A post-processing method for impact crater extraction based on marker point process

Abstract

The present invention relates to a post-processing method for crater extraction based on a marker point process. The method comprises the following steps: Step S1: establishing a Gibbs energy model based on the texture and geometric features of the craters in the image; establishing a priori terms of the model using the topological properties between the craters; constructing a phase direction density function for the local phase weighting of the crater edges using the phase magnitude and phase direction of the crater edges under certain lighting conditions; and constructing a likelihood term of the model based on the phase direction density function; Step S2: optimizing and solving the Gibbs energy model using a reversible jump Markov Monte Carlo algorithm and a simulated annealing algorithm to obtain an optimized crater image. Compared with existing technologies, the method of the present invention can effectively eliminate erroneously extracted craters and optimize the location and size of candidate craters.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite image processing, and in particular to a post-processing method for impact crater extraction based on a marking point process. Background Art

[0002] Impact craters are one of the important landforms on the surface of planets. Their location, distribution, and size information have great research and practical value for the planning and implementation of planetary exploration missions. For example, in engineering applications such as safe landing site selection and obstacle avoidance, accurate information on the location and size of obstacles is very important.

[0003] Image-based crater extraction methods can be categorized into traditional pattern recognition methods and machine learning methods. Traditional pattern recognition methods typically employ a large number of prior geometric or texture distribution rules to detect crater edges or bright-dark distribution features. Commonly used techniques include Hough transforms, template matching, likelihood clustering, ellipse fitting, and Markov chain Monte Carlo algorithms. Machine learning and deep learning methods also play an important role in image-based crater extraction algorithms, such as methods based on convolutional neural networks, genetic algorithms, random forests, and support vector machines. In practical applications, these algorithms often focus on statistically extracting the number of craters, but lack discussion of the accuracy of crater location and size.

[0004] In existing crater extraction algorithms, the definition of correctly extracted craters is mostly measured by the IOU factor, that is, the current extracted crater is considered to be correctly extracted if the relative coverage rate with the ground truth reaches 1%, or it is mostly marked with boxes in deep learning, ignoring the precise positioning and size of each extracted crater.

[0005] In summary, the existing technology does not fully utilize the advantages of target texture and geometric features in the point marking process, making it difficult to effectively eliminate erroneously extracted craters, and the positions and sizes of the obtained candidate craters are not accurate enough. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a post-processing method for impact crater extraction based on a marking point process, which can effectively eliminate erroneously extracted impact craters and optimize the position and size of candidate impact craters.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] The present invention provides a post-processing method for impact crater extraction based on a marking point process, the method comprising the following steps:

[0009] Step S1: Establish a Gibbs energy model based on the texture and geometric features of the impact craters in the image; establish a priori terms of the model through the topological properties between the impact craters, use the phase size and phase direction of the impact crater edge under certain lighting conditions to construct a phase direction density function that is weighted by the local phase of the impact crater edge, and construct a likelihood term of the model based on the phase direction density function;

[0010] Step S2: Optimize and solve the Gibbs energy model using the reversible jump Markov Monte Carlo algorithm and the simulated annealing algorithm to obtain an optimized crater image.

[0011] Preferably, an ellipse is used as a marker for the crater in combination with the shape of the crater in the image; each crater is represented by a five-tuple C i =(v i ,u i ,l i ,w i ,α i ) description, (v i ,u i ) represents the center of the ellipse, that is, a point belonging to the process of realizing the point, while the other three are marks, corresponding to the major axis, minor axis and direction;

[0012] The value range of the quintuple is:

[0013] S=[0,M]×[0,N]×[a m ,a M ]×[b m ,b M ]×[0,π] (1)

[0014] Where [M × N] is the sampling range of the impact crater center, which is determined by the center and radius of each impact crater initially extracted; [a m ,a M ] is the range of the main axis, [b m ,b M ] is the range of the minor axis, and [0,π] is the set of all possible directions.

[0015] Preferably, the Gibbs energy model in step S1:

[0016]

[0017] Where Z is the normalization constant; U D (C i ) and U p (C i ) represent the data likelihood constraint factor and the prior constraint factor respectively.

[0018] Preferably, the constraints of the Gibbs energy model include a priori energy factor constraints and likelihood energy factor constraints.

[0019] Preferably, the a priori energy factor constraint is based on the a priori knowledge of introducing the overlap constraint between targets, and penalizes the overlapping targets; wherein the overlap constraint U of the overlapping targets is p (C i ) is:

[0020]

[0021] Among them, C i and C j Represents two samples, U D (C i ,C j ) represents the overlap coefficient between two ellipses.

[0022] Preferably, the likelihood energy factor constraint is determined based on the size and direction of the estimated edge gradient of the impact crater, and the corresponding data likelihood U D (C i ) is:

[0023] U D (C i )=U D,1 (C i )+U D,2 (C i ) (4)

[0024] Where U D,1 (C i ), U D,2 (C i ) represent the correlation of the phase direction density function of the local phase size constraint and the ratio of the number of correct samples to the total number of samples, respectively. The expressions are:

[0025]

[0026]

[0027] Among them, cor(·) is the correlation function, K is the total number of samples, and th cor ,th num is the set threshold.

[0028] Preferably, for each candidate impact crater, define i (x i ,y i )∈C sam is the center of the circle, R i ∈R samis a sampling instance of radius, where C sam and R sam Represents the sampling space of the location and size of each crater respectively; for each candidate crater, there are K samples, k∈[1,k], where K represents the total number of samples;

[0029] For each sample C sam k (i) Using the local phase amplitude A(x i ) and orientation θ(x i ), calculate the phase direction density function of the local phase magnitude constraint:

[0030]

[0031] Among them, ξ(·) is a uniform kernel, A(x i ,y i ) is the local phase amplitude, ξ(θ(x i ,y i )) is the local phase.

[0032] Preferably, if the current sampling just covers the edge of the crater, P ori (C sam k (i)) The peak is located in a specific direction range; the obtained P ori (C sam k (i)) is measured relative to an ideal Gaussian distribution whose mean cor(C sam k (i)) is the direction opposite to the illumination direction, and the relevant process is calculated as follows:

[0033] cor ori (C sam k (i))=∫P ori (C sam k (i))ζ μori (μ ori ,σ ori )d(θ(x i ,y i )) (8)

[0034] Among them, μori is the expected Gaussian distribution density function, σ ori is a deviation determined by experience.

[0035] Preferably, the simulated annealing algorithm in step S2 adopts a geometric series decreasing method to reduce the temperature, and the temperature reduction calculation formula is:

[0036] T t =T0×α t (9)

[0037] Where T0 is the initial temperature; α is the cooling factor, α∈(0,1); and t is the number of cooling times.

[0038] Preferably, each iteration uses a reversible jump Markov Monte Carlo algorithm for sampling, and the transfer kernel adopts four types of transfer kernels: extinction, translation, scaling, and merging.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1) In view of the lack of post-processing of impact craters in existing impact crater extraction algorithms, the impact crater post-processing method based on the marker point process of the present invention can optimize the location and size of impact craters in a fully automatic manner, and its performance is not affected by the selection of hyperparameters;

[0041] 2) The present invention uses the prior information of the initial crater extraction to construct a sampling space for the optimized crater position and size. The markers of the extracted craters, the Gibbs energy model, and the transfer kernel in the RJMCMC algorithm are applied to the prior sampling space to achieve the optimization of the crater position and size.

[0042] 3) By designing a phase direction density function with local phase size constraints, the present invention fully utilizes the texture and geometric features of the crater, effectively constructs the likelihood energy factor constraint of the Gibbs energy model, and performs an optimization solution to effectively eliminate erroneously extracted craters and optimize the location and size of candidate craters.

[0043] 4) Using the reversible jump Markov Monte Carlo algorithm and simulated annealing algorithm to optimize the solution, ensuring that the Gibbs energy model converges to the global optimal solution under any initial state, avoiding falling into the local optimal solution, with higher accuracy and faster solution speed;

[0044] 5) The simulated annealing algorithm uses a geometric series decreasing method to reduce the temperature, which reduces the computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 is a schematic diagram of solid geometry and multi-view geometry; among them, Figure 2 (a) is the basic information of the ellipse, Figure 2 (b) is a schematic diagram of the marking process;

[0047] Figure 3 Schematic diagram of ray tracing method;

[0048] Figure 4 Schematic diagram of obtaining initial three-dimensional point coordinates for two types of connection points in solid geometry; Figure 4 (a)-(c) Selected impact craters with different diameters and degradation characteristics. Figure 4 d is the selected non-crater area, Figure 4 (e)-4(h) are the optimized crater sampling processes shown by the fitted circles. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0050] Example

[0051] This paper proposes a method based on a marker-point process for optimizing the location and size of impact craters in a fully automated manner, whose performance is unaffected by the choice of hyperparameters. While the proposed marker-point process model eliminates the need for complex parameter tuning, accurately designing the data likelihood energy is crucial for solving this problem. To this end, a phase direction density function weighted by the local phase of the crater rim is proposed to construct the data likelihood term.

[0052] This method first establishes a Gibbs energy model based on the geometric features of the impact crater in the image, establishes the data items of the model through the consistency of the target, and establishes the prior items of the model through the spatial characteristics such as the topological properties of the target; then, the reversible jump Markov Monte Carlo algorithm (RJMCMC) and simulated annealing algorithm are used to optimize the solution.

[0053] Next, the method of this embodiment is introduced in detail.

[0054] 1. Modeling of impact crater location and size based on the marker process

[0055] A set of points randomly distributed in a certain space according to certain statistical laws forms a random point process. The implementation of the marked point process is the configuration of objects, and each object is described by a marked point. Similar to Markov modeling, under the assumption of the marked point process, the maximum a posteriori criterion can be proved to be equivalent to the minimization of a suitable energy function. The design of the energy function must take into account the interaction between geometric objects and their relationship with the image expression. The process of extracting craters from images can be regarded as a Poisson process in the spatial point process. Combined with the shape of the crater in the image, the proposed method uses an ellipse as the marker of the crater. Each crater is represented by a five-tuple Ci =(v i ,u i ,l i ,w i ,α i ) description, (v i ,u i ) represents the center of the ellipse, i.e. a point belonging to the process of realizing a point, while the other three are marks corresponding to the major axis, minor axis and direction, e.g. Figure 2 (a) is shown. The value range of the quintuple is:

[0056] S=[0,M]×[0,N]×[a m ,a M ]×[b m ,b M ]×[0,π] (1)

[0057] Where [M × N] is the sampling range of the crater center, which is determined by the center and radius of each crater initially extracted in the proposed method; [a m ,a M ] is the range of the main axis, [b m ,b M ] is the range of the minor axis, and [0,π] is the set of all possible directions. Figure 2 The “*” in (b) represents a point process formed by a series of points randomly distributed in the frame space, and an elliptical mark is added to each point in the point process to obtain a marked point process.

[0058] In the framework of the marking process, the elimination of mismatches, position and size optimization of impact craters is an energy minimization problem. This embodiment uses the Gibbs energy model U(C i ) describes the point process. Impact crater C i The optimal configuration of is obtained by maximizing the probability density based on the Gibbs distribution, thereby minimizing the energy function.

[0059] Gibbs energy model U(C i ) is defined as follows:

[0060]

[0061] Where Z is the normalization constant. D (C i ) and U p (C i ) represent the data likelihood constraint factor and the prior constraint factor respectively.

[0062] Prior energy factor constraint: The prior constraint factor established in this embodiment is mainly based on prior knowledge such as the overlap constraint between targets. Its essence is to limit the overlap between targets and establish a model suitable for non-overlapping targets. Each area can only have one label, that is, overlapping targets are penalized. p (C i ) is defined as the overlap constraint of the overlapping target:

[0063]

[0064] Among them, C i and C j Represents two samples, U D (C i ,C j ) represents the overlap coefficient between two ellipses.

[0065] Likelihood energy factor constraint: data likelihood U D (C i ) is designed based on the magnitude and direction of the estimated edge gradient of the impact crater. D (C i ) is defined as:

[0066] U D (C i )=U D,1 (C i )+U D,2 (C i ) (4)

[0067] Where U D,1 (C i ), U D,2 (C i ) represent the correlation of the phase direction density function of the local phase size constraint and the ratio of the number of correct samples to the total number of samples, respectively. The expressions are:

[0068]

[0069]

[0070] Among them, cor(·) is the correlation function, K is the total number of samples, and th cor ,th num is the set threshold. In this embodiment, th num =0.6.

[0071] In order to build U D (C i), a new crater edge determination and optimization operator is proposed, which is called the phase direction density function based on local phase magnitude constraint. Considering that the gradient-based edge descriptor is easily affected by terrain and degradation features, the local phase amplitude A(x i ) and orientation θ(x i For each candidate impact crater, define i (x i ,y i )∈C sam is the center of the circle, R i ∈R sam is the sampling strength of the radius, where C sam and R sam Represents the sampling space of the location and size of each crater. For each candidate crater, there are K samples, k∈[1,k], where K represents the total number of samples. For each sample C sam k (i) Calculation method of the phase direction density function constrained by local phase size:

[0072]

[0073] Among them, ξ(·) is a uniform kernel. Then, if the current sampling just covers the edge of the impact crater, as analyzed above, P ori (C sam k The peak of (i)) should be located in a specific direction range, preferably opposite to the illumination direction, that is, ±180°. Figure 4 As shown in the left figure, the corresponding illumination is about 45°. ori (C sam k The ideal peak of (i)) is located at about 225°. This characteristic can be obtained by ori (C sam k (i)) is measured in relation to an ideal Gaussian distribution whose mean cor(C sam k (i)) is the direction opposite to the illumination direction. The relevant process can be calculated as follows.

[0074]

[0075] Among them, μori is the expected Gaussian distribution density function, σ ori is the deviation, which is determined by experience. Figure 3As shown in Figure 2, from top to bottom, the scores of cor(Csamk(i)) decrease in sequence, corresponding to correct and optimal sampling, correct non-optimal sampling, and wrong sampling).

[0076] 2. Optimization solution

[0077] The essence of the method of the present invention is to solve the global minimum energy of the Gibbs energy model, achieve the best match between the sampling instance and the real data, and thus achieve the optimal geometric configuration of each candidate crater. This paper uses a method combining the simulated annealing algorithm and the RJMCMC sampling algorithm to ensure that the Gibbs energy model converges to the global optimal solution under any initial state, avoiding falling into the local optimal solution. Because the feasibility of computational complexity must be considered, the proposed method uses a geometric series reduction method to reduce the temperature. The cooling calculation formula is:

[0078] T t =T0×α t (9)

[0079] Where T0 is the initial temperature; α is the cooling factor, α∈(0,1); and t is the number of cooling steps. This cooling method yields a solution close to the optimal solution. During the cooling process, a cooling step is performed once per iteration to achieve energy balance at each temperature. Each iteration uses the RJMCMC algorithm for sampling, using four transfer kernels: annihilation, translation, scaling, and merging.

[0080] 3. Experimental results and discussion

[0081] The proposed algorithm was evaluated using crater extraction results from LROC NAC imagery of the area near the Apollo 17 landing zone. The Apollo 17 landing zone is characterized by a rich distribution of lunar morphologies, including mature maternal regeneration rocks and highlands with varying slopes and properties. The topography of the region near the landing zone can be divided into smoother plains, the so-called Mare Old (MO), adjacent to the Central Cluster (CC), which has more rugged and striated areas. The Central Area (CA) appears similar to the CC, but has fewer large craters. Three craters of varying sizes and degraded features were first selected as representative examples to illustrate the size and location optimization of positive candidate craters. In addition, an example from a non-cratered area was selected for comparison with the corrected craters. Figure 4 (a)-(c) show impact craters with diameters of 23.2 m, 21.0 m, and 11.4 m, respectively, with strong, clear, and faint degradation features. Figure 4 (d) shows a non-crater area. Figure 4(e)-(h) clearly illustrate the optimized crater sampling process. The thick circles represent the final optimization results, while the thin circles represent the sampling instances during the optimization process. It can be seen that, according to the defined correct extraction criteria, these blue circles contain correctly sampled instances; however, their positions and sizes are less accurate than those of the red circles for true craters. Therefore, it can be seen that the proposed method can optimize the positions and sizes of craters of varying sizes and degrees of degradation, while effectively eliminating incorrectly extracted craters.

[0082] In order to quantitatively evaluate the proposed algorithm, the crater optimization results were compared with the ground truth. The ground truth is the crater manually identified using the CraterTools plug-in in ArcGIS software. Considering the different degradation characteristics of the craters, the degree of blurring of their edges is also different, so the difficulty of accurately fitting the edges is also different. In order to obtain a more objective evaluation, the position and size accuracy of each morphological category before and after optimization were compared. The quantitative analysis indicators defined are: (1) diameter ratio mean_R r , defined as the mean of the ratio of the current crater diameter to the true crater diameter; (2) the standard deviation of the diameter ratio std_R r , defined as the standard deviation of the ratio of the current crater diameter to the true crater diameter; (3) the mean of the distance ratio mean_R d , defined as the mean of the ratio of |current crater center position - true crater center position| to the true crater diameter, where |·| is the absolute value operator; (4) standard deviation of the distance ratio std_R d , defined as the standard deviation of the ratio of |current crater center position - true crater center position| to the true crater diameter.

[0083] First, the optimization effect of the proposed algorithm on crater diameters is analyzed. Table 1 shows the quantitative analysis of the crater diameters before and after optimization compared to the true diameters. In the table, the morphological categories "strong," "obvious," and "faint" are denoted as "Category 1," "Category 2," and "Category 3," respectively. For the morphological category with strong light-dark contrast, the diameter accuracy only improved slightly, with the standard deviation decreasing from 0.12 to 0.1, due to the distinct contrast between highlight and shadow features and the sharp edges. For the categories with "obvious" and "faint" light-dark contrast, the improvement in diameter accuracy was significant, with their average diameter ratios increasing from 0.7 to 0.85 and 0.6 to 0.8, respectively (the closer to 1, the better). Furthermore, the standard deviations of their diameter ratios decreased from 0.15 to 0.1 and 0.12 to 0.1, respectively (the closer to 0, the better). Based on these results, it can be concluded that the edge fitting accuracy varies for craters with different degradation characteristics; however, the optimization method can effectively improve diameter accuracy for craters of different degradation categories. In essence, since more sampling can be performed, the diameter of the crater can be fitted according to the characteristics of the entire object during the optimization process, effectively resisting the local noise caused by adverse factors (such as terrain, degradation, lighting, etc.).

[0084] Secondly, the optimization effect of the proposed algorithm on the crater position is analyzed. Table 1 shows the mean and standard deviation of the ratio of the position difference between the crater and the ground truth relative to its diameter before and after optimization. The smaller the position difference / diameter, the more accurate the center position. For the categories of "strong", "obvious" and "faint", their centers during fitting moved from 0.06 to 0.04, 0.11 to 0.05, and 0.11 to 0.06, respectively. In general, all positioning accuracies have been improved to some extent. This shows that the optimization method is effective in improving the position accuracy. Such an improvement percentage usually corresponds to a distance of 2 to 4 pixels in the image. For the proposed method, this indicator is also used in the process of comprehensively utilizing image and structural features to determine the crater. When mean_R d When the value of is too large, the instance is considered to be a false detection.

[0085] Table 1 Quantitative evaluation of the optimization effect of the proposed algorithm on the location and size of the impact crater

[0086]

[0087] 4. Conclusion

[0088] The present invention proposes an effective method for post-processing of crater extraction, namely, eliminating mismatches of craters and optimizing the position and size of craters based on a marking point process. Current crater extraction algorithms lack discussion on post-processing of craters. To address the above issues, the present invention proposes using a marking point process to process mismatches of initially extracted craters and optimize the position and center of craters. The present invention constructs a sampling space for optimized crater positions and sizes by utilizing the prior information of the initial extraction of craters. The markers of the extracted craters, the Gibbs energy model, and the transfer kernel in the RJMCMC algorithm are applied to the prior sampling space to optimize the position and size of the craters. In particular, by designing a phase direction density function with local phase size constraints, the texture and geometric features of the craters are fully utilized, and the likelihood energy factor constraints of the Gibbs energy model are effectively constructed.

[0089] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A post-processing method for impact crater extraction based on a marker point process, characterized in that: The method comprises the following steps: Step S1: Establish a Gibbs energy model based on the texture and geometric features of the impact craters in the image; establish a priori terms of the energy model through the topological properties between the impact craters, construct a phase direction density function for the local phase weighting of the impact crater edge using the phase magnitude and phase direction of the impact crater edge under certain lighting conditions, and construct a likelihood term of the energy model based on the phase direction density function; Step S2: Optimizing and solving the Gibbs energy model using a reversible jump Markov Monte Carlo algorithm and a simulated annealing algorithm to obtain an optimized impact crater image; The Gibbs energy model in step S1 is: Where Z is the normalization constant; U D (C i ) and U p (C i ) represent the data likelihood constraint factor and the prior constraint factor respectively; For each candidate crater, define i (x i ,y i )∈C sam is the center of the circle, R i ∈R sam is a sampling instance of radius, where C sam and R sam Represents the sampling space of the location and size of each crater respectively; for each candidate crater, there are K samples, k∈[1,k], where K represents the total number of samples; For each sample C sam k (i) Using the local phase amplitude A(x i ) and orientation θ(x i ), calculate the phase direction density function of the local phase magnitude constraint: Among them, ξ(·) is a uniform kernel, A(x i ,y i ) is the local phase amplitude, ξ(θ(x i ,y i )) is the local phase.

2. The post-processing method for impact crater extraction based on a marker point process according to claim 1, characterized in that: Combined with the shape of the crater in the image, the ellipse is used as the mark of the crater; each crater is represented by a five-tuple C i =(v i ,u i ,l i ,w i ,α i ) description, (v i ,u i ) represents the center of the ellipse, that is, a point belonging to the process of realizing the point, while the other three are marks, corresponding to the major axis, minor axis and direction; The value range of the quintuple is: S=[0,M]×[0,N]×[a m ,a M ]×[b m ,b M ]×[0,π] (1) Where [M × N] is the sampling range of the impact crater center, which is determined by the center and radius of each impact crater initially extracted; [a m ,a M ] is the range of the main axis, [b m ,b M ] is the range of the minor axis, and [0,π] is the set of all possible directions.

3. The post-processing method for impact crater extraction based on a marker point process according to claim 2, characterized in that: The constraints of the Gibbs energy model include a priori energy factor constraints and likelihood energy factor constraints.

4. The method for post-processing impact crater extraction based on a marker point process according to claim 3, characterized in that: The prior energy factor constraint is based on the prior knowledge of the overlap constraint between targets, which penalizes the overlapping targets. p (C i ) is: Among them, C i and C j Represents two samples, U D (C i ,C j ) represents the overlap coefficient between two ellipses.

5. The method for post-processing impact crater extraction based on a marker point process according to claim 4, characterized in that: The likelihood energy factor constraint is determined based on the size and direction of the estimated edge gradient of the crater, and the corresponding data likelihood U D (C i ) is: U D (C i )=U D,1 (C i )+U D,2 (C i ) (4) Where U D,1 (C i ), U D,2 (C i ) represent the correlation of the phase direction density function of the local phase size constraint and the ratio of the number of correct samples to the total number of samples, respectively. The expressions are: Among them, cor(·) is the correlation function, K is the total number of samples, and th cor ,th num is the set threshold.

6. The method for post-processing impact crater extraction based on a marker point process according to claim 5, characterized in that: If the current sampling just covers the edge of the crater, P ori (C sam k (i)) The peak is located in a specific direction range; the obtained P ori (C sam k (i)) is measured relative to an ideal Gaussian distribution whose mean cor(C sam k (i)) is the direction opposite to the illumination direction, and the relevant process is calculated as follows: Among them, μori is the expected Gaussian distribution density function, σ ori is a deviation determined by experience.

7. The method for post-processing impact crater extraction based on a marker point process according to claim 1, characterized in that: In step S2, the simulated annealing algorithm adopts a geometric series decreasing method to reduce the temperature. The temperature reduction calculation formula is: T t =T0×α t (9) Where T0 is the initial temperature; α is the cooling factor, α∈(0,1); and t is the number of cooling times.

8. The method for post-processing impact crater extraction based on a marker point process according to claim 1, characterized in that: Each iteration uses the reversible jump Markov Monte Carlo algorithm for sampling, and the transfer kernel uses four types of transfer kernels: extinction, translation, scaling, and merging.

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