CN114187529A - Small celestial body surface complex terrain feature detection method - Google Patents
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Abstract
The invention discloses a method for detecting complex terrain features of a small celestial body surface, and belongs to the technical field of deep space exploration. The implementation method of the invention comprises the following steps: obtaining shadow areas and bright areas of the navigation features of the small celestial body surface by extracting the features of the maximum stable extremum regions and according to the regional gray mean value by using the navigation images shot by the detector, and combining the maximum stable extremum regions by using distance constraint to remove repeated regions; and setting the size of an initial pairing search window according to the number of pixels in the shadow area, and realizing the coarse extraction of the edge of the same navigation feature. Aiming at the problem of false detection of meteor crater edges in an overlapping area, the number of public edge points searched in two shadow areas is used as feedback information, the principle of minimum geometric mean square distance is established to realize dynamic adjustment of search radius, and accurate detection is realized on meteor crater features with the overlapping area. The invention can provide an accurate autonomous detection method for detecting the complex terrain features in the deep space, thereby providing accurate and reliable navigation road signs for a navigation system of the detector.
Description
Technical Field
The invention relates to a method for detecting complex topographic features of a small celestial body surface, in particular to a method for extracting complex topographic features such as overlapping meteor craters and the like of the small celestial body surface, and belongs to the technical field of deep space exploration.
Background
In a small celestial body detection task, because the small celestial body is far away from the earth, a ground station measurement and control mode has larger measurement delay, and the navigation real-time performance and reliability are difficult to guarantee. With the breakthrough of computer hardware technology and the development of optical sensitive devices, the optical autonomous navigation method based on the planet surface features (meteor crater and rock) becomes a research hotspot. The meteorite crater is used as a terrain feature of small celestial body surface wide distribution, has relatively consistent geometric shape and clear outline, has small influence of illumination change on the geometric shape, and is an ideal landing navigation terrain feature. Considering that the terrain of an area with scientific research value on the surface of a small celestial body is often complex, and how to accurately identify the characteristics of the complex terrain is the key for realizing high-precision autonomous navigation of the detector.
In the proposed meteorite crater feature identification and detection method, the technology (Meng Y, Cui H, Yang T.A new advanced base on creator detection and matching for visual navigation in planar mapping [ J ]. Advances in Space Research,2014,53(12): 1810) 1821.) proposes a region-based meteorite crater detection algorithm, which takes the extracted shadow region as the center, determines the search radius by setting empirical parameters, finds the bright region belonging to the same meteorite crater, and thus realizes meteorite crater detection. Because the method uses empirical parameters to set the search radius, the overlapping meteorite crater features cannot be accurately identified. Therefore, research needs to be carried out on a detection method of complex terrain features on the surface of a small celestial body so as to realize high-precision navigation of a detector under the complex terrain.
Disclosure of Invention
The invention discloses a method for detecting complex terrain features of a small celestial body surface, which aims to solve the problems that: aiming at the complex terrain of the small celestial body surface, the edge and the area of a navigation image shot by a detector are extracted, the maximum stable extremum area is merged by utilizing distance constraint to eliminate the repeated area, the number of public edge points searched in the shadow area is used as feedback information aiming at the problem of false detection of the meteor crater edge in the overlapped area, the dynamic adjustment of the search radius is realized by establishing the principle of minimum geometric mean square distance, and the accurate detection of the meteor crater characteristic with the overlapped area is realized.
The invention is realized by the following technical scheme.
The invention discloses a method for detecting complex terrain features of a small celestial body surface, which is characterized in that shadow areas and bright areas of the small celestial body surface navigation features are obtained by utilizing a navigation image shot by a detector, extracting maximum stable extremum region features and according to a region gray mean value. And setting the size of an initial pairing search window according to the number of pixels in the shadow area, and realizing the coarse extraction of the edge of the same navigation feature. Aiming at the problem of false detection of meteor crater edges in an overlapped area, the number of public edge points searched in two shadow areas is used as feedback information, dynamic adjustment of search radius is achieved, a fitting principle with the minimum geometric mean square distance is established, ellipse fitting is carried out on an extraction result, an optimal fitting scheme is obtained, and an accurate autonomous detection method is provided for deep space detection of complex terrain features.
The invention discloses a method for detecting complex terrain features of a small celestial body surface, which comprises the following steps:
step 1: the method comprises the steps of carrying out image processing on an image shot by a navigation optical camera, extracting edge and region information, utilizing distance constraint to merge a maximum stable extremum region to remove repeated detection results of the same region, and extracting a shadow region of small celestial body surface navigation features according to a region gray average value.
The specific implementation method of the step 1 comprises the following steps:
step 1.1, edge detection is carried out on the meteor crater on the surface of the small celestial body in the image of the navigation camera, so that edge information of the image is obtained, and short edges and false edges are removed.
Based on a canny edge detection algorithm, edge detection is carried out on the meteor crater on the surface of the small celestial body, short edges are removed through connected region marks, extracted binary image edge information marks are B (u, v), corresponding gradient vectors are marked as g (u, v), and u and v respectively represent horizontal and vertical coordinates of edge pixel points in an image. The gradient direction of the false edge detected in the meteorite crater is opposite to the gradient direction of the true edge of the meteorite crater, and the elimination of the false edge characteristic can be realized through the illumination direction. The included angle between the gradient direction of the meteorite crater edge and the light source direction is less than 90 degrees, and for the image gradient vector g (u, v) of the edge and the direction vector n of the light source in the image plane, the true edge of the meteorite crater meets the following conditions:
and (3) utilizing the constraint shown in the formula (1) to realize false edge elimination, and obtaining the edge information of the image.
Step 1.2, extracting a maximum stable extremum region of the navigation image, utilizing distance constraint to realize region merging and remove repeated detection results of the same topographic features, and extracting a shadow region of the navigation features of the small celestial body surface according to a regional gray average value.
Based on MSER characteristics of the maximum stable extremum region, image processing is carried out on the meteor crater on the small celestial body surface, the region characteristics of the image are obtained, and the meteor crater image is initially divided into a shadow region image and a bright region image. The MSER is based on the basic principle that the gray level image is subjected to binarization processing by sequentially taking increasing threshold values, and in all the obtained binary images, an area with small change of a connected area is called as a maximum stable extremum area. And marking the obtained MSER feature center as L (u, v), combining the obtained region features through distance constraint according to the constraint conditions shown in formula (2) to remove repeated detection results of the same feature, and extracting a shadow region of the small celestial body surface navigation feature according to the region gray average value.
L(ui,vi)-L(uj,vj)＞ε (2)
Wherein u isi、viRepresents the horizontal and vertical coordinates of the center of the ith characteristic region in the image, and epsilon isAnd (3) regarding the parameters which are customized by the user and do not meet the constraint (2) as the same regional characteristics, and combining the two regional characteristics. Dividing the region into a shadow region and an illumination region through the region gray average value, and recording the extracted shadow region binary image of the navigation characteristics as BS(u, v) the number of shaded areas is denoted nS。
Step 2: according to the shape characteristics of the shadow area, setting the size of an initial search window, carrying out edge search on the navigation features to obtain the detected meteorite crater edges, carrying out ellipse fitting on the detected meteorite crater edges based on the principle of minimum geometric mean square distance, realizing the initial detection of the navigation features, and obtaining the geometric mean square error GRMSE of each fitting ellipse.
Because the shadow area extracted in the step 1 is elliptical and the bright area is non-elliptical, performing elliptical fitting on the shadow area according to the imaging characteristics of the area shape, taking the ellipse center obtained by fitting as the shadow area center, and marking as BC＝(uc,vc). And (3) taking the center of the shadow area as the center of the search window, setting the size of the search window according to the area size of the shadow area, and searching all edges of the same meteorite crater on the edge detection result in the step (1). The purpose of the local search is to reduce the calculation amount of global search imaging matching and improve the search efficiency.
The search window is a shaded area with a center BCUsing R as radius circular area as circle center, searching all edges of same meteorite crater in the area, defining the size of the circle as k times of total number of pixels in shadow area, then searching radius R of nth shadow areanThe calculation formula of (a) is as follows:
where k is a custom search parameter. DAIs the number of pixels contained in the nth shadow region.
And carrying out ellipse fitting based on the principle of minimum geometric mean square distance on the detected meteorite pit edge to realize the initial detection of the navigation characteristic and obtain the geometric mean square error GRMSE of each fitting ellipse, wherein the calculation steps are as follows.
The fitted approximate mean square error of the two-dimensional curve is:
q is the number of two-dimensional point gathers, f is described by finite parameters, denoted as f (x) is ≡ phi (alpha, x), alpha is a smooth function, and for a particular alpha (alpha)1···αr)TF can be written as f ═ phiα(x) α is called a parameter, and x is called a variable.
In ellipse fitting, the minimization problem of equation (4) can be reduced to a generalized eigenvector problem, when equation (4) becomes:
in the formula
Is a covariance matrix and trace represents the trace of the matrix.
The fitting constraint is:
in the formula
Is a symmetric non-negative definite matrix and D represents the differential of the function.
Ellipse fitting is calculation using discrete points
And
and solving the generalized eigenvector problem M.c ═ λ N.c, the smallest eigenvalue λ and corresponding eigenvector c give the elliptic conditionThe solution of (1). λ is the geometric mean square error and c is the coefficient of the quadratic equation representing the optimal ellipse.
And step 3: aiming at the problem of false detection of meteor crater edges in the overlapping area, the number of public edge points searched in the shadow area is used as feedback information to realize dynamic adjustment of the search radius, ellipse fitting is carried out on the characteristic edge again until the obtained geometric mean square error is minimum, and accurate detection of the meteor crater characteristics in the overlapping area is realized.
The dynamic adjustment principle of the search radius refers to that: searching radius R according to public edge point number pair searched by shadow regionnAnd (4) adjusting until the geometric mean square error GRMSE of each fitting ellipse obtained in the step (2) reaches the minimum value, and the specific implementation mode is as follows.
Through the ellipse preliminary detection in the step 2, most meteorite craters on the surface of the small celestial body can be successfully identified, but the edges of adjacent features can be searched when the overlapping meteorite craters are searched, and the fitting accuracy is poor. The public points searched by two overlapped meteorite craters are counted as PnStructural adjustment coefficient
To RnAnd carrying out dynamic adjustment until an optimal solution of ellipse fitting is found. Beta is a scaling coefficient between 0 and 1, and the search radius is adjusted
So far, the ellipse fitting problem is converted into the calculation of alpha.
Written as a constraint problem as shown in equations (7), (8), (9):
and (3) when the minimum value is obtained in the formula (7), the corresponding ellipse is the optimal ellipse, and the precise detection of the meteor crater characteristic in the overlapped region is realized.
Has the advantages that:
1. aiming at the problem of false detection of meteor crater edges in an overlapping area, the method for detecting the complex terrain features on the surface of the small celestial body uses the number of public edge points searched in a shadow area as feedback information to realize dynamic adjustment of a search radius, establishes a principle of minimum geometric mean square distance to obtain an optimal result of ellipse fitting, and realizes accurate detection of the meteor crater features in the overlapping area, thereby providing an accurate and reliable navigation road sign for a navigation system of a detector.
2. The method for detecting the complex terrain features on the surface of the small celestial body combines the maximum stable extremum regions by using distance constraint, and effectively eliminates repeated detection results of the same features.
3. Due to the fact that the complex morphology of the surface of the small celestial body can cause the situation that a plurality of meteorite craters are overlapped, the method for detecting the complex terrain features of the surface of the small celestial body can dynamically adjust the searching radius of each feature through the common point obtained by detecting every two meteorite craters, so that the method is suitable for the situation that the plurality of meteorite craters are overlapped, and therefore the detection rate of navigation signposts on the surface of the small celestial body is improved.
Drawings
FIG. 1 is a schematic flow chart of a method for detecting the navigation characteristics of the surface of a small celestial body according to the present invention;
FIG. 2 is an original navigation image taken by a deep space probe used in the simulation in the example of the present invention;
FIG. 3 is a schematic representation of the imaging of the shaded and shiny areas within the meteorite crater in an example of the invention;
FIG. 4 is an edge detection diagram through step 1 in the present example, where FIG. 4(a) is a diagram after small area region culling, and FIG. 4(b) is an edge detection result after false edge culling;
FIG. 5 is the merle crate shadow extracted at step 1 in an example of the invention;
FIG. 6 is a graph of the results of step 2 navigation feature edge ellipse fitting in an example of the present invention;
FIG. 7 is a diagram of the results of the ellipse fitting after dynamically adjusting the search radius at step 3 in the example of the present invention.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
In order to verify the feasibility of the invention, a mathematical simulation verification is performed by using a truly photographed meteor crater image on the planet surface, as shown in fig. 2.
As shown in fig. 1, the method for detecting complex terrain features on the surface of a small celestial body disclosed in this embodiment includes the following specific implementation steps:
step 1: the method comprises the steps of carrying out image processing on an image shot by a navigation optical camera, extracting edge and region information, utilizing distance constraint to merge a maximum stable extremum region to remove repeated detection results of the same region, and extracting a shadow region of small celestial body surface navigation features according to a region gray average value.
The specific implementation method of the step 1 comprises the following steps:
step 1.1, edge detection is carried out on the meteor crater on the surface of the small celestial body in the image of the navigation camera, so that edge information of the image is obtained, and short edges and false edges are removed.
And (3) carrying out edge detection on the meteor crater of the small celestial body surface based on a canny edge detection algorithm on the topographic image of the small celestial body surface of the target shot by the navigation optical camera as shown in figure 2. And (3) solving 8 connected regions from the obtained edge detection result, and removing short edges, wherein the extracted binary image edge information is marked as B (u, v), the corresponding gradient vector is marked as g (u, v), and u and v respectively represent horizontal and vertical coordinates of edge pixel points in the image, as shown in FIG. 4 (a). Under the illumination condition, the meteorite craters have imaging characteristics as shown in figure 3, because the meteorite craters are bowl-shaped, a bright area and a shadow area can sequentially appear in one meteorite crater along the illumination direction, the boundary of the bright area and the shadow area is a pseudo edge characteristic, the gradient direction of the pseudo edge detected in the meteorite crater is opposite to the gradient direction of the real edge of the meteorite crater, and the elimination of the pseudo edge characteristic can be realized through the illumination direction. The included angle between the gradient direction of the meteorite crater edge and the light source direction is less than 90 degrees. For the image gradient vector g (u, v) of the edge and the direction vector n of the light source in the image plane, the meteor crater true edge satisfies:
the pseudo-edge elimination is realized by using the constraint, and the result is shown in fig. 4 (b).
Step 1.2, extracting a maximum stable extremum region of the navigation image, utilizing distance constraint to realize region merging and remove repeated detection results of the same topographic features, and extracting a shadow region of the navigation features of the small celestial body surface according to a regional gray average value.
Based on the characteristics of the Maximum Stable Extremum Region (MSER), image processing is carried out on the meteorite crater on the surface of the small celestial body, the regional characteristics of the image are obtained, and the meteorite crater image is initially divided into a shadow region image and a bright region image. The MSER is based on the basic principle that the gray level image is subjected to binarization processing by sequentially taking increasing threshold values, and in all the obtained binary images, an area with small change of a connected area is called as a maximum stable extremum area. And recording the obtained MSER feature center as L (u, v), and carrying out region merging on the obtained region features through distance constraint, wherein the constraint conditions are as follows:
L(ui,vi)-L(uj,vj)＞ε (11)
wherein u isi、viAnd (3) representing the horizontal and vertical coordinates of the center of the ith characteristic region in the image, wherein epsilon is a user-defined parameter, and the characteristic which does not meet the constraint (2) is regarded as the same region characteristic, and the horizontal and vertical coordinates and the epsilon are combined. Dividing the combined region into a shadow region and an illumination region by the region gray average value, wherein the extracted meteorite crater shadow region is shown in figure 5, and the binary image of the shadow region is marked as BS(u, v) the number of shaded areas is denoted nS。
Step 2: according to the shape characteristics of the shadow area, setting the size of an initial search window, carrying out edge search on the navigation features to obtain the detected meteorite crater edges, carrying out ellipse fitting on the detected meteorite crater edges based on the principle of minimum geometric mean square distance, realizing the initial detection of the navigation features, and obtaining the geometric mean square error GRMSE of each fitting ellipse.
Because the shadow area extracted in the step 1 is elliptical and the bright area is non-elliptical, performing elliptical fitting on the shadow area according to the imaging characteristics of the area shape, taking the ellipse center obtained by fitting as the shadow area center, and marking as BC＝(uc,vc). And (3) taking the center of the shadow area as the center of the search window, designing the size of the search window according to the area size of the shadow area, and searching all edges of the same meteorite crater on the edge detection result in the step (1). The purpose of the local search is to reduce the calculation amount of the global search imaging matching and improve the search efficiency.
The search window is a shaded area with a center BCUsing R as radius circular area as circle center, searching all edges of same meteorite crater in the area, defining the size of the circle as k times of total number of pixels in shadow area, then searching radius R of nth shadow areanThe calculation formula of (a) is as follows:
wherein, k is a self-defined search parameter, and k is 4. DAIs the number of pixels contained in the nth shadow region.
And carrying out ellipse fitting based on the principle of minimum geometric mean square distance on the detected meteorite pit edge to realize the initial detection of the navigation characteristic and obtain the geometric mean square error GRMSE of each fitting ellipse, wherein the calculation steps are as follows.
The fitted approximate mean square error of the two-dimensional curve is:
q is the number of two-dimensional point gathers, f is described by finite parameters and can be expressed as f (x) is ≡ phi (alpha, x), alpha is a smooth function, and for a particular alpha ═ f (a, x)α1···αr)TF can be written as f ═ phiα(x) We refer to α as a parameter and x as a variable.
In ellipse fitting, the minimization problem of equation (4) can be reduced to a generalized eigenvector problem, when equation (4) becomes:
in the formula
Is a covariance matrix and trace represents the trace of the matrix.
The fitting constraint is:
in the formula
Is a symmetric non-negative definite matrix and D represents the differential of the function.
Ellipse fitting is calculation using discrete points
And
and solving the generalized eigenvector problem M · c ═ λ N · c, the smallest eigenvalue λ and the corresponding eigenvector c give the solution to the elliptic condition. λ is the geometric mean square error and c is the coefficient of the quadratic equation representing the optimal ellipse. The ellipse fitting result of this example is shown in fig. 6.
And step 3: aiming at the problem of false detection of meteor crater edges in the overlapping area, the number of public edge points searched in the shadow area is used as feedback information to realize dynamic adjustment of the search radius, ellipse fitting is carried out on the characteristic edge again until the obtained geometric mean square error is minimum, and accurate detection of the meteor crater characteristics in the overlapping area is realized.
The above dynamic adjustment principle means: searching radius R according to public edge point number pair searched by shadow regionnAnd (4) adjusting until the geometric mean square error GRMSE of each fitting ellipse obtained in the step (2) reaches the minimum value, and the specific implementation mode is as follows.
Through the ellipse detection in the step 2, most meteorite craters on the surface of the small celestial body can be successfully identified, but the edges of adjacent features can be searched when the overlapping meteorite craters are searched, and the fitting accuracy is poor. This step searches for the radius R based on the common point pairs found by the two featuresnDynamic adjustment is performed until GRMSE reaches a minimum value.
The public points searched by two overlapped meteorite craters are counted as PnStructural adjustment coefficient
To RnAnd carrying out dynamic adjustment until an optimal solution of ellipse fitting is found. q is a scaling factor between 0 and 1, and the search radius is adjusted
So far, the ellipse fitting problem is converted into the calculation of alpha, and the following constraint problem is written:
the ellipse corresponding to the minimum value obtained in equation (7) is the optimal ellipse, the ellipse fitting result of the present embodiment is shown in fig. 7, and the fitting geometric mean square error of each meteorite crater is shown in the following table:
TABLE 1 Merle fitting mean square error
Indicates that this merle crate has an overlapping region with other merle crates.
And then, completing the detection of the complex topographic features of the surface of the small celestial body required in the deep space probe navigation system.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (4)
1. The method for detecting the complex terrain features of the surface of the small celestial body is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
step 1: processing images shot by a navigation optical camera, extracting edge and region information, combining maximum stable extremum regions by using distance constraint to eliminate repeated detection results of the same region, and extracting a shadow region of the small celestial body surface navigation feature according to a region gray average value;
step 2: setting the size of an initial search window according to the shape characteristics of a shadow area, carrying out edge search on the navigation features to obtain detected meteor crater edges, carrying out ellipse fitting on the detected meteor crater edges based on the principle of minimum geometric mean square distance, realizing the initial detection of the navigation features, and obtaining the geometric mean square error GRMSE of each fitting ellipse;
and step 3: aiming at the problem of false detection of meteor crater edges in the overlapping area, the number of public edge points searched in the shadow area is used as feedback information to realize dynamic adjustment of the search radius, ellipse fitting is carried out on the characteristic edge again until the obtained geometric mean square error is minimum, and accurate detection of the meteor crater characteristics in the overlapping area is realized.
2. The method for detecting the complex terrain features on the surface of the small celestial body according to claim 1, wherein: the step 1 is realized by the method that,
step 1.1, performing edge detection on the meteor crater on the surface of the small celestial body in the image of the navigation camera so as to obtain edge information of the image and eliminate short edges and false edges;
based on a canny edge detection algorithm, performing edge detection on the meteor crater on the surface of the small celestial body, eliminating short edges through connected region marks, marking extracted binary image edge information as B (u, v), marking corresponding gradient vectors as g (u, v), and respectively representing horizontal and vertical coordinates of edge pixel points in an image by u and v; the gradient direction of the detected false edge in the meteorite crater is opposite to the gradient direction of the real edge of the meteorite crater, and the elimination of the false edge characteristic can be realized through the illumination direction; the included angle between the gradient direction of the meteorite crater edge and the light source direction is less than 90 degrees, and for the image gradient vector g (u, v) of the edge and the direction vector n of the light source in the image plane, the true edge of the meteorite crater meets the following conditions:
utilizing the constraint shown in the formula (1) to realize false edge elimination to obtain the edge information of the image;
step 1.2, extracting a maximum stable extremum region of a navigation image, utilizing distance constraint to realize region merging and remove repeated detection results of the same topographic features, and extracting a shadow region of the navigation features of the surface of the small celestial body according to a regional gray average value;
based on MSER characteristics of the maximum stable extremum region, image processing is carried out on meteor craters on the surface of the small celestial body to obtain the region characteristics of the image, and the meteor crater image is initially divided into a shadow region image and a bright region image; the MSER is based on the basic principle that the gray level image is subjected to binarization processing by sequentially taking an increasing threshold value, and in all obtained binary images, an area with small change of a connected area is called as a maximum stable extremum area; marking the obtained MSER feature center as L (u, v), combining the obtained region features through distance constraint according to the constraint conditions shown in formula (2) to remove repeated detection results of the same feature, and extracting a shadow region of the small celestial body surface navigation feature according to the region gray average value;
L(ui,vi)-L(uj,vj)＞ε (2)
wherein u isi、viRepresenting the horizontal and vertical coordinates of the center of the ith characteristic region in the image, wherein epsilon is a user-defined parameter, and if the parameter does not meet the constraint (2), the parameter is regarded as the same region characteristic, and the two are combined; dividing the region into a shadow region and an illumination region through the region gray average value, and recording the extracted shadow region binary image of the navigation characteristics as BS(u, v) the number of shaded areas is denoted nS。
3. The method for detecting the complex terrain features on the surface of the small celestial body according to claim 2, wherein: the step 2 is realized by the method that,
because the shadow area extracted in the step 1 is elliptical and the bright area is non-elliptical, performing elliptical fitting on the shadow area according to the imaging characteristics of the area shape, taking the ellipse center obtained by fitting as the shadow area center, and marking as BC＝(uc,vc) (ii) a Taking the center of the shadow area as the center of the search window, setting the size of the search window according to the area size of the shadow area, and searching all edges of the same meteorite crater on the edge detection result in the step 1; the purpose of the local search is to reduce the calculation amount of global search imaging matching and improve the search efficiency;
the search window is a shaded area with a center BCUsing R as radius circular area as circle center, searching all edges of same meteorite crater in the area, defining the size of the circle as k times of total number of pixels in shadow area, then searching radius R of nth shadow areanThe calculation formula of (a) is as follows:
wherein k is a self-defined search parameter; dAIs the number of pixels contained in the nth shadow region;
carrying out ellipse fitting based on the principle of minimum geometric mean square distance on the edge of the detected meteorite crater to realize the initial detection of navigation characteristics and obtain the geometric mean square error GRMSE of each fitting ellipse, wherein the calculation steps are as follows;
the fitted approximate mean square error of the two-dimensional curve is:
q is the number of two-dimensional point gathers, f is described by finite parameters, denoted as f (x) is ≡ phi (alpha, x), alpha is a smooth function, and for a particular alpha (alpha)1···αr)TF can be written as f ═ phiα(x) α is called parameter, x is called variable;
in ellipse fitting, the minimization problem of equation (4) can be reduced to a generalized eigenvector problem, when equation (4) becomes:
in the formula
Is a covariance matrix, trace represents the trace of the matrix;
the fitting constraint is:
in the formula
Is a symmetric non-negative definite matrix, D represents the differential of the function;
ellipse shapeFitting is calculation using discrete points
And
solving the generalized eigenvector problem M.c ═ λ N.c, and giving a solution of the ellipse condition by the minimum eigenvalue λ and the corresponding eigenvector c; λ is the geometric mean square error and c is the coefficient of the quadratic equation representing the optimal ellipse.
4. The method for detecting the complex terrain features on the surface of the small celestial body according to claim 3, wherein: the dynamic adjustment principle of the search radius refers to that: searching radius R according to public edge point number pair searched by shadow regionnAdjusting until the geometric mean square error GRMSE of each fitting ellipse obtained in the step 2 reaches the minimum value, and concretely realizing the method as follows,
through the ellipse preliminary detection in the step 2, most meteorite craters on the surface of the small celestial body can be successfully identified, but the edges of adjacent features can be searched when the overlapping meteorite craters are searched, and the fitting precision is poor; the public points searched by two overlapped meteorite craters are counted as PnStructural adjustment coefficient
To RnCarrying out dynamic adjustment until an optimal solution of ellipse fitting is found; beta is a scaling coefficient between 0 and 1, and the search radius is adjusted
So far, the ellipse fitting problem is converted into the calculation of alpha;
written as a constraint problem as shown in equations (7), (8), (9):
and (3) when the minimum value is obtained in the formula (7), the corresponding ellipse is the optimal ellipse, and the precise detection of the meteor crater characteristic in the overlapped region is realized.
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