Point cloud denoising method based on improved whale optimization algorithm

Abstract

The invention discloses a point cloud denoising method based on an improved whale optimization algorithm. The method comprises the following steps: (1) collecting noise point cloud; (2) initializing parameters of a white whale optimization algorithm and a white whale population, wherein individuals in the population are parameters of a point cloud denoising algorithm; (3) the individuals are substituted into a point cloud denoising algorithm to process noise point clouds, the denoised point clouds are evaluated by using evaluation indexes to determine fitness, and the current optimal individual and the position of the current optimal individual are determined; (4) selecting a white whale search behavior according to the balance factor and the whale falling probability, updating a population position and fitness, and determining an optimal individual and a position thereof; (5) judging whether the number of iterations reaches an upper limit or not; if yes, taking the optimal individual as a final parameter of a point cloud denoising algorithm, and substituting the optimal individual into the point cloud denoising algorithm to process the noise point cloud so as to obtain a denoised three-dimensional point cloud; otherwise, executing the step 6; and (6) sorting the populations according to the fitness by using an elite selection strategy to obtain a new population, and returning to the step (3). According to the method, the algorithm generalization ability is improved while high-precision denoising is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the field of three-dimensional point cloud denoising, and particularly relates to a point cloud denoising method based on an improved beluga optimization algorithm. Background Art

[0002] The principle of three-dimensional laser scanning technology is to project a high-frequency laser beam onto the surface of an object, perform ranging scans on the target, and obtain the point cloud data of the target after processing. Due to factors such as equipment accuracy and environmental noise, the point cloud data often contains a certain amount of noise, which interferes with the data analysis and processing of subsequent experiments. Therefore, the research on three-dimensional point cloud data denoising methods has become one of the hot issues in current research. Almost every point cloud denoising method provides default thresholds or parameters, which largely determine the performance of the model.

[0003] However, the default parameters cannot make the model performance reach the optimal effect for different types of point cloud data. Improper parameter settings are likely to lead to overfitting of noise or underfitting of real signals, making the denoising effect limited by artificially set conditions. Among them, manual adjustment is the most common method, which means that users must adjust the set parameters multiple times and have a full understanding of the denoising method. This method takes a long time and is inefficient.

[0004] Considering that evolutionary optimization algorithms are easy to implement and perform well in non-differentiable and non-convex problems, they have been applied to parameter optimization in various fields. The beluga optimization algorithm is a meta-heuristic algorithm that simulates the social behavior of beluga whales, with the advantages of simple programming, easy implementation, fast optimization speed, etc., and can effectively solve complex optimization problems. However, the original beluga optimization algorithm has two disadvantages: (1) The lack of diversity in the initial population limits the search ability of the algorithm; (2) The exploration stage and the exploitation stage are unbalanced, and it is easy to fall into local optimum during optimization. Summary of the Invention

[0005] Aiming at the deficiencies in the prior art, the present invention provides a point cloud denoising method based on an improved beluga optimization algorithm, and selects the parameters involved in the point cloud denoising algorithm through the beluga optimization algorithm, aiming to find the optimal parameters that maximize the objective function. This method can solve the problems of low comprehensive performance and poor generalization ability of the point cloud denoising method.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A point cloud denoising method based on an improved beluga optimization algorithm, comprising the following steps:

[0008] Step 1: Collect noisy three-dimensional point clouds through three-dimensional laser scanning;

[0009] Step 2: Initialize each parameter of the beluga optimization algorithm, and initialize the beluga population using the Piecewise chaotic map. The individuals in the population are regarded as a set of parameters of the point cloud denoising algorithm;

[0010] Step 3: Substitute the individuals in the population into the point cloud denoising algorithm to process the noisy 3D point cloud, and use the evaluation index to evaluate the denoised point cloud. The value of the evaluation index is regarded as the fitness value corresponding to this individual, and the current optimal individual and its corresponding position are determined according to the fitness value;

[0011] Step 4: Select the beluga search behavior according to the balance factor and the whale fall probability, update the population position and fitness value, and determine the optimal individual and its corresponding position;

[0012] Step 5: Judge whether the number of iterations reaches the upper limit; if it reaches, use the optimal individual, that is, the optimal parameter value, as the final parameter configuration of the point cloud denoising algorithm, substitute it into the point cloud denoising algorithm to process the noisy 3D point cloud, and obtain the denoised 3D point cloud; if it does not reach, continue to execute Step 6;

[0013] Step 6: Use the elite selection strategy to sort the population according to the fitness value, retain the elite individuals to obtain a new population, and return to Step 3.

[0014] To optimize the above technical solution, the specific measures taken also include:

[0015] Further, in Step 2, the specific parameters for initializing the beluga optimization algorithm are: initialize the population size Npop, the maximum number of iterations T max , the upper bound lb of the search space, the lower bound ub of the search space, the dimension nD, and the objective function fobj;

[0016] The specific process of initializing the beluga population using the Piecewise chaotic map is expressed by the formula:

[0017]

[0018] Among them, x i represents the position of the initial population individual before the Piecewise chaotic map, and x i+1 represents the position of the population individual after the Piecewise chaotic map; P represents a piecewise control factor used to divide the 4 parts of this piecewise function, and R represents the upper and lower bounds of the population.

[0019] Further, in Step 2, the point cloud denoising algorithm is specifically the SOR filtering algorithm, and a set of parameters of the point cloud denoising algorithm includes: the number of neighbor points and the threshold for outlier determination.

[0020] Further, in Step 3, the calculation formula for the fitness value is:

[0021]

[0022] Among them, fitv is the fitness value, which is used to evaluate the comprehensive performance of parameter configuration; Pd is the precision rate, which measures the proportion of actual noise points among all points marked as noise points; Rd is the recall rate, which focuses on the proportion of actually existing noise points that are successfully identified and removed.

[0023] Furthermore, in step 4, the calculation formulas for the balance factor and the whale fall probability are as follows:

[0024] B f = B0(1 - T / 2T max )

[0025] W f = 0.1 - 0.05T / T max

[0026] Among them, B f is the balance factor, W f is the whale fall probability, B0 is a random number in the range (0, 1), T is the current iteration number, and T max is the maximum iteration number of the population.

[0027] Furthermore, the specific process of step 4 is as follows:

[0028] Step 4.1: When B f > 0.5, the algorithm is in the exploration stage. The search step size is dynamically adjusted using the adaptive factor α, and the individual position is calculated according to the position update formula;

[0029] Step 4.2: When B f ≤ 0.5, the algorithm is in the exploitation stage. The search step size is dynamically adjusted using the adaptive factor α, and the Levy flight strategy is dynamically adjusted using the β factor of the adaptive weight. The individual position is calculated according to the position update formula;

[0030] Step 4.3: When B f < W f the algorithm is in the whale fall stage. The step size is adjusted using the adaptive factor α, and the elite reverse learning strategy is introduced. The individual position is calculated according to the position update formula;

[0031] The calculation formula for the adaptive factor α is as follows:

[0032]

[0033] Among them, r represents a random number between (0, 1), T represents the current iteration number, and T max represents the maximum iteration number.

[0034] Further, in step 4.1, the calculation of the individual position according to the position update formula is specifically as follows:

[0035]

[0036] Wherein, represents the position of the i-th individual in the j-th dimension at the next iteration, and P j is a random integer within the range of [1, D], and D represents the dimension. represents the position of the i-th individual in the random dimension P j at the current iteration, r1 and r2 represent random numbers between (0, 1), and α represents an adaptive factor for adjusting the search step size. represents the position of the r-th beluga individual randomly selected at the current iteration in the reference dimension P1.

[0037] Further, in step 4.2, the calculation of the individual position according to the position update formula is specifically as follows:

[0038]

[0039] Wherein, represents the position of the i-th individual at the next iteration, represents the position of the i-th individual at the current iteration, represents the best individual position at the current iteration, represents the random individual position at the current iteration, r3 and r4 represent random numbers between (0, 1), α represents an adaptive factor for adjusting the search step size, C1 represents the random jump degree, and L F represents a random number conforming to the Levy distribution.

[0040] Further, the calculation formula of the random number L F conforming to the Levy distribution is specifically as follows:

[0041]

[0042] Wherein, m and n represent random numbers subject to the normal distribution, T represents the current iteration number, T max represents the maximum iteration number, β represents a number within the range of [1, 1.5] that decreases with the iteration, Γ(·) represents the gamma function for calculating the standard deviation, and σ represents the standard deviation for describing the distribution characteristics of the variable.

[0043] Further, in step 4.3, the introduction of the elite opposition-based learning strategy and the calculation of the individual position according to the position update formula are specifically as follows:

[0044]

[0045] Among them, represents the position of the i-th individual in the next iteration, represents the position of a random individual in the current iteration, r5, r5, and r7 represent random numbers between (0, 1), and α represents an adaptive factor used to adjust the search step size, represents the diving step size of the whale, represents the opposite position of the i-th individual in the next iteration;

[0046] The elite opposition-based learning strategy calculates and the fitness values f and f' and compares their magnitudes to obtain the final individual position in the whale fall stage: when f > f', the final individual position is when f < f', the final individual position is

[0047] The beneficial effects of the present invention are:

[0048] (1) Through the Piecewise chaotic mapping and the adaptive strategy, the present invention enhances the search ability in high-dimensional spaces and complex optimization problems. The chaotic mapping can make the population distribution more uniform than the probability-dependent random generation, increasing the diversity of population individuals.

[0049] (2) Dynamically adjusting the search step size according to the number of iterations and adopting the Levy flight strategy and the elite opposition-based learning strategy, the algorithm can widely search for potential solutions in the exploration stage while deeply mining high-quality solutions in the exploitation stage, ensuring that the global optimal or near-global optimal parameter values are finally found.

[0050] (3) The present invention improves the beluga whale optimization algorithm and uses the improved algorithm to complete the intelligent selection of the relevant parameters of the point cloud denoising algorithm, overcoming the defects of the traditional method such as excessive dependence on its own experience and low efficiency in parameter selection, and improving the efficiency and accuracy of parameter selection.

[0051] (4) Due to the advantages of evolutionary optimization algorithms in dealing with non-differentiable and non-convex problems, the present invention is applicable to different types of point cloud data, has good generalization ability, and thus makes the denoising results more robust. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flowchart of the point cloud denoising method based on the improved beluga whale optimization algorithm proposed by the present invention;

[0053] Figure 2 is a comparison chart of the convergence curves of point cloud denoising of the point cloud denoising method based on the improved beluga whale optimization algorithm proposed by the present invention on four models;

[0054] Among them,Figure 2 (a) The flower model is used. Figure 2 (b) The legoleg model is used. Figure 2 (c) The cup model is used. Figure 2 (d) The bunny model is used;

[0055] Figure 3 This is the point cloud denoising effect diagram of the point cloud denoising method based on the improved beluga optimization algorithm proposed by the present invention;

[0056] Among them, Figure 3 (a) is the denoised flower image optimized by the improved beluga optimization algorithm, Figure 3 (b) is the denoised legoleg image optimized by the improved beluga optimization algorithm, Figure 3 (c) is the denoised cup image optimized by the improved beluga optimization algorithm, Figure 3 (d) is the denoised bunny image optimized by the improved beluga optimization algorithm. Specific implementation manner

[0057] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0058] Embodiment 1

[0059] The present invention proposes a point cloud denoising method based on an improved beluga optimization algorithm. The flowchart of this method is as Figure 1 shown, including the following steps:

[0060] Step 1: Collect noisy three-dimensional point clouds through three-dimensional laser scanning;

[0061] Step 2: Initialize each parameter of the beluga optimization algorithm, including the population size Npop, the maximum number of iterations T max , the upper bound lb of the search space, the lower bound ub of the search space, the dimension nD, and the objective function fobj; use the Piecewise chaotic mapping to initialize the beluga population, and the individuals in the population are regarded as a set of parameters of the point cloud denoising algorithm; the specific process of using the Piecewise chaotic mapping to initialize the beluga population is expressed by the formula:

[0062]

[0063] Among them, x iRepresents the initial population individual position without Piecewise chaotic mapping, x i+1 Represents the population individual position after Piecewise chaotic mapping; P represents a piecewise control factor used to divide the 4 parts of the piecewise function, and R represents the upper and lower bounds of the population.

[0064] The point cloud denoising algorithm of this embodiment uses the SOR filtering algorithm. A set of parameters of the point cloud denoising algorithm includes: the number of neighbor points and the threshold for outlier determination.

[0065] Step 3: Substitute the individuals in the population into the point cloud denoising algorithm to process the noisy three-dimensional point cloud, and use the evaluation index to evaluate the denoised point cloud. The value of the evaluation index is regarded as the fitness value corresponding to this individual. Determine the current optimal individual and its corresponding position according to the fitness value; the calculation formula of the fitness value is:

[0066]

[0067] Among them, fitv is the fitness value used to evaluate the comprehensive performance of the parameter configuration; Pd is the precision rate, which measures the proportion of actual noise points among all points marked as noise points; Rd is the recall rate, which focuses on the proportion of all actually existing noise points that are successfully identified and removed.

[0068] Step 4: Select the beluga search behavior according to the balance factor and the whale fall probability, update the population position and fitness value, and determine the optimal individual and its corresponding position; the calculation formulas of the balance factor and the whale fall probability are:

[0069] B f = B0(1 - T / 2T max )

[0070] W f = 0.1 - 0.05T / T max

[0071] Among them, B f is the balance factor, W f is the whale fall probability, B0 is a random number in the range (0, 1), T is the current iteration number, and T max is the maximum iteration number of the population.

[0072] The specific process of Step 4 is:

[0073] Step 4.1: When B f > 0.5, the algorithm is in the exploration stage. Use the adaptive factor α to dynamically adjust the search step size, and calculate the individual position according to the position update formula; the position update formula is as follows:

[0074]

[0075] Among them, represents the position of the i-th individual in the j-th dimension at the next iteration, P j is a random integer within the range of [1, D], where D represents the dimension, represents the position of the i-th individual in a random dimension P at the current iteration j r1 and r2 represent random numbers between (0, 1), α represents an adaptive factor for adjusting the search step size, represents the position of the r-th beluga individual randomly selected at the current iteration on the reference dimension P1.

[0076] Step 4.2, when B f ≤ 0.5, the algorithm is in the exploration stage. The search step size is dynamically adjusted using the adaptive factor α, and the Levy flight strategy is dynamically adjusted using the β factor of the adaptive weight. The individual position is calculated according to the position update formula. The position update formula is as follows:

[0077]

[0078] Among them, represents the position of the i-th individual at the next iteration, represents the position of the i-th individual at the current iteration, represents the best individual position at the current iteration, represents the random individual position at the current iteration, r3 and r4 represent random numbers between (0, 1), α represents an adaptive factor for adjusting the search step size, C1 represents the random jump degree, L F represents a random number conforming to the Levy distribution. The calculation formula of L F is specifically as follows:

[0079]

[0080] Among them, m and n represent random numbers subject to the normal distribution, T represents the current number of iterations, T max represents the maximum number of iterations, β represents a number in the range of [1, 1.5] that decreases with the iteration, Γ(·) represents the gamma function for calculating the standard deviation, σ represents the standard deviation for describing the distribution characteristics of variables.

[0081] Step 4.3, when B f <W f the algorithm is in the whale fall stage. The step size is adjusted using the adaptive factor α, and the elite reverse learning strategy is introduced. The individual position is calculated according to the position update formula. Specifically:

[0082]

[0083] Among them, represents the position of the i-th individual in the next iteration, represents the position of a random individual in the current iteration, r5, r6, and r7 represent random numbers between (0, 1), and α represents an adaptive factor used to adjust the search step size. represents the diving step size of the whale, represents the opposite position of the i-th individual in the next iteration;

[0084] The elite opposition-based learning strategy calculates and the fitness values f and f' and compares their magnitudes to obtain the final individual position in the whale fall stage: when f > f', the final individual position is when f < f', the final individual position is

[0085] The calculation formula for the adaptive factor α is as follows:

[0086]

[0087] where r represents a random number between (0, 1), T represents the current iteration number, and T max represents the maximum iteration number.

[0088] Step 5: Determine whether the iteration number reaches the upper limit; if so, use the optimal individual, i.e., the optimal parameter value, as the final parameter configuration of the point cloud denoising algorithm, substitute it into the point cloud denoising algorithm to process the noisy three-dimensional point cloud, and obtain the denoised three-dimensional point cloud; if not, continue to execute Step 6;

[0089] Step 6: Use the elite selection strategy to calculate the fitness values through the optimal positions of the existing individuals and the new individual positions obtained in the current iteration, sort the population according to the fitness values, retain the elite individuals to obtain a new population, and return to Step 3.

[0090] The experiment of the present invention was carried out in the software environment of MATLAB. This experiment used the point cloud denoising dataset publicly available in the open-source project PointCleanNet to test the proposed improved beluga whale optimization algorithm.

[0091] When performing point cloud data analysis, in order to improve the processing efficiency and optimize the algorithm performance, the present invention performed downsampling on the original point cloud data. By maintaining the ratio of noise points to non-noise points, randomly extracting the target number of points to reduce the dataset size, the number of sample points in the experiment was set to 14,000, and the proportion of noise points was 10%.

[0092] For the point cloud denoising algorithm, the optimal parameters are selected using the beluga optimization algorithm and the improved beluga optimization algorithm respectively. The basic parameters are set as follows: the population size Npop is set to 50, the maximum number of iterations Max_it is 500, the dimension nD of the decision variable is set to 2, the upper bound ub of the parameter is [200, 200], and the lower bound lb of the parameter is [2, 1]. Among them, the population initialization of the improved beluga optimization algorithm adopts the Piecewise chaotic mapping method, and the parameter P is taken as 0.3. After the algorithm iterative calculation, the optimal parameters and the corresponding objective function value F1 as shown in Table 1 are obtained. The finally obtained optimal parameters are shown in Table 1, and the comparison diagram of the convergence curves corresponding to the two algorithms is as Figure 2 shown, and the point cloud denoising effect diagram based on the improved beluga optimization algorithm is as Figure 3 shown.

[0093] Table 1 is a comparison table of the point cloud denoising algorithm parameters obtained by the traditional beluga optimization algorithm and the improved beluga optimization algorithm and their corresponding F1 scores of the objective function.

[0094] Table 1

[0095]

[0096] The improved beluga optimization algorithm proposed by the present invention and the original beluga optimization algorithm (BWO) are respectively compared and tested on four different point cloud denoising models, and good results are obtained. It can be seen from Figure 2 that the algorithm in the present invention has the largest fitness value after iteration and also has a relatively fast convergence speed, which proves that the present invention can solve the disadvantages of using the original beluga optimization algorithm.

[0097] Through the chaotic mapping technology, the algorithm can generate a diverse solution space in the initialization stage, enhancing the global search ability; at the same time, the introduction of the adaptive strategy optimizes the search process, improving the adaptability and denoising efficiency of the algorithm for different noise environments; the elite opposition-based learning technology explores the reverse solution space of the elite solutions, thereby enhancing the diversity of solutions and the global search ability; the introduction of the elite selection mechanism ensures that higher-quality solutions are retained in each generation, improving the stability and denoising effect of the algorithm.

[0098] Those of ordinary skill in the art can realize that, combining the units and algorithm steps of each example described in the embodiments disclosed in the present application, they can be implemented by electronic hardware or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present application.

[0099] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A point cloud denoising method based on an improved beluga whale optimization algorithm, characterized in that It includes the following steps: Step 1: Collect noisy three-dimensional point clouds through three-dimensional laser scanning; Step 2: Initialize each parameter of the beluga whale optimization algorithm, and use the Piecewise chaotic mapping to initialize the beluga whale population. The individuals in the population are regarded as a set of parameters of the point cloud denoising algorithm; Step 3: Substitute the individuals in the population into the point cloud denoising algorithm to process the noisy three-dimensional point cloud, and use the evaluation index to evaluate the denoised point cloud. The value of the evaluation index is regarded as the fitness value corresponding to this individual, and the current optimal individual and its corresponding position are determined according to the fitness value; Step 4: Select the beluga whale search behavior according to the balance factor and the whale fall probability, update the population position and fitness value, and determine the optimal individual and its corresponding position; Step 5: Judge whether the number of iterations reaches the upper limit; If it reaches, use the optimal individual, that is, the optimal parameter value, as the final parameter configuration of the point cloud denoising algorithm, substitute it into the point cloud denoising algorithm to process the noisy three-dimensional point cloud, and obtain the denoised three-dimensional point cloud; if it does not reach, continue to execute Step 6; Step 6: Use the elite selection strategy to sort the population according to the fitness value, retain the elite individuals to obtain a new population, and return to Step 3.

2. The point cloud denoising method based on the improved beluga optimization algorithm according to claim 1, wherein In step 2, the specific parameters for initializing the beluga optimization algorithm are as follows: initialize the population size Npop, the maximum number of iterations T max , the upper bound lb of the search space, the lower bound ub of the search space, the dimension nD, and the objective function fobj; The specific process of initializing the beluga whale population using the Piecewise chaotic mapping is expressed by the formula: Among them, x i represents the position of an individual in the initial population that has not undergone the Piecewise chaotic mapping, and x i+1 represents the position of an individual in the population after the Piecewise chaotic mapping; P represents a piecewise control factor used to divide the four parts of the piecewise function, and R represents the upper and lower bounds of the population.

3. The point cloud denoising method based on the improved beluga whale optimization algorithm according to claim 1, wherein In Step 2, the point cloud denoising algorithm is specifically the SOR filtering algorithm. A set of parameters of the point cloud denoising algorithm includes: the number of neighbor points and the threshold for outlier determination.

4. The point cloud denoising method based on the improved beluga optimization algorithm according to claim 1, wherein In Step 3, the calculation formula for the fitness value is: Among them, fitv is the fitness value, which is used to evaluate the comprehensive performance of the parameter configuration; Pd is the precision rate, which measures the proportion of actual noise points among all points marked as noise points; Rd is the recall rate, which focuses on the proportion of all actual existing noise points that are successfully identified and removed.

5. The point cloud denoising method based on the improved beluga whale optimization algorithm according to claim 1, characterized in that, In Step 4, the calculation formulas for the balance factor and the whale fall probability are: B f = B0(1 - T / 2T max ) W f = 0.1 - 0.05T / T max Among them, B f is the balance factor, W f is the whale fall probability, B0 is a random number in the range (0, 1), T is the current iteration number, and T max is the maximum iteration number of the population.

6. The point cloud denoising method based on the improved beluga whale optimization algorithm according to claim 5, characterized in that, The specific process of Step 4 is: Step 4.

1. When B f > 0.5, the algorithm is in the exploration stage. The search step size is dynamically adjusted using the adaptive factor α, and the individual position is calculated according to the position update formula; Step 4.

2. When B f ≤ 0.5, the algorithm is in the development stage. The search step size is dynamically adjusted using the adaptive factor α, and the Levy flight strategy is dynamically adjusted using the β factor with adaptive weights. The individual position is calculated according to the position update formula; Step 4.

3. When B f <W f occurs, the algorithm is in the whale fall stage. The step size is adjusted using the adaptive factor α, and the elite opposition-based learning strategy is introduced to calculate the individual position according to the position update formula; The calculation formula for the adaptive factor α is as follows: Among them, r represents a random number between (0, 1), T represents the current iteration number, and T max represents the maximum number of iterations.

7. The point cloud denoising method based on the improved beluga optimization algorithm according to claim 6, wherein In Step 4.1, the specific calculation of the individual position according to the position update formula is: Among them, represents the position of the $i$-th individual in the $j$-th dimension at the next iteration, $P$ j is a random integer within the range of $[1, D]$, where $D$ represents the dimension, represents the position of the $i$-th individual in the random dimension $P$ j at the current iteration, $r1$ and $r2$ represent random numbers between $(0, 1)$, and $\alpha$ represents an adaptive factor used to adjust the search step size, represents the position of the randomly selected $r$-th beluga individual in the reference dimension $P1$ at the current iteration.

8. The point cloud denoising method based on the improved beluga optimization algorithm according to claim 6, characterized in that, In Step 4.2, the specific calculation of the individual position according to the position update formula is: Among them, represents the position of the i-th individual in the next iteration, represents the position of the i-th individual in the current iteration, represents the position of the best individual in the current iteration, represents the position of a random individual in the current iteration, r3 and r4 represent random numbers between (0, 1), α represents an adaptive factor for adjusting the search step size, C1 represents the random jump degree, L F represents a random number conforming to the Levy distribution.

9. The point cloud denoising method based on the improved beluga optimization algorithm according to claim 8, wherein The random number L that conforms to the Levy distribution F has the following specific calculation formula: where m and n denote random numbers subject to a normal distribution, T represents the current iteration number, T max represents the maximum iteration number, β represents a number in the range of [1, 1.5] that decreases with iteration, G(·) represents the gamma function used to calculate the standard deviation, σ represents the standard deviation used to describe the distribution characteristics of variables.

10. The point cloud denoising method based on the improved beluga optimization algorithm according to claim 6, characterized in that, In Step 4.3, introduce the elite opposition-based learning strategy, and the specific calculation of the individual position according to the position update formula is: Among them, represents the position of the i-th individual in the next iteration, represents the position of a random individual in the current iteration, r5, r6, and r7 represent random numbers between (0, 1), and α represents an adaptive factor used to adjust the search step size, represents the diving step size of the whale, represents the opposite position of the i-th individual in the next iteration; The elite reverse learning strategy calculates and the fitness values f and f' and compares their magnitudes to obtain the final individual position in the whale fall stage: when f > f', the final individual position is when f < f', the final individual position is

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