFAR) detection is performed on the corrected image data x′(i,j). The detection process includes statistical analysis of information from three windows: the target window T. a The radius parameters for the three types of windows—protection window P, background window B, and background window—are as follows: r P and r B The target window mainly includes the grayscale information of the target to be detected; the protection window mainly includes the grayscale information between the target and the background, which is used to protect the diffuse part of the target from being counted in the background window; the background window mainly covers the star noise information.

[0101] The criterion for determining whether a target has been detected within the target window is:

[0102]

[0103] in, μ is the mean of the target window. B σ is the mean of the background window. B T represents the standard deviation of the background window. Thr =1.2;

[0104] The radius r of background window B BThe value of r = 31 is determined by the camera angle and the number of CCD pixels, and is inversely proportional to the former and directly proportional to the latter. Once the camera design is fixed, r... B fixed;

[0105] Target window T a radius The size is determined by the brightness statistics within the background window B:

[0106]

[0107] Here, it is assumed that the brightness set inside the background window B is mainly composed of the target brightness. Therefore, the radius of the target window is determined based on the brightness statistics within the area each time the screen slides, which can effectively increase the coverage of the target window's effective information.

[0108] The result of the binary image is:

[0109]

[0110] Step 4: Iteratively process the binary image based on morphological erosion calculation, and restore each pixel by performing iterative erosion calculations until the results before and after processing are consistent, thus obtaining the reconstructed grayscale image of the binary image.

[0111] Let x rt (i,j) represents x″ b (i,j)=x′ b (i,j)x(i,j) is the grayscale image restored after morphological erosion, x min =min(x″) b (i,j))=0 indicates the minimum value of the original data under the binary image mask;

[0112] First, let x rt (i,j)=0;

[0113] Then, the operation is performed on individual pixels of the entire image, if x″ b (i,j)=x min =0, then x rt (i,j)=x rt (i,j)+1;

[0114] Finally, regarding x″ b (i,j) is subjected to erosion and iterated. B is a 3×3 matrix erosion template, z 2 Indicates the eroded image region, updates image x″ b =x″ b，next Repeat the previous step until x″ b With x″ b，next equal;

[0115] The obtained x rt (i,j) is the reconstructed grayscale image. Figure 5 The binary image grayscale reconstruction image and the local magnified image are given.

[0116] Step 5: Interpolate and Gaussian fit the reconstructed grayscale image to obtain a high-resolution image of the star and the target, and determine the centroid position using the centroid method.

[0117] For the reconstructed image x rt (i,j) are subjected to interpolation and Gaussian filtering fitting, and x′ is defined. rt (i′,j′)(i′,j′∈[0,DN-1],i′,j′∈Z), D=4 represents the multiple of the one-dimensional data after interpolation;

[0118] Initialize x′ rt (i′,j′)=0,x′ rt The interpolation calculation process for (i′,j′) is x′ rt (0:4:16383,0:4:16383)=x rt (:,:);

[0119] Gaussian filtering was applied to the interpolated result, and the result was... h represents a two-dimensional Gaussian filter. Considering engineering-level pipelined computation, a small order p (p∈Z) is generally chosen. + (p≥3); Repeat the iterations on the filtered fitting results, with the number of iterations generally chosen as p. 2 = 16 times, that is:

[0120]

[0121] The final iterative result of formula (10) is the image data x″. rt Binarization:

[0122]

[0123] Connected component labeling of the binarization result yields star and target coverage information:

[0124]

[0125] The positions of each star and the target's center of mass are:

[0126]

[0127] Figure 6 Comparison images of magnified local parts before and after interpolation and Gaussian fitting are provided, showing that the signal-to-noise ratio is maintained while the resolution of stars and the target itself is improved. Compared with traditional algorithms, the accuracy of centroid extraction for faint targets is significantly improved.

[0128] The above technical solutions are merely exemplary embodiments of the present invention. For those skilled in the art, based on the application methods and principles disclosed in the present invention, it is easy to make various types of improvements or modifications, and not limited to the methods described in the specific embodiments of the present invention. Therefore, the methods described above are merely preferred and not restrictive.

Claims

1. A method for extracting the centroid of a faint spatial target based on morphological reconstruction, comprising the following steps: S1: Perform histogram statistics on the optical spatial target image, estimate the parameters of the two types of Gaussian mixture models (background noise distribution and star / target distribution) in the histogram, and obtain the ideal histogram; S2: Match the ideal histogram obtained in step S1 with the histogram of the original image, and perform grayscale correction on the original image based on the matching result; S3: Perform adaptive two-parameter threshold segmentation on the grayscale-corrected image to obtain a binary image; S4: Based on morphological erosion calculation, the binary image is iteratively processed. Each pixel is restored by the number of iterative erosion calculations until the results before and after processing are consistent, and the reconstructed grayscale image of the binary image is obtained. S5: Interpolate and Gaussian fit the reconstructed grayscale image to obtain high-resolution images of stars and targets, and determine the centroid position using the centroid method.

2. The method according to claim 1, characterized in that, Step S1 specifically includes: grayscale image data of spatial targets , , To obtain the histogram statistics of the image pixel count, we can... : (1) in, , This represents the histogram error function; and Histograms representing the Gaussian statistical distributions of background noise and stars / targets, respectively: (2) in, and This represents the mean. and Indicates variance; right and The parameter estimates are as follows: for maximum value ,exist corresponding x-coordinate ;for variance ,exist ; definition and ,satisfy and ,in This represents the area of ​​the total histogram. If the area ratio threshold is used, then: ， ； Considering that the centers of the two types of Gaussian distribution histograms will not exist outside the boundaries of the effective gray-level pixel region, then for , , and The estimate is equivalent to (3) Because in interval sum , Let be a monotonic function. ; First of all, let ,search Within the range Upon its establishment, it received The best estimate of the mean ; Then, let ,search Within the range When the minimum condition is met, we get The best estimate of the mean ; Finally, consider exist The function is monotonic within the range; search Within the range, when When the minimum value is reached, the optimal parameter estimates for the two types of Gaussian mixture models can be obtained. , , and ; This yields the histogram estimation results for the original data. .

3. The method according to claim 2, characterized in that, Step S2 specifically includes: Calculate separately and cumulative distribution function (4) in, ; turn up and The set of coordinates of the closest values ​​between them : (5) in, , For the mean window, ; Mapped corrected image after histogram matching ,according to In coordinate set The corresponding values ​​in the table are obtained as follows: (6)。 4. The method according to claim 3, characterized in that, In step S2, the coordinate set is found. Specific methods include: The cumulative distribution function of the original image histogram ,exist Calculate the mean within the range and estimate the cumulative distribution function of the histogram. Find the difference between the vectors, obtain the coordinates of the minimum difference, and store them in a coordinate set. .

5. The method according to claim 3 or 4, characterized in that, Step S3 specifically includes: Based on the corrected image data, three windows are set up: the target window. Protect window and background window The three types of window radius parameters are as follows: , and The target window is used to include the grayscale information of the target to be detected; the protection window is used to include the grayscale information of the transition from the target to the background; and the background window is used to cover the star noise information. Background window radius The size is determined by the camera angle and the number of CCD pixels, and is inversely proportional to the former and directly proportional to the latter; Target window radius Size determined by background window The brightness statistics within the area determine: (8) The criterion for determining whether a target has been detected within the target window is: (7) in, The mean of the target window. This is the average value of the background window. The standard deviation of the background window. For comparison thresholds; The result of the binary image is: (9)。 6. The method according to claim 5, characterized in that, The comparison threshold The value is between 1 and 2.

7. The method according to claim 6, characterized in that, Step S4 specifically includes: make express Grayscale image restored after morphological erosion processing This represents the minimum value of the original data under the binary image mask; First of all, let ; Then, the operation is performed on individual pixels of the entire image, if... ,but ; Finally, for Perform corrosion treatment and iterate. , For corrosion template, Indicates the eroded image region, updates the image. Repeat the previous step until... and equal; Received This is the reconstructed grayscale image.

8. The method according to claim 7, characterized in that, Step S5 specifically includes: definition , , Indicates the multiple of the one-dimensional data after interpolation; initialization , The interpolation calculation process is as follows: ; Gaussian filtering was applied to the interpolated result, and the result was... , This represents a two-dimensional Gaussian filter; the filter fitting result is iterated repeatedly, with the number of iterations selected... Second-rate, ,Right now: (10) The final iterative result of equation (10) is the image data. Binarization: (11) Connected component labeling of the binarization result yields star and target coverage information: (12) The positions of each star and the target's center of mass are: (13)。 9. The method according to claim 8, characterized in that, In step S5, select .

Images