A POINT CLOUD FILTERING METHOD BY TIGHTENING UNDER GEOMETRIC CONSTRAINTS INTENDED FOR THE THREE-DIMENSIONAL RECONSTRUCTION OF THE SEA SURFACE

Description

2 However, existing techniques have two major limitations. On the one hand, traditional point cloud filtering methods (such as statistical filtering or ray filtering) rely mainly on local characteristics, particularly the distribution of distances between neighboring points, to detect noise points. They only allow the identification of isolated noise points and do not take into account the global geometric constraints of the sea surface. Given that the sea surface has a continuous and smooth surface morphology, some locally plausible points may in reality fail to respect global consistency and become false interior points. The failure to take this global geometric correlation into account thus leads to erroneous deletions of valid points or the retention of noisy points, ultimately affecting the accuracy of the reconstruction. On the other hand, the fitting methods represented by RANSAC15 allow for a global estimation of the model,but present an intrinsic limitation in marine scenes: they only minimize the geometric residue without integrating constraints of geometric validity of the surface (such as the regularity of the surface or the continuity of curvature). When the point cloud contains noise due to reflections or occultations, the algorithm tends to adapt excessively to these noisy points in order to reduce the residue, which deforms the natural morphology of the sea surface and leads to a loss of geometric coherence. BE2026 / 7404 3 The most critical limitation of the prior art lies in the separation of the filtering and fitting steps: traditional filtering is first applied to partially eliminate the noise, then a RANSAC model is used on the remaining point cloud, without any coordination mechanism between the two steps. This decoupled process does not allow the use of global geometric constraints to guide the filtering, nor the exploitation of the filtering results to improve the fitting model.This prevents any significant improvement in accuracy in complex marine environments. Based on these limitations, it is necessary to propose an improved method based on global geometric constraints and integrating the filtering and fitting steps, by transforming the geometric characteristics of the sea surface (such as surface continuity and curvature) into constraints of the fitting process, and by introducing a RANSACa-type architecture to guide the filtering of the point cloud by the quality of the fit, thus enabling unified collaboration between geometric fitting and point selection, and overcoming the accuracy limitations in complex marine scenes. CONTENT OF THE INVENTION: To find remedies for the shortcomings of the prior art,The present invention proposes a point cloud filtering method using geometrically constrained adjustments for the three-dimensional reconstruction of the sea surface. This method guides the selection of points in the point cloud based on the consistency and relevance of the adjustment model, thus integrating the filtering and geometric adjustment operations. BE2026 / 7404 4 It fundamentally solves the essential problems of traditional techniques, namely the failure to consider global geometric characteristics in classical filtering methods, and the lack of constraints on sea surface morphology in RANSAC-type approaches. It significantly improves the accuracy of the three-dimensional reconstruction of the sea surface morphology, the rendering of details such as wave height and shape, and the robustness of the algorithm in complex marine environments.providing reliable technical support for high-precision applications such as ocean monitoring and intelligent navigation. The technical solution adopted by the present invention is as follows: a point cloud filtering method by adjustments under geometric constraints intended for the three-dimensional reconstruction of the sea surface, comprising the following steps: step 1): acquisition, using three-dimensional data acquisition equipment, of raw three-dimensional point cloud data of the sea surface, pre-processing and elimination of invalid values ​​in the raw point cloud in order to obtain initial basic point cloud data to be filtered; step 2): adoption of a combined voxel filtering and statistical filtering solution, successive elimination of invalid and isolated points in the point cloud, then performing voxel subsampling to obtain a high-quality initial point cloud; 25 BE2026 / 7404 5 step 3): selection of a quadratic surface model as the basis for fitting,random sampling of 6 non-coplanar points from the high-quality point cloud to be fitted, then solving the parameters of the initial model by the least squares method; step 4): construction of a global error function comprising a 5 geometric residual term, a normal vector coherence constraint term and a curvature continuity constraint term, then minimization of said function by a gradient descent algorithm in order to optimize the model parameters and obtain optimized model parameters; step 5): validation of the validity of the optimized model parameters, including first determining the conformity of the model to the morphology of the surface of the matrix by means of a constraint on the quadratic coefficients, then selecting the valid interior points according to a distance threshold and eliminating the exterior points constituting noise; step 6): repeat the process from steps 3 to 5 until an iteration stopping condition is met, then select, as a filtered point cloud,of the set of valid interior points corresponding to the model with the largest number of valid interior points; 20 step 7): output of a filtered point cloud, said filtered point cloud being used for the subsequent adjustment of the sea surface. Preferably, in step 1): (1) the three-dimensional data acquisition equipment is a binocular camera, the base length of said binocular camera being 25 of 0.08m, the focal length being 0.035m and the pixel size being 0.000035m; BE2026 / 7404 6 (2) the raw point cloud obtained by generating a disparity map from a pair of captured images using a semi-global block matching algorithm, then by conversion according to the principle of rangefinding; the disparity of pixel ,ij in said disparity map is (,)Dij, the coordinates of the center of the pixel are 00,uv,where 0u is the coordinate of the central pixel in the direction of the image columns and 0v is the coordinate of the central pixel in the direction of the image lines; the formula for converting the image coordinates into three-dimensional coordinates in the camera's coordinate system is as follows: 10 depth coordinate (Z coordinate): (,) Bf Z Dijd    (representing the vertical distance between the pixel point and the origin of the camera's coordinate system); horizontal coordinate (x coordinate): 0() (,) juZd x Dij   (representing the position of the pixel point in the x direction of the camera's coordinate system); vertical coordinate (y-coordinate): 0() (,) ivZd y Dij   (representing the position of the pixel point in the y-direction of the camera's coordinate system); said invalid values ​​include NaNetinf.20 values. Preferably, in step 2): BE2026 / 7404 7 (1) for statistical filtering, the number of nearest neighboring points is k=20,a distance threshold being determined by calculating the average distance between each point and its nearest neighboring points in order to eliminate isolated noise points; (2) For voxel filtering, the edge lengths of the voxels in the 5 directions X, Y and Z are all equal to 0.05m, voxel subsampling being carried out by calculating the average value of the coordinates of all the points contained in a voxel, this average value replacing all the points contained in the voxel; the formula for the average value of the coordinates is 1 1m kk pp m     , where m represents the number of points contained in the voxel, kp represents the coordinates of an individual point contained in the voxel, and p is used to replace the origin points contained in the voxel in order to complete the subsampling. Preferably, in step 3):15 (1) the equation of the quadratic surface model is 22AxByCxyDxEyFZ++++++= , in which A, B, C, D, E and F are the parameters to be determined, and ( ),,xyZ represents the three-dimensional coordinates of a point in the high-quality point cloud to be fitted; 20 (2) when solving the initial parameters of the model by the least squares method, the 6 sampled points are substituted into the equation of the quadratic surface in order to construct a system of linear equations MZ(22,,,,,1iiiiiiMxyxyxy,1,2,,6i; ,,,,, T ABCDEF , the solution formula being  1TTMMMZ  .25 BE2026 / 7404 8 Preferably, in step 4): (1) the global error function is  resnormcurvEEEE ,where 、、represents a weighting coefficient (0.6,0.2,0.2); (2) The term of the geometric residual is ( ) 2 1 1 , n reskkk Edp n   ,5 1 / max,,kkn,where k represents the weight of the point cloud, k represents the density of points in the 5-point neighborhood of the k-th point, the density being defined as the ratio between the number of points, equal to 5, and the volume of the spatial region formed by 5 points, and   22 22 ,221 kkkkkkk k kkkk AxByCxyDxEyFZ dp AxCyDByCxE     ;10 (3)the term of coherence constraint of the normal vectors is  2 1 1 1cos n normkk E n   ,where k represents the angle between the local normal vector of the point cloud and the normal vector of the quadratic surface, , , coskk kk pp k pp nn nn       ( kpn  representing the normal vector of the (plan fitted from the 10 neighboring points of the point considered);15 (3)the coherence constraint term of the normal vectors is [] 2 1 1 1cos n normkk E n   ,where k represents the angle between the local normal vector of the point cloud and the normal vector of the quadratic surface, , , coskk kk pp k pp nn nn       ( kpn  representing the normal vector of the plane fitted from the 10 neighboring points of the point considered)20 ,2,2,1 kpkkkknAxCyDByCxE  ; BE2026 / 7404 9 (4)the curvature continuity constraint term is  12 11 1 1 m curvttt EKK m     ,where tK represents the average Bure-Gaussian curve of the fitted surface in the t-th mesh ( ) 2 2221 xxyyxy xy fff K ff    , 2xkkfAxCyD、2ykkfByCxE、2xxfA、2yyfB、xyfC); the convergence condition of the gradient descent algorithm is that the difference between (E) two successive iterations is 510, or that the number of iterations reaches 500 times. Preferably, in step 5): (1) the constraint threshold of the quadratic coefficients is 0.05δ = , namely 0.050.050.05ABC ≤ ≤ ≤; 10 (2) the distance threshold is 0.3T = , and the distance ( ), koptdpθ, ( ), koptdpTθ < between each point of the high-quality point cloud to be fitted and the optimized quadratic surface is calculated, the points satisfying the condition being determined as valid interior points. Preferably, in step 6): the iteration stopping condition is that the proportion of valid interior points is greater than 70%, or that the number of iterations reaches 1000; if the proportion of interior points is not satisfied after reaching a maximum number of iterations,The model with the largest number of interior points is selected as the optimal model. 20 Preferably, in step 2): BE2026 / 7404 10 Invalid points eliminated are points whose coordinates exceed a predefined range, said range being defined according to the acquisition range of the three-dimensional data capture equipment and the actual scenario of the sea surface, the coordinate range being fixed here at [] [] [] 0,100,83,10XYZ, (in meters), 5 Points whose coordinates exceed the reasonable range are eliminated, in order to obtain an initially cleaned point cloud. Preferably, in step 4): (1) the normal vector consistency constraint term limits the angle 15° k < between the surface normal vector and the local normal vector of the point cloud; (2) the curvature continuity constraint term controls the curvature difference 10.01ttKK--< between adjacent regions,in accordance with the physical properties of continuity and smoothness of the sea surface. Advantages or beneficial effects of the invention: The method allows for a deep integration of point cloud filtering and geometric adjustment of the sea surface, using global geometric constraints (such as the quadratic surface shape, the coherence of normal vectors, etc.) to guide point selection. It thus addresses the fundamental problem of the lack of coordination in traditional "filter then adjust" approaches. This approach avoids both the erroneous deletion of valid points and the maintenance of false interior points caused by local filtering methods, while overcoming distortions due to the absence of shape constraints in classical adjustment methods, thus significantly improving the overall accuracy of the three-dimensional reconstruction of the sea surface. BE2026 / 7404 11 By integrating into the global error function essential constraints such as surface regularity and curvature continuity,The optimized model strictly respects the intrinsic geometric characteristics of the sea surface. Compared to traditional RANSAC-type methods, which aim only to minimize residual noise, the proposed process effectively resists disturbances due to reflections, occultations, and other noise sources, avoiding shape distortion caused by over-adaptation to noisy points. It thus allows for an accurate reconstruction of the natural morphology of the sea surface as well as details such as wave height and shape. DESCRIPTION OF FIGURES Figure 1: Schematic principle of the flow of the cloud filtering process of points under geometric constraints according to the present invention; Figure 2: Reconstruction result obtained by the process according to the present invention. METHODS FOR REALIZING DETAILS In what follows,The present invention is described in detail with reference to the drawings and embodiments. Examples of embodiments are illustrated in the figures. The embodiment described below with reference to Figure 1 is given by way of illustration and aims to explain the present invention, without however limiting its scope. BE2026 / 7404 12 Example of embodiment In order to illustrate the point cloud filtering method by adjustments under geometric constraints intended for the three-dimensional reconstruction of the sea surface proposed by the present invention, the ocean scene is used as a typical application scenario and point cloud filtering as a representative task,without the present invention being limited to this scenario or this task; the three-dimensional reconstruction method can also be applied to other scenarios and tasks. The process comprises the following steps: 10 Step 1) Acquisition of raw point cloud data of the sea surface and preprocessing. A pair of stereoscopic images of the sea surface is captured synchronously using a camera with a base length B of 0.08 m, a focal length f of 0.035 m, and a pixel size of 0.000035 m. The image size is 24482048 × 10⁴. A disparity map is generated using a block semi-global matching algorithm. All pixels of the disparity map are traversed, and invalid values ​​are eliminated (NaN representing the points of no match and tinfre representing the 20 points exhibiting an abnormal deviation), for a total of 200,000 pixels. Invalid data removed. By combining the intrinsic parameters of the camera and the principle of triangulation,The valid disparity is converted into a three-dimensional point cloud in the camera's coordinate system, which ultimately yields 5,000,000 initial 25-base points. BE2026 / 7404 13 step 2) noise reduction, removal of redundant points and filtering To reduce the data volume, eliminate redundant information, remove invalid points and smooth the point cloud, a combination of voxel filtering and statistical filtering is applied to the 5,000,000 points obtained in step 1), as follows: (1) elimination of invalid points: traversal of the initial point cloud, definition of a coordinate range of [ ] [ ] [ ] 0,100,83,10XYZ , elimination of points whose coordinates exceed the reasonable range, which allows obtaining 4,000,000 points after the first cleaning; (2) Elimination of isolated points: application of a statistical filter on the cleaned point cloud, calculating the average distance of each point to its 20 nearest neighbors. A distance threshold is defined as 1.5 times the average distance.and points whose distance is greater than these thresholds are removed (these points generally correspond to noise or erroneous matches), which allows obtaining 3,800,000 points; (3) Voxelic subsampling: the three-dimensional space containing the point cloud is divided into a set of devoxels of the same size, the edges of the voxels in the X, Y and Z directions being 0.05m. For each voxel, the set of points it contains is statistically analyzed, and the average of the coordinates of these points is calculated; this average replaces the set of points of the voxel, thus reducing redundancy while preserving the overall morphology of the point cloud, which finally allows obtaining 440,000 points constituting the high-quality point cloud to be fitted. BE2026 / 7404 14 step 3) surface model selection and initial fitting (1) model selection criteria Given that the morphology of the sea surface presents physical characteristics of continuity and regularity (absence of abrupt discontinuities and relatively gradual local variations in curvature5),The planar models commonly used in traditional RANSAC-type methods do not allow for an accurate description of the undulation structures of wave crests and troughs. Consequently, a quadratic surface model is retained as a 10-based fit. The model equation is as follows: 22AxByCxyDxEyFZ+++++++=(1) where A, B, C, D, E and F are the six parameters to be determined of the quadratic surface model, and (x, y, Z) represents the three-dimensional coordinates of a point in the point cloud consisting of 44000015 points. (2) Initial sampling and model parameter resolution. At each iteration, 6 non-coplanar points are randomly selected from a point cloud of 440,000 points (these 6 points uniquely determine the 6 parameters of the quadratic surface), the set of sampled points being denoted [ ] 126,,Ssss = . The sampled points are substituted into equation (3) in order to construct a system of linear equations: 22 1111111 22 22222222 22 6666666 AxByCxyDxEyFZ AxByCxyDxEyFZ AxByCxyDxEyFZ        25 (2) BE2026 / 7404 15 This system can be expressed in matrix form MZ, where 22,,,,,1iiiiiiMxyxyxy(i=1,2,…,6,corresponding to the characteristics of the coordinates of the 6 sampled points), ,,,,, T ABCDEF, 126,,, T ZZZZ(((corresponding to the depth coordinates of the 6 sampled points).By the least squares method5 ( 1TTMMMZ  ), the initial parameters of the surface model init are obtained by solving this equation. step 4) optimization of the model based on global geometric constraints. To solve the pure least squares problem, which consists of fitting only the data while ignoring geometric consistency,A global error function Eθ is constructed. Minimizing Eθ by a gradient descent algorithm allows us to achieve a balance between fitting the point cloud to the surface and the geometric consistency of the shape.15 The optimization objective is as follows: ααβγ = (3) where αβγ, βγ, βγ, βγ are weighting coefficients (preferably 0.6, 0.2, 0.2). αβγ = (1 / 2) ... point cloud to the initial surface (the smaller the distance, the better the fit; the weights are defined according to the local density of the point cloud, with points of high density having a higher weight); BE2026 / 7404 16 normE also represents the constraint term for the consistency of normal vectors, which limits the angle between the normal vector of the surface and the local normal vector of the point cloud (an angle less than 15° being considered a consistent orientation,in order to avoid good geometric fit but bad surface orientation); 5 curvE finally represents the term of the curvature continuity constraint, which controls the local variations of the surface (the difference in curvature between adjacent regions being less than 0.01, in accordance with the characteristics of smooth variations of the sea surface). The global error function θ(E) is minimized by a gradient descent algorithm, and the model parameters are iteratively updated until convergence of θ(E) (the convergence condition being that the difference of θ(E) between two successive iterations is less than 510, or that the number of iterations reaches 500). In this implementation, error convergence is reached after 320 iterations, and the optimized model parameters are obtained, denoted `optθ`. The example parameters are as follows: 0.00150.00090.00060.14440.00637.3694ABCDEF、、、、、; step 5) Validation of the validity of the model In order to guarantee that the optimized model opt conforms to the 20 physical characteristics of the sea surface,Two validity checks are performed to eliminate non-conforming models: BE2026 / 7404 17 (1) Constraints on quadratic coefficients. The quadratic coefficients A, B, and C directly determine the degree of curvature of the surface. If the absolute value of these coefficients is too high, the surface becomes excessively curved and no longer corresponds to the actual morphology of sea waves. Consequently, a constraint 0.05 ≤ ABC is defined (adjustable according to actual sea conditions). If this constraint is satisfied, the model is considered valid. In this embodiment, the optimized parameters are 0.0015 ≤ 0.0009 ≤ 0.0006 ABC. satisfy all the defined constraints, and the model is therefore deemed valid. 10 (2) Selection of internal points A distance threshold T=0.3m is defined (adjustable according to the noise level of the sea surface). The distance between each of the 440,000 points of the cloud to be adjusted and the optimized surface is calculated. Points whose distance is less than 0.3m are considered as 15 valid internal points,while the others are considered as external points (noise or points of erroneous correspondence). Step 6) Iterative convergence and determination of the best model. The iterative calculation process is repeated according to steps 3) to 5) (adjustment, optimization and validation of the model): 20 During the 1st iteration, the rate of internal points is 28%. During the 500th iteration, the rate of internal points reaches 61%. During the 582nd iteration, the rate of internal points reaches 71%, satisfying the stopping condition "rate of internal points > 70%". The iteration is then stopped. The cloud of 310,000 internal points 25 corresponding to the 582nd iteration is selected as the optimal filtering result. BE2026 / 7404 18 The right-hand part of Figure 1 shows the visualization of this point cloud, allowing the shape of the waves (crests and troughs) to be clearly reconstructed.without significant noise. Step 7) Output of the filtering result. The final cloud of 310,000 valid points is generated. This cloud can be directly used for the subsequent reconstruction of the sea surface and provides a high-quality database for simulating ocean waves. The embodiments described above are only preferred examples of the invention and are intended to help the reader understand the process implemented. They should not be interpreted as limiting the scope of protection of the invention. Any equivalent transformation of the structure or process described in this description and the,

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