A hierarchical noise reduction graph optimization method and system

Abstract

The present invention belongs to the technical field of graph optimization processing, and relates to a graph optimization method and system for hierarchical noise reduction, including the following steps: S1 Divide the entire network into several modules and calculate the local positioning results of each module; S2 Obtain the edges whose endpoints are in two different modules, set them as key edges, and smooth the key edges; S3 According to the smoothed key edges in step S2, synchronize the local positioning results in step S1 to the same global coordinate system, thereby obtaining a denoised image. It can solve the graph optimization problem under a large-scale network, at the same time find out the key factors when the measurement results are noisy, sparse or uneven and the existing optimization algorithms perform poorly, and based on this, propose an effective noise processing method, and finally apply it to the network positioning problem. Implement a reliable and noise-resistant graph optimization method.

Description

Technical Field

[0001] The present invention relates to a graph optimization method and system for hierarchical noise reduction, belonging to the technical field of graph optimization processing, and particularly to the technical field of noise processing in images. Background Art

[0002] Currently, network localization mainly locates nodes in the network through infrastructure such as satellite-free and GPS. This technology is widely used in fields such as sensor networks, unmanned aerial vehicle networks, and robot networks, and mainly includes two steps:

[0003] 1. Information collection: Nodes measure each other through sensors, and these measurements include distance measurement, angle measurement, etc.;

[0004] 2. Position calculation: Convert the measurement information collected in step 1 into position information.

[0005] In the research of mobile robots, Simultaneous Localization and Mapping (SLAM technology) is one of the key technologies. Specifically, when a robot is in an unknown environment, its motion trajectory is determined through observations of the environment, and at the same time, an environmental map is constructed. SLAM based on the environmental map includes two steps:

[0006] 1. Environmental map construction: Using the pose of the robot as a vertex, the relationships between poses (such as odometer measurements, pose transformation matrices, loop detection, etc.) form edges. This step is often referred to as the front end, and is often a pile of sensor information.

[0007] 2. Environmental map optimization: Adjust the robot pose vertices to best satisfy the edge constraints. That is, the back end.

[0008] Both network localization and robot SLAM can be divided into two steps: information accumulation and position calculation. The graph optimization method is a key step among them. Graph optimization is essentially an optimization problem, and the existing solution methods mainly include the following three:

[0009] a) Graph rigidity-based method: The research objective is a given specific measurement set, and it is judged whether a unique localization result can be obtained, usually by judging the rigidity attribute of the graph.

[0010] b) Optimization-based method: Represent network localization as an optimization problem, and the objective is to minimize the root mean square error between the measurement values and the network coordinate estimates.

[0011] c) Module stitching-based method: Divide the entire network into several modules, calculate the local localization results of each module, and finally synchronize the local results by iteratively calculating rotation and transfer matrices to generate the global localization result.

[0012] In network localization or SLAM problems, due to the accumulation of front-end information, a large-scale optimization problem often arises. When the scale of the existing graph optimization method is very large, due to the large number of variables to be optimized simultaneously and the large amount of data processing, the calculation speed is slow and the requirements for equipment are high. In addition, the existing methods lack efficient and effective noise processing methods to ensure the positioning accuracy. Summary of the Invention

[0013] Aiming at the above problems, the purpose of the present invention is to provide a hierarchical noise reduction graph optimization method and system, which can solve the graph optimization problem under a large-scale network, and at the same time find out the key factors when the existing optimization algorithms perform poorly when the measurement results are noisy, sparse or uneven, and based on this, propose an effective noise processing method, and finally apply it to the network localization problem to achieve a reliable and noise-resistant graph optimization method.

[0014] To achieve the above purpose, the present invention adopts the following technical solutions: A hierarchical noise reduction graph optimization method includes the following steps: S1 Divide the entire network into several modules and calculate the local positioning results of each module; S2 Obtain the edges whose endpoints are in two different modules, set them as key edges, and smooth the key edges; S3 According to the smoothed key edges in step S2, synchronize the local positioning results in step S1 to the same global coordinate system, so as to obtain a denoised image.

[0015] Further, the specific calculation method of step S1 is: Cluster the nodes in the entire network to form several modules, so that the connections between the points within the module are dense, while the connections between the points in different modules are sparse; The G2O graph optimization algorithm is used to calculate the local structure of each module is a vector including the local structures of all modules, is the local structure of the i-th module, n c is the number of modules.

[0016] Further, the method for smoothing the key edges in step S2 is: S2.1 Propose a quantization index for measuring the noise degree of the key edges; S2.2 According to the quantization index of the noise degree, for each key edge allocate an adjustment vector Δ i , for any loop, then there is A L Δ = b L A L is the K-dimensional row vector of the loop L, b LIt is a quantization index of the noise level of loop L, and K is the number of critical edges; S2.3 Find no less than K loops containing critical edges, and establish a system of equations AΔ = b, where A is the K-dimensional coefficient matrix of all loops, and b is the quantization index of the noise level of all loops; S2.4 Solve the K-dimensional coefficient A of all loops, and then solve the adjustment vector Δ of each edge according to the coefficient matrix A.

[0017] Furthermore, in step S2.1, the quantization index is the closed-loop error, and the closed-loop error is the difference between the partial derivative J of the loop L containing l edges and the zero vector. The formula for the closed-loop error is:

[0018]

[0019] where represents the measurement information between nodes, represents the distance measurement between nodes, and θ ij represents the angle measurement between nodes.

[0020] Furthermore, the calculation formula for the adjustment vector Δ is: Δ = (A T A) -1 A T b, where A is the loop construction coefficient matrix.

[0021] Furthermore, the method for solving the loop construction coefficient matrix A in step S2.4 is: For any two edges among the K critical edges, find the shortest path through the corresponding vertices so that these two edges form a loop, thereby constructing loops, forming an overdetermined system of equations for the adjustment matrix Δ of all critical edges; or only use the loops formed by the critical edges between adjacent modules to form an overdetermined system of equations for the adjustment matrix Δ of all critical edges.

[0022] Furthermore, the specific method for step S3 is: S3.1 Arbitrarily select a representative point in each module in step S1, and project the smoothed critical edges in step S2 onto the edges between the representative points to form a backbone graph; S3.2 Solve the backbone graph to obtain the global results of the representative points; S3.3 According to the local results and global results of the representative points, expand the backbone graph to obtain the global results of the conversion of the critical edge vertices; S3.4 According to the local results and global results of the critical edge vertices, through the point cloud alignment method, the local results of each module in step S1 obtain the global results of each module

[0023] Furthermore, the global result of the conversion of the critical edge vertices in step S3.3 is:

[0024]

[0025] where is the global result of the key-edge vertices, is the local result of the key-edge vertices, is the global result of the i-th representative point, is the global result of the i-th representative point.

[0026] Furthermore, in step S3.4, the global results of each module are obtained from the local results of each module using the formula:

[0027]

[0028]

[0029] The present invention also discloses a hierarchical noise reduction graph optimization system, including: a network layering module for dividing the entire network into several modules and calculating the local positioning results of each module; a key-edge processing module for obtaining edges with endpoints in two different modules, setting them as key edges, and smoothing the key edges; a global result obtaining module for synchronizing the local positioning results in the network layering module to the same global coordinate system according to the smoothed key edges in the key-edge processing module, thereby obtaining a denoised image.

[0030] Due to the above technical solutions, the present invention has the following advantages:

[0031] 1. In the present invention, the key that affects the positioning result in a noisy environment is found, that is, the relatively few key measurement edges between modules. It is precisely these few pieces of inter-module information that are the key to global synchronization.

[0032] 2. The present invention designs a measurement edge noise quantization index: the closed-loop error, and smooths the key edge measurements through the closed-loop error, improving the reliability of the key edge information.

[0033] 3. The present invention adopts a hierarchical processing method, making it more suitable to adopt a parallel processing scheme in practical applications, with higher efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is a schematic structural diagram of the hierarchical noise reduction graph optimization method in an embodiment of the present invention;

[0035] Figure 2 is a diagram (a) of three modules of the hierarchical noise reduction graph optimization system in an embodiment of the present invention, and its corresponding backbone graph (b);

[0036] Figure 3 is a schematic diagram of the method for synchronizing the local results of each module to the global results in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0037] To enable those skilled in the art to better understand the technical direction of the present invention, the present invention is described in detail through specific embodiments. However, it should be understood that the provision of the specific embodiments is only for better understanding of the present invention, and they should not be construed as limitations on the present invention. In the description of the present invention, it should be understood that the terms used are only for the purpose of description and cannot be construed as indicating or implying relative importance.

[0038] The present invention relates to a hierarchical noise reduction graph optimization method and system. The overall network is divided into several dense modules. Since classical algorithms are good at processing dense modules, their local positioning results are reliable. For the unreliable key edges between modules, the concept of closed-loop error and the method of minimizing the closed error are proposed to increase the reliability of these key edges. Finally, through a conversion method, the local results are restored to the backbone graph to realize the structure of the whole graph. In addition, since local positioning can be calculated in parallel, the reliability, noise resistance and calculation efficiency are improved. The solutions of the present invention are described in detail below with reference to the accompanying drawings through two embodiments.

[0039] Embodiment 1

[0040] This embodiment discloses a hierarchical noise reduction graph optimization method, as Figure 1 shown, including the following steps:

[0041] S1 Divide the entire network into several modules and calculate the local positioning results of each module.

[0042] Cluster the nodes in the entire network to form several modules, such that the connections between the points within the modules are dense, while the connections between the points of different modules are sparse. There are various types of module division metrics, such as those based on measurement edge redundancy metrics, community density metrics or community modularity metrics, etc., which can be selected according to specific application scenarios. In this embodiment, it is preferably divided based on the community modularity metric. The divided modules can be represented by where n c is the number of modules.

[0043] For each module obtained according to the community modularity metric, due to its high modularity and dense measurement edges inside the module, according to statistical laws, the local positioning results of such modules can be obtained by classical methods. In this embodiment, the general G2O graph optimization algorithm is preferably used to calculate the local structure of each module is a vector including the local structures of all modules, is the local structure of the i-th module, and n c is the number of modules.

[0044] S2 obtains the edges with endpoints in two different modules, sets them as key edges, and smooths the key edges to eliminate the influence of these key edges on the accuracy of structure calculation.

[0045] The method for smoothing the key edges is as follows:

[0046] S2.1 proposes a quantization index for measuring the noise level of the key edges;

[0047] If the objective function of the given optimization problem is as follows:

[0048]

[0049] where, stores the position estimates of the entire network, is the position estimate of node v i and, is the optimal solution of the optimization problem (1). E represents all the measurements in the network. If node v i and node v j are within the ranging range of each other, then there exists (v i , v j ) ∈ E, represents the measurement information between nodes, represents the distance measurement between nodes, and θ ij represents the angle measurement between nodes. To make the objective function (1) take the minimum value, that is, to make its first derivative be the zero vector, then the following formula is obtained:

[0050]

[0051] where, N(v i ) is the neighboring set of node v i . Making the first derivative J = [0…0] T in formula (2) can establish n linear equations about and . Therefore, for a loop L containing l edges, the condition for its partial derivative J to be the zero vector is: That is, the loop condition. Obviously, in actual measurements, due to the existence of noise, the sum of the measurement vectors corresponding to a certain loop is basically impossible to be the zero vector. Therefore, the noise of the measurement is quantified according to the difference between the actual loop and the zero vector, that is, the quantization index of the noise level is: That is, the closed-loop error. The closed-loop error of the loop reflects the deviation between the measured information and the optimal situation.

[0052] S2.2 Process the measured information in the network according to the quantization index of the noise level, i.e., the closed-loop error. Through the module division in step S1, the key edges can be obtained. Let the number of key edges be K, which can be expressed as For each key edge allocate an adjustment vector Δ i , so that the closed-loop error of the loop formed by all adjusted key edges is zero. The adjustment matrix of all key edges can be expressed as: Δ = [Δ1, Δ2, … Δ K T , then the fact that the closed-loop error of a certain loop L is zero can be expressed by the following formula:

[0053]

[0054] Let A L be the K-dimensional row vector of loop L. If node v i is in the current loop, then the i-th element of A L is 1, otherwise it is 0. Then for any loop, formula (3) can be written as:

[0055] A L Δ = b L (4)

[0056] where b L is the quantization index of the noise level of loop L, i.e., the closed-loop error,

[0057] To solve the adjustment matrix of all key edges, more than K equations like formula (4) need to be constructed, and these equations are linearly independent. The construction method is: find no less than K loops containing key edges, and establish the equation system AΔ = b, where A is the K-dimensional coefficient matrix of all loops, and b is the quantization index of the noise level of all loops.

[0058] S2.4 Solve the K-dimensional coefficient A of all loops, and then according to the following formula: Δ = (A T A) -1 A T b to solve the adjustment vector Δ of each edge i , and finally substitute each key edge into the following formula for smoothing:

[0059]

[0060] The sum of the closed-loop errors of the loops formed by the key edges adjusted according to formula (5) is minimized.

[0061] Among them, the method for solving the loop construction coefficient matrix A is: for any two edges among the K key edges, find the shortest path through the corresponding vertices so that these two edges form a loop, thereby constructing ​Form a system of overdetermined equations for the adjustment matrix Δ of all critical edges; or considering that the critical edges between different modules often do not repeat, so only the loops formed by the critical edges between adjacent modules can be used to form a system of overdetermined equations for the adjustment matrix Δ of all critical edges. The number of equations constructed in this way can be greatly reduced, and the solution speed can be accelerated.

[0062] S3 Synchronize the local positioning results in step S1 to the same global coordinate system according to the smoothed critical edges in step S2, so as to obtain a denoised image.

[0063] S3.1 First, construct a backbone graph (Backbone Graph, BG), as Figure 2 shown. Arbitrarily select a representative point in each module in step S1, and project the smoothed critical edges in step S2 onto the edges between the representative points to form a backbone graph. Since only one representative point is selected for each module, but there can be multiple critical edges between two modules, the constructed backbone graph is a multi-graph, that is, there may be multiple edges between the same pair of vertices.

[0064] S3.2 Solve the backbone graph to obtain the global results of the representative points. This backbone graph can be solved using the G2O graph optimization algorithm mentioned above, and its results are more reliable than ordinary graphs. In this embodiment, the positioning results of the backbone graph are used as the global results, denoted by The global result of the i-th representative point is

[0065] S3.3 Expand the backbone graph according to the local and global results of the representative points to obtain the global results of the critical edge vertices after conversion.

[0066] The global results of the critical edge vertices after conversion are:

[0067]

[0068] where is the global result of the critical edge vertex, is the local result of the critical edge vertex, is the global result of the i-th representative point, is the local result of the i-th representative point.

[0069] S3.4 According to the local and global results of the critical edge vertices, through the point cloud alignment method, as Figure 3 shown, the local results of each module in step S1 are

[0070] to obtain the global results of each module The formula is as follows:

[0071]

[0072]

[0073] The hierarchical architecture of the present invention is easy to parallelize. Local positioning and the backbone graph can be carried out simultaneously in multiple threads. Their implementation results are converted into the global result through final synchronization. This hierarchical implementation method does not change the reliable local implementation results, and improves the synchronization accuracy by smoothing the critical edges.

[0074] Embodiment 2

[0075] Based on the same inventive concept, this embodiment discloses a hierarchical noise reduction graph optimization system, including:

[0076] A network hierarchical module, used to divide the entire network into several modules and calculate the local positioning results of each module;

[0077] A critical edge processing module, used to obtain the edges whose endpoints are in two different modules, set them as critical edges, and smooth the critical edges;

[0078] A global result obtaining module, used to synchronize the local positioning results in the network hierarchical module to the same global coordinate system according to the smoothed critical edges in the critical edge processing module, so as to obtain a denoised image.

[0079] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: it is still possible to modify the specific implementation manners of the present invention or make equivalent replacements, and any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the protection scope of the claims of the present invention. The above content is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, and all should be covered by the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A graph optimization method for hierarchical noise reduction, characterized in that, Including the following steps: S1 Divide the entire network into several modules and calculate the local positioning results of each module; S2 Obtain the edges whose endpoints are in two different modules, set them as key edges, and smooth the key edges; S3 According to the smoothed key edges in step S2, synchronize the local positioning results in step S1 to the same global coordinate system, thereby obtaining a denoised image; The method for smoothing the key edges in step S2 is as follows: S2.1 Propose a quantization index for measuring the noise level of the key edges; S2.2 According to the quantization index of the noise level, for each critical edge allocate an adjustment vector , for any loop, there is , is the K-dimensional row vector of loop L, is the quantization index of the noise level of loop L, and K is the number of critical edges ； S2.3 Find no less than K loops containing critical edges and establish a system of equations , where A is the K-dimensional coefficient matrix of all loops and b is the quantization index of the noise level of all loops; S2.4 Solve the K-dimensional coefficient A of all loops, and then solve the adjustment vector of each edge according to the coefficient matrix A ; The method for solving the loop structure coefficient matrix A in step S2.4 is as follows: For any two of the K critical edges, find the shortest path for the corresponding vertices so that these two edges form a loop, thereby constructing loops, forming an overdetermined system of equations for the adjustment vectors of all critical edges; or only use the loops formed by the critical edges between adjacent modules to form an overdetermined system of equations for the adjustment vectors of all critical edges; The specific method of step S3 is as follows: S3.1 Arbitrarily select a representative point in each module in step S1, and project the smoothed key edges in step S2 onto the edge between the representative points to form a backbone graph; S3.2 Solve the backbone graph to obtain the global results of the representative points; S3.3 According to the local results and global results of the representative points, expand the backbone graph to obtain the global results of the key edge vertices after conversion; S3.4 According to the local results and global results of the key-edge vertices, through the point cloud alignment method, the local results of each module in step S1 Obtain the global results of each module .

2. The graph optimization method for hierarchical noise reduction according to claim 1, characterized in that, The specific calculation method of step S1 is as follows: cluster the nodes in the entire network to form several modules, making the connections between points within the modules dense, while the connections between points in different modules sparse; the G2O graph optimization algorithm is used to calculate the local structures of each module , is a vector including the local structures of all modules, is the local structure of the i-th module, n c is the number of modules.

3. The graph optimization method for hierarchical noise reduction according to claim 2, characterized in that, In the step S2.1, the quantization index is the closed-loop error, and the closed-loop error is the difference between the partial derivative J of the loop L including l edges and the zero vector. The formula for the closed-loop error is: Among them, represents the measurement information between nodes, represents the distance measurement between nodes, represents the angle measurement between nodes.

4. The graph optimization method for hierarchical noise reduction according to claim 3, characterized in that, Adjustment vectors for all critical edges The calculation formula is as follows: .

5. The graph optimization method for hierarchical noise reduction according to claim 1, characterized in that, The global results of the key edge vertices after conversion in step S3.3 are: Among them, is the global result of the critical edge vertex, is the local result of the critical edge vertex, is the global result of the i-th representative point, is the global result of the i-th representative point.

6. The graph optimization method for hierarchical noise reduction according to claim 5, characterized in that, In step S3.4, the global results of each module are obtained from the local results of each module using the formula: 。 7. A graph optimization system for hierarchical noise reduction, characterized in that, Used to implement the hierarchical denoising graph optimization method according to any one of claims 1-6, including: A network hierarchical module for dividing the entire network into several modules and calculating the local positioning results of each module; A key edge processing module for obtaining the edges whose endpoints are in two different modules, setting them as key edges, and smoothing the key edges; A global result obtaining module for synchronizing the local positioning results in the network hierarchical module to the same global coordinate system according to the smoothed key edges in the key edge processing module, thereby obtaining a denoised image.

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