Lunar surface three-dimensional terrain variation iteration reconstruction method
Through the iterative reconstruction method of lunar surface variation, combined with image luminosity and laser footprint information, the problems of accuracy and detail recovery in lunar surface reconstruction are solved, and the high-precision lunar terrain reconstruction effect is achieved.
Patent Information
- Application Number
- CN202510232109.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-28
- Publication Date
- 2025-07-18
AI Technical Summary
The existing technology cannot take into account the accurate low frequency and rich details of three-dimensional topographic reconstruction on the lunar surface. The traditional method has low image information utilization rate and relies on initial value constraints, resulting in insufficient recovery accuracy of morphological details.
The lunar surface 3D topography variational iterative reconstruction method is used to convert the lunar surface terrain and laser point data to the star solid rectangular coordinate system, project remote sensing image data, build a physical reflection model and photometric functional, minimize the cost function through numerical iteration, and fuse laser and image data to reconstruct the three-dimensional terrain.
High-precision reconstruction of the three-dimensional terrain on the moon surface is achieved, combining image photometric morphology details and laser elevation information to improve the accuracy and detail recovery effect of terrain reconstruction.
Smart Images
Figure CN120339529A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of terrain reconstruction, and in particular to a variational iterative reconstruction method for lunar surface three-dimensional terrain with joint constraints of laser elevation and image photometry. Background Art
[0002] High-resolution lunar topography is a necessary preparation for lunar surface exploration activities. At present, the main data sources for high-precision topographic mapping of the lunar surface include direct laser measurement data and indirect remote sensing image data. Among them, the image-based high-resolution terrain reconstruction methods include multi-view photogrammetry (Photogrammetry) and photometry (Shape-from-Shading, or Photoclinometry). At present, direct laser measurement is the best means to obtain reliable and high-precision lunar topography, but due to equipment and technical conditions, the laser points on the lunar surface are extremely sparse compared to images. For example, in the LOLA data currently used for lunar measurement, holes with diameters of hundreds of meters or even kilometers are not uncommon. Therefore, using image data to make up for holes that are not directly collected by laser measurement data is of great significance in the current field of aerospace remote sensing.
[0003] Traditional multi-view photogrammetry reconstructs 3D topography by extracting parallax information between multi-view images. The utilization rate of image information is low, and the accuracy of restoring topographic details is difficult to reach the pixel level. Traditional photometry introduces known light source positions and directly inverts the terrain from the image grayscale information through a physical reflection model, which can obtain pixel-level topographic details. However, the low-frequency accuracy of terrain data in the inversion process is extremely dependent on initial value constraints, that is, all changes that deviate from the initial value of the terrain are punished in the terrain inversion. This approach is similar to a kind of neutralization. On the one hand, it limits the topographic inversion accuracy of the photometric method, and on the other hand, it cannot fully guarantee the low-frequency accuracy during the terrain inversion process.
[0004] In summary, the three-dimensional terrain reconstruction scheme of the lunar surface in related technologies cannot take into account both accurate low-frequency and rich-detail pixel-level terrain reconstruction. Summary of the invention
[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a method for iterative reconstruction of lunar three-dimensional topography that can combine the morphological detail information in the image photometry and the high-precision elevation information in the laser footprint.
[0006] The purpose of the present invention can be achieved by the following technical solutions:
[0007] A method for iterative reconstruction of lunar surface three-dimensional topography, the method comprising:
[0008] Convert the initial topography and laser point data of the lunar surface to the satellite-fixed rectangular coordinate system;
[0009] Project the remote sensing image data onto the initial terrain surface;
[0010] Construct a physical reflection model and establish a functional between the terrain and the image photometric using the physical reflection model;
[0011] Construct a cost function;
[0012] Reconstruct the three-dimensional lunar surface terrain integrating laser and image by minimizing the cost function through numerical iteration.
[0013] As a preferred technical solution, the constructing a physical reflection model and establishing a functional between the terrain and the image photometric using the physical reflection model includes:
[0014] The relationship between the terrain and the image is:
[0015] I = A × R
[0016] where I is the generated image intensity; A is the surface reflectivity; R is the reflectance generated by the shape;
[0017] Obtain the functional between the terrain and the image photometric based on the Lambert model:
[0018] R(h(x, y)) = cos(i)
[0019] where h(x, y) represents the terrain; i represents the angle between the normal of the object surface and the incident light.
[0020] As a preferred technical solution, the constructing a physical reflection model further includes:
[0021] Obtain the functional between the terrain and the image photometric based on the moon-Lambert model:
[0022]
[0023] where e is the angle between the terrain normal and the observation direction, i.e., the emission angle; α is the angle between the illumination direction and the observation direction, i.e., the phase angle; Λ(α) is the specular reflection coefficient of the lunar surface.
[0024] As a preferred technical solution, Λ(α) is estimated by the following formula:
[0025] Λ(α) = 1 - 0.019α + 2.42×10 -4 α 2 -1.46×10 -6 α 3 .
[0026] As a preferred technical solution, the constructing a cost function includes:
[0027] Establish a photometric constraint based on the functional between the terrain and the image photometry; wherein, the photometric constraint is used to constrain the difference between the simulated photometry of the terrain and the image photometry.
[0028] As a preferred technical solution, the constructing of the cost function includes:
[0029] Establish a laser footprint constraint based on the average terrain elevation and the footprint elevation value; the laser footprint constraint is used to constrain the difference between the average terrain elevation and the footprint elevation value.
[0030] As a preferred technical solution, the constructing of the cost function includes:
[0031] Construct a smoothing regularization term to penalize the abrupt change of the terrain slope with a small weight.
[0032] As a preferred technical solution, the constructing of the cost function includes:
[0033] Construct a cost function with the weighted sum of squares of the first term and the second term; wherein, the first term is the photometric constraint; the second term is the laser footprint constraint.
[0034] As a preferred technical solution, the cost function is:
[0035]
[0036] Wherein, k is the number of images; I k is the pixel value of the k-th image; h(x, y) is the terrain elevation value at the (x, y) coordinate; T k is the exposure parameter; μ is the footprint constraint coefficient; nth_f is the footprint range of the n-th laser point; h L (n) is the elevation measurement value of the n-th laser point; mean(h(x, y)| nth_f ) is the average terrain elevation within the footprint range of the n-th laser point; v is the smoothing regularization coefficient; ∑ k [I k (h(x, y)) - T k A(x, y)R k (h(x, y))] 2 is the photometric constraint; ∑ n μ 2 [h L (n) - mean(h(x, y)| nth_f )] 2 is the laser footprint constraint; is the smoothing regularization term.
[0037] As a preferred technical solution, the reconstructing the three-dimensional lunar surface terrain integrating laser and image by numerically iteratively minimizing the cost function includes:
[0038] Using an optimization solver, the cost function is iteratively solved to reconstruct the three-dimensional lunar surface terrain that fuses laser and imagery.
[0039] Compared with the prior art, the present invention has the following beneficial effects:
[0040] Good reconstruction effect: The variational iterative reconstruction method for the three-dimensional lunar surface terrain provided by the present invention can combine the topographic detail information in the image photometry and the high-precision elevation information in the laser footprint to obtain a fused terrain that takes into account the advantages of both, which is beneficial to improving the reconstruction effect of the three-dimensional lunar surface terrain. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 It is a schematic flowchart of the variational iterative reconstruction method for the three-dimensional lunar surface terrain provided by an embodiment of the present invention;
[0042] Figure 2 It is a schematic diagram of the projection image of the target area and the laser point distribution in a certain application scenario provided by an embodiment of the present invention;
[0043] Figure 3 It is a schematic diagram of the photometric rendering of the initial laser terrain in a certain application scenario provided by an embodiment of the present invention;
[0044] Figure 4 It is a schematic diagram of the photometric rendering of the output fused terrain in a certain application scenario provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0045] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.
[0046] As Figure 1 shown, an embodiment of the present invention provides a variational iterative reconstruction method for the three-dimensional lunar surface terrain, and the method includes:
[0047] Step S110: Convert the initial terrain and laser point data of the lunar surface to the star-fixed rectangular coordinate system;
[0048] Step S120: Project the remote sensing image data onto the surface of the initial terrain;
[0049] Step S130: Construct a physical reflection model and establish a functional of the terrain and image photometry using the physical reflection model;
[0050] Step S140: Construct a cost function;
[0051] Step S150: Reconstruct the three-dimensional lunar surface topography integrating laser and imagery by minimizing the cost function through numerical iteration.
[0052] The initial topography in the above-mentioned step S110 refers to the initial topography constructed based on laser data, which is used as the starting point of the iteration and generally has low resolution and accuracy.
[0053] The physical reflection model in the above-mentioned step S130 is introduced as follows:
[0054] A connection needs to be established between the topography and the imagery through the albedo model. The relationship between the image intensity and the three-dimensional topography can be written as:
[0055] I = A × R
[0056] The above equation describes the relationship between the generated image intensity I, the surface reflectivity A, and the reflectance ratio R generated by the shape. The reflectivity and the reflectance ratio can be expressed as the ratio of the incident energy at a position to the reflected energy captured by the sensing system due to the surface material properties and its geometry. Therefore, these ratios cannot be negative and cannot exceed 1. The reflection model R defines the relationship between the image intensity I and the three-dimensional topography. This model relates the surface topography, the illumination conditions, and the image intensity. Depending on the application scenario and data conditions, multiple albedo models can be used. The basic albedo model is the Lambert model:
[0057] R(h(x, y)) = cos(i)
[0058] where h(x, y) represents the topography; i represents the angle between the normal to the object surface and the incident light
[0059] This model assumes that there is only perfect diffuse reflection on the object surface, and the reflectance ratio R only depends on the angle (angle of incidence) i between the normal to the object surface and the incident light. This model is often insufficient to describe the precise reflection conditions. The moon-Lambert model is a linear combination of the Lambert model and the Lommel-Seeliger law:
[0060]
[0061] where e is the angle between the normal to the topography and the observation direction, i.e., the emission angle; α is the angle between the illumination direction and the observation direction, i.e., the phase angle; Λ(α) is the specular reflection coefficient of the lunar surface.
[0062] Λ(α) can be estimated by an empirical formula of a third-order polynomial:
[0063] Λ(α) = 1 - 0.019α + 2.42×10 -4 α 2 - 1.46×10 -6 α3 。
[0064] The following is an introduction to the solution for constructing the cost function in step S140 above:
[0065] Optionally, step S140 above includes: establishing a photometric constraint based on the functional between terrain and image photometry; where the photometric constraint is used to constrain the difference between the simulated photometry of the terrain and the image photometry.
[0066] Optionally, step S140 above includes: establishing a laser footprint constraint based on the average terrain elevation and the footprint elevation value; the laser footprint constraint is used to constrain the difference between the average terrain elevation and the footprint elevation value.
[0067] Optionally, step S140 above includes: constructing a smoothing regularization term to penalize abrupt changes in terrain slope with a small weight.
[0068] Optionally, step S140 above includes: constructing a cost function with the weighted sum of squares of the first term and the second term; where the first term is the photometric constraint and the second term is the laser footprint constraint.
[0069] The cost function can be expressed as:
[0070]
[0071] where k is the number of images; I k is the pixel value of the kth image; h(x, y) is the terrain elevation value at the (x, y) coordinate; T k is the exposure parameter; μ is the footprint constraint coefficient; nth_f is the footprint range of the nth laser point; h L (n) is the elevation measurement value of the nth laser point; mean(h(x, y)| nth_f ) is the average terrain elevation within the footprint range of the nth laser point; v is the smoothing regularization coefficient; ∑ k [I k (h(x, y)) - T k A(x, y)R k (h(x, y))] 2 is the photometric constraint; ∑ n μ 2 [h L (n) - mean(h(x, y)| nth_f )] 2 is the laser footprint constraint; is the smoothing regularization term.
[0072] The above photometric constraint requires that the simulated photometry of the terrain be as consistent as possible with the image photometry. The laser footprint constraint requires that the average terrain elevation within the laser footprint coverage be as consistent as possible with the footprint elevation value. The smoothing regularization term is used to ensure the stability of the variational iteration process.
[0073] The parameters to be optimized in the above cost function are the terrain h(x,y), albedo A(x,y), and exposure parameter T. k . These parameters can be optimized simultaneously, or the albedo and exposure parameters can be kept unchanged while the terrain is optimized alone. The footprint constraint coefficient μ is empirically determined according to the number of images and laser density, and μ should be greater than 1. The smoothing regularization term coefficient ν should be as small as possible while ensuring stable convergence of the iteration. Substituting the functional form into the above cost function and using a general optimization solver, the iterative solution of the fused terrain can be carried out to reconstruct the three-dimensional lunar surface terrain fused with laser and images.
[0074] The following provides a specific application scenario to prove the effectiveness of the above variational iteration reconstruction method for three-dimensional lunar surface terrain:
[0075] In this scenario, a small area of 200×200 meters near the lunar pole is selected as the target area. LOLA is used as the laser altimetry data source, and the LRO NAC image M139811097LR / LE is used as the image data source for 1-meter resolution fused terrain inversion.
[0076] Figure 2 The projected image of the target area and the laser point distribution are plotted. Figure 3 The initial terrain rendering interpolated to 1-meter resolution at the image acquisition time is plotted. Figure 4 The final terrain rendering at 1-meter resolution is plotted. Combining Figure 2 、 Figure 3 and Figure 4 , it can be clearly seen that, compared with the laser initial terrain, the fused terrain obtained by using the above three-dimensional terrain variational iteration reconstruction method contains very obvious rich morphological details from the images, and the photometric rendering of the fused terrain is visually very similar to the real images. Analyzing the elevation error between the fused terrain and LOLA laser points, the average error is 0.08 meters, the standard deviation is 0.09 meters, and the maximum error is only 0.73 meters. The error is much lower than the terrain data made solely based on images in the traditional method.
[0077] As described above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims
1. A method for variational iterative reconstruction of the three-dimensional lunar surface topography, characterized in that The method includes: Converting the initial topography of the lunar surface and the laser point data to the star-fixed rectangular coordinate system; Projecting the remote sensing image data onto the surface of the initial topography; Constructing a physical reflection model and establishing a functional between the topography and the image photometric using the physical reflection model; Constructing a cost function; Reconstructing the three-dimensional topography of the lunar surface integrated with laser and image by minimizing the cost function through numerical iteration.
2. The lunar surface three-dimensional terrain variational iteration reconstruction method according to claim 1, characterized in that The constructing of the physical reflection model and establishing a functional between the topography and the image photometric using the physical reflection model includes: The relationship between the topography and the image is: I = A × R where I is the generated image intensity; A is the surface reflectivity; R is the reflectance generated by the shape; Obtaining the functional between the topography and the image photometric based on the Lambert model: R(h(x, y)) = cos(i) where h(x, y) represents the topography; i represents the angle between the normal of the object surface and the incident light.
3. The lunar surface three-dimensional terrain variational iteration reconstruction method according to claim 2, wherein The constructing of the physical reflection model further includes: Obtaining the functional between the topography and the image photometric based on the moon-Lambert model: where e is the angle between the topography normal and the observation direction, i.e., the emission angle; α is the angle between the illumination direction and the observation direction, i.e., the phase angle; Λ(α) is the specular reflection coefficient of the lunar surface.
4. The lunar surface three-dimensional terrain variational iteration reconstruction method according to claim 3, characterized in that The Λ(α) is estimated by the following formula: Λ(α) = 1 - 0.019α + 2.42×10 -4 α 2 - 1.46×10 -6 α 3 。 5. The method for variational iterative reconstruction of the three-dimensional lunar surface topography according to claim 1, wherein The constructing of the cost function includes: Establishing a photometric constraint based on the functional between the topography and the image photometric; where the photometric constraint is used to constrain the difference between the simulated photometric of the topography and the image photometric.
6. The method for three-dimensional lunar surface terrain variational iterative reconstruction according to claim 1, characterized in that The constructing of the cost function includes: Establishing a laser footprint constraint based on the average topography elevation and the footprint elevation value; the laser footprint constraint is used to constrain the difference between the average topography elevation and the footprint elevation value.
7. The method for variational iterative reconstruction of the three-dimensional lunar surface topography according to claim 1, wherein The constructing of the cost function includes: Constructing a smoothing regularization term to penalize the sudden change of the topography slope with a small weight.
8. The method for variational iterative reconstruction of the three-dimensional lunar surface topography according to claim 1, wherein The constructing of the cost function includes: Constructing the cost function with the weighted sum of squares of the first term and the second term; where the first term is the photometric constraint; the second term is the laser footprint constraint.
9. The method for variational iterative reconstruction of the three-dimensional lunar surface topography according to claim 8, wherein The cost function is: where k is the number of images; I k is the pixel value of the k-th image; h(x, y) is the terrain elevation value at the (x, y) coordinates; T k is the exposure parameter; μ is the footprint constraint coefficient; nth_f is the footprint range of the n-th laser point; h L (n) is the elevation measurement value of the n-th laser point; mean(h(x, y)| nth_f ) is the average terrain elevation within the footprint range of the n-th laser point; v is the smoothing regularization coefficient; ∑ k [I k (h(x, y)) - T k A(x, y)R k (h(x, y))] 2 is the photometric constraint; ∑ n μ 2 [h L (n) - mean(h(x, y)| nth_f )] 2 is the laser footprint constraint; is the smoothing regularization term.
10. The method for variational iterative reconstruction of the three-dimensional lunar surface topography according to claim 1, wherein The reconstructing of the three-dimensional topography of the lunar surface integrated with laser and image by minimizing the cost function through numerical iteration includes: Using an optimization solver to iteratively solve the cost function and reconstruct the three-dimensional topography of the lunar surface integrated with laser and image.