Image geometry estimation method based on delaunay triangulation guidance

Abstract

The present application belongs to the field of computer vision and robot perception technology, and is especially a kind of image geometric estimation method based on Delaunay triangulation guidance.The present application includes the following steps: S1: Delaunay triangulation;S2: multi-dimensional loss function design;S3: joint weight optimization;S4: parameter fine-tuning and output.The present application initiatively encodes the neighborhood topological relationship of inliers by Delaunay triangulation, combines edge-level geometric consistency constraint and spatial distribution regularization, and fuses multi-dimensional loss to construct a weighted optimization model.The present application not only inherits the core advantages of traditional estimation algorithms, such as anti-out-point interference and basic geometric stability, but also effectively solves the problems of insufficient cooperation between geometry and space optimization, poor robustness in complex scenes and difficult guarantee of accuracy, realizes the current optimal inlier screening and model refinement, and completes the high-precision and high-robust image geometric parameter estimation in a sparse inlier and strong noise environment.

Description

Technical Field

[0001] This invention relates to the fields of computer vision and robot perception technology, specifically to an image geometric estimation method based on Delaunay triangulation guidance. Background Technology

[0002] With the development of computer vision-related technologies, achieving reliable image geometric estimation from noisy matching points has become a core problem in robot perception systems, and its results have been widely applied in fields such as robot visual localization, autonomous navigation, simultaneous localization and mapping.

[0003] The core objective of image geometric estimation is to accurately solve for geometric parameters such as homography matrix, fundamental matrix, essential matrix, and camera relative pose from feature matching pairs of multi-view images, providing spatial relationships and motion state information for downstream tasks. However, in practical applications, matching pairs often contain a large number of interference points due to imaging noise, feature mismatches, and other factors, severely reducing the accuracy and robustness of image geometric estimation and becoming a key bottleneck restricting the implementation of the technology. To address these issues, existing geometric estimation algorithms mainly focus on three types of improvements within the random sampling consensus framework: first, hypothesis generation improvements, which optimize the sampling process through strategies such as feature quality ranking, spatial neighborhood selection, and neural network guidance to increase the probability of inlier sampling; second, model refinement improvements, which optimize model parameters through local iterative parameter tuning, probability-weighted fitting, and the introduction of geometric constraints to reduce noise and outlier interference; and third, hypothesis verification improvements, which reduce invalid model verification and improve computational efficiency through pre-testing, sequential probability ratio testing, and early exit mechanisms.

[0004] However, these three types of methods generally have significant limitations: none of them achieve synergistic optimization of geometric fitting accuracy and uniformity of interior point spatial distribution, and they are prone to fitting bias or insufficient robustness in complex scenarios such as dense noise and interior point clustering; the hypothesis generation improvement class relies too much on prior rules or data distribution characteristics, lacks consideration of spatial structure, and the sampling quality is easily affected by scene changes; the model refinement improvement class focuses on single parameter optimization, severing the intrinsic relationship between geometric consistency and spatial distribution, and it is difficult to balance local fitting and global structural stability; the hypothesis verification improvement class only optimizes the verification efficiency, does not fundamentally solve the model's adaptability to complex data, and some methods improve efficiency through complex computational logic, which exacerbates the "accuracy-efficiency" contradiction; more importantly, the existing methods have limited adaptability to real-world scenarios such as uneven interior point distribution and strong noise, and even through multiple iterations or complex energy optimization, it is difficult to simultaneously guarantee estimation accuracy, robustness, and real-time performance. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0006] To address the aforementioned technical problems, according to one aspect of the present invention, the present invention provides the following technical solution: an image geometric estimation method based on Delaunay triangulation guidance, comprising the following steps: S1: Delaunay triangulation: the initial set of interior points obtained from the initial screening of random sampling consistency. Perform Delaunay triangulation to construct a topological graph. , For vertex set, It is a neighborhood edge set; the partition follows the "empty circumcircle property": the circumcircle of any triangle contains only its own three vertices; S2: Multi-dimensional loss function design: Innovatively define edge-level geometric consistency loss and spatial distribution loss, and construct constraints by combining classic point-level geometric loss; S3: Joint weight optimization: For each interior point First, calculate the average edge-level geometric consistency loss. and average spatial distribution loss Introducing a balance factor Integrate the two into a unified loss ,in Optimization weights are used to balance geometric consistency and spatial distribution, preventing any single constraint from excessively dominating the optimization process. The uniform loss is then converted into interior point weights, ensuring that interior points with strong geometric consistency and uniform spatial distribution receive higher weights, while outliers or severely clustered interior points are effectively weighted lower. Finally, a weight matrix is ​​constructed. , This represents the number of interior points; S4: Parameter Fine-tuning and Output: Based on the Weight Matrix The optimal geometric parameters are solved by weighted least squares. The optimization objective is to minimize the weighted residual sum. .

[0007] As a preferred embodiment of the image geometric estimation method based on Delaunay triangulation guided by the present invention, the specific operation steps of Delaunay triangulation in S1 are as follows: Initialize the point set bounding box: with the initial inlier set Based on the extreme coordinates of all points, a minimum bounding box is constructed to ensure that the bounding box completely covers all initial interior points, thus determining the effective range of the subdivision; Construct a super triangle: Generate a super triangle whose three vertices coordinates must exceed the initial interior point set. The bounding box is constructed to ensure that all initial interior points are located inside the super triangle, serving as the initial mesh structure for subdivision; Point-by-point insertion and local repartitioning: Insert the interior points of the initial interior point set into the current triangular mesh one by one in a random order. For each insertion point, perform the following operations: Traverse the current triangular mesh and locate the target triangle containing the insertion point; Connect the insertion point to the three vertices of the target triangle and divide the target triangle into three new sub-triangles. Empty circumcircle property verification and adjustment: Perform empty circumcircle property verification on the newly generated sub-triangle and its adjacent triangles. If the circumcircle of an adjacent triangle contains the insertion point, delete the common edge of the adjacent triangle, reconnect the vertices to form a new triangle, and repeat this verification process until all triangles satisfy the empty circumcircle property. Trim super triangle vertices: Traverse the final triangular mesh, delete all triangles containing super triangle vertices, and the remaining set of triangles is the Delaunay triangular mesh consisting only of the initial interior points.

[0008] As a preferred embodiment of the image geometric estimation method guided by Delaunay triangulation described in this invention, the specific steps for designing the multi-dimensional loss function in S2 are as follows: Point-level geometric loss : As a fundamental constraint to ensure the core fitting accuracy of the model, the residuals are calculated based on the geometric task type: Fundamental matrix : Polar constraints; homography matrix : Projection constraints; Relative pose : Rigid body motion constraints ; Point-level loss is the square of the residual: ; Edge-level geometric consistency loss : Based on the geometric characteristics of camera motion, this design addresses each edge in the topological graph. Redefining loss:

[0009] in: for and The pixel distance is normalized by the image diagonal length to ensure consistent weights across images of different resolutions. , These are the pixel lengths of the corresponding edges in the query image and the reference image, respectively. When the camera rotates, the edge lengths of correctly matched edges remain consistent, while mismatches will result in significant deviations in length. When the camera pans, the edge lengths of points within close proximity are more likely to remain consistent due to similar depths, while the edge lengths of points within distant proximity may be inconsistent due to differences in depth. Introducing weights Strengthen the geometric consistency constraints of near interior points, as these interior points are more likely to have similar depths, and their geometric relationships are more stable during camera movement. In contrast, far interior points are more affected by perspective distortion, so the constraint weights should be appropriately reduced. Spatial distribution loss : By quantifying the uniformity of the spatial distribution of interior points using the geometric properties of triangles, and suppressing local overfitting caused by interior point clustering, an area descriptor is first defined. and shape descriptors :

[0010]

[0011] in: For the first The number of adjacent triangles of each interior point can be obtained by traversing the triangulation results and counting them. For the first The area of ​​each adjacent triangle, area descriptor The smaller the value, the closer the area of ​​the triangles adjacent to the interior point is to the global mean, and the more uniform the spatial distribution. The largest interior angle of the triangle, shape descriptor The smaller the value, the closer the triangle is to an equilateral triangle, and the more stable the grid structure. The spatial distribution loss is the product of the two descriptors, which comprehensively reflects the spatial uniformity of the interior points: .

[0012] As a preferred embodiment of the image geometric estimation method based on Delaunay triangulation guided by the present invention, the specific steps of joint weight optimization in S3 are as follows: Loss fusion: for each inlier For all its adjacent edges Take the arithmetic mean For all adjacent triangles Take the arithmetic mean The averaging operation weakens the interference of a single outlier edge or triangle on the overall loss.

[0013] This is a balancing factor used to adjust the weight ratio of geometric consistency and spatial distribution in the optimization process. Weight matrix construction: using an exponential decay function:

[0014] Will Convert to interior point weights, so that Smaller interior point weights rise rapidly. Larger interior point weights decrease slowly while constructing a weight matrix. By using weighted differential modulation, effective interior points play a dominant role in subsequent parameter refinement, while the influence of interference points is significantly suppressed.

[0015] As a preferred embodiment of the image geometric estimation method guided by Delaunay triangulation described in this invention, the specific steps of parameter fine-tuning and output in S4 are as follows: Based on the weight matrix The optimal parameters are solved by weighted least squares. The optimization objective is:

[0016] in, Let i be the weight of the i-th interior point. The residual function is defined according to the geometric task type. It is a point-level geometric loss.

[0017] Compared with existing technologies, the advantages of this invention are as follows: This invention innovatively encodes the neighborhood topological relationships of interior points through Delaunay triangulation, combines edge-level geometric consistency constraints and spatial distribution regularization, and integrates multi-dimensional losses to construct a weighted optimization model. It not only inherits the core advantages of traditional estimation algorithms in resisting out-point interference and maintaining basic geometric stability, but also effectively solves the problems of insufficient coordination between geometric and spatial optimization, poor robustness in complex scenes, and difficulty in guaranteeing accuracy. It achieves the current best interior point selection and model refinement, completing high-precision and highly robust image geometric parameter estimation under sparse interior point and strong noise environments. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a flowchart of an image geometric estimation method based on Delaunay triangulation guided by the present invention; Figure 2 The figures show the experimental results of the six algorithms of this invention on three types of image geometric estimation tasks; Figure 3 This is a sensitivity analysis diagram of the spatial distribution loss balance factor in an embodiment of the present invention; Figure 4 This is a sensitivity analysis diagram of the regularization term weight scaling parameter in an embodiment of the present invention. Detailed Implementation

[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0020] Secondly, the present invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0022] This invention discloses an image geometric estimation method (DLOSAC) guided by Delaunay triangulation. Its key technologies include three core steps: Delaunay triangulation, multi-dimensional loss calculation, and joint weight optimization. By deeply fusing geometric consistency and spatial distribution information, it achieves robust and accurate geometric parameter estimation under conditions of uneven interior point distribution and strong noise. Specifically, it includes: S1: Delaunay triangulation: the initial set of interior points obtained from the initial screening of random sampling consistency. Perform Delaunay triangulation to construct a topological graph. ( For vertex set, (The set of neighborhood edges). The decomposition follows the "empty circumcircle property": the circumcircle of any triangle contains only its own three vertices. This property maximizes the minimum interior angle of all triangles while effectively avoiding the generation of degenerate triangles with narrow or obtuse angles, ensuring the uniformity and numerical stability of the triangular mesh. Furthermore, Delaunay triangulation naturally induces graph structure, explicitly encoding the neighborhood topological relationships between interior points, providing accurate neighboring point associations and geometric attribute support for subsequent edge-level geometric consistency analysis and spatial distribution loss calculation. This technique only decomposes the set of interior points after initial screening, rather than all original matching points, significantly reducing the computational cost of the model and ensuring the efficiency of the algorithm.

[0023] The specific steps for Delaunay triangulation are as follows: 1. Initialize the point set bounding box: using the initial inlier set Based on the extreme coordinates of all points, a minimum bounding box is constructed to ensure that the bounding box completely covers all initial interior points, thus determining the effective range of the subdivision; 2. Construct a super triangle: Generate a super triangle whose three vertices must exceed the initial interior point set. The bounding box is constructed to ensure that all initial interior points are located inside the super triangle, serving as the initial mesh structure for subdivision; 3. Point-by-point insertion and local re-subdivision: Insert the interior points of the initial interior point set into the current triangular mesh one by one in random order. For each insertion point, perform the following operations: a. Traverse the current triangular mesh and locate the target triangle containing the insertion point; b. Connect the insertion point to the three vertices of the target triangle to divide the target triangle into three new sub-triangles; 4. Verification and adjustment of empty circumcircle property: Verify the empty circumcircle property of the newly generated sub-triangle and its adjacent triangles. If the circumcircle of an adjacent triangle contains the insertion point, delete the common edge of the adjacent triangle, reconnect the vertices to form a new triangle, and repeat this verification process until all triangles satisfy the empty circumcircle property. 5. Trim super triangle vertices: Traverse the final triangular mesh and delete all triangles that contain super triangle vertices. The remaining set of triangles is the Delaunay triangular mesh consisting only of the initial interior points.

[0024] Through the above steps, a Delaunay triangular mesh that satisfies the property of an empty circumcircle can be efficiently constructed, providing a high-quality geometric foundation for subsequent topology graph construction. At the same time, this partitioning process is only performed on the interior point set after the initial screening, which greatly reduces the computational overhead and ensures the efficiency of the algorithm.

[0025] S2: Multi-dimensional loss function design: Innovatively define edge-level geometric consistency loss and spatial distribution loss, and combine them with classic point-level geometric loss to construct constraints, breaking through the limitations of traditional methods with single point-level residual constraints.

[0026] The specific steps for designing a multi-dimensional loss function are as follows: (1) Point-level geometric loss ): As a fundamental constraint to ensure the core fitting accuracy of the model, the residuals are calculated based on the geometric task type: Fundamental matrix : (Polar constraint); homography matrix : (Projection constraints); Relative pose : (rigid body motion constraints, ); Point-level loss is the square of the residual: .

[0027] (2) Edge-level geometric consistency loss ): Based on the geometric characteristics of camera motion, this design addresses each edge in the topological graph. Redefining loss:

[0028] in: for and The pixel distance is normalized by the image diagonal length to ensure consistent weights across images of different resolutions. , These are the pixel lengths of the corresponding edges in the query image and the reference image, respectively. When the camera rotates, the edge lengths of correctly matched edges remain consistent, while mismatches will result in significant deviations in length. When the camera pans, the edge lengths of points within close proximity are more likely to remain consistent due to similar depths, while the edge lengths of points within distant proximity may be inconsistent due to differences in depth. Introducing weights Strengthen the geometric consistency constraints on nearby interior points. These interior points are more likely to have similar depths, so their geometric relationships are more stable during camera movement. However, distant interior points are more affected by perspective distortion, so the constraint weights are appropriately reduced.

[0029] (3) Spatial distribution loss ): By quantifying the uniformity of the spatial distribution of interior points using the geometric properties of triangles, and suppressing local overfitting caused by interior point clustering, an area descriptor is first defined. and shape descriptors :

[0030]

[0031] in: For the first The number of adjacent triangles of each interior point can be obtained by traversing the triangulation results and counting them. For the first The area of ​​each adjacent triangle, area descriptor The smaller the value, the closer the area of ​​the triangles adjacent to the interior point is to the global mean, and the more uniform the spatial distribution. The largest interior angle of the triangle (in radians), shape descriptor. The smaller the value, the closer the triangle is to an equilateral triangle, and the more stable the grid structure. The spatial distribution loss is the product of the two descriptors, which comprehensively reflects the spatial uniformity of the interior points:

[0032] Compared to traditional geometric estimation methods, this design breaks through the limitations of single-point residual constraints and constructs a joint constraint of "point-level, edge-level, and spatial distribution". It accurately describes the geometric validity and spatial distribution uniformity of interior points, providing a multi-dimensional complementary loss basis for subsequent joint weight optimization and parameter refinement, and solving the problem of insufficient coordination between geometric fitting and spatial distribution from the constraint level.

[0033] S3: Joint weight optimization: For each interior point First, calculate the average edge-level geometric consistency loss. and average spatial distribution loss Introducing a balance factor Integrate the two into a unified loss ,in Optimization weights are used to balance geometric consistency and spatial distribution, preventing any single constraint from excessively dominating the optimization process. The uniform loss is then converted into interior point weights to ensure that interior points with strong geometric consistency and uniform spatial distribution ( Smaller points receive higher weights, while outliers or heavily clustered inliers receive higher weights. Larger components are effectively weighted less. Finally, a weight matrix is ​​constructed. ( (where the number of interior points is 1), this technique enhances the contribution of effective interior points through weight modulation, significantly suppressing the influence of interfering points.

[0034] The specific steps for joint weight optimization are as follows: Loss fusion: for each inlier For all its adjacent edges Take the arithmetic mean For all adjacent triangles Take the arithmetic mean The averaging operation weakens the interference of a single outlier edge or triangle on the overall loss.

[0035] This is a balancing factor used to adjust the weighting of geometric consistency and spatial distribution in the optimization process.

[0036] Weight matrix construction: using an exponential decay function:

[0037] Will Convert to interior point weights, so that Smaller interior point weights rise rapidly. Larger interior point weights decrease slowly, a design that ensures both robustness and sensitivity in optimization. A weight matrix is ​​also constructed. By using weighted differential modulation, effective interior points play a dominant role in subsequent parameter refinement, while the influence of interference points is significantly suppressed.

[0038] Compared to traditional geometric estimation methods, this design strengthens the contribution of high-quality interior points while suppressing the influence of interference points, providing accurate weighting basis for subsequent weighted least squares parameter refinement, and solving the problems of traditional methods having a single weight allocation and not taking into account geometric and spatial characteristics.

[0039] S4: Parameter Fine-tuning and Output: Based on the Weight Matrix The optimal geometric parameters are solved by weighted least squares. The optimization objective is to minimize the weighted residual sum. This optimization technique fully utilizes the precise weight allocation brought about by the joint loss, making the model parameter estimation more closely resemble the real geometric laws, and finally outputs the optimal geometric model parameters and the final interior point set, achieving high-precision and highly robust image geometric estimation.

[0040] The specific steps for parameter fine-tuning and output are as follows: Based on the weight matrix The optimal parameters are solved using weighted least squares (WLS). The optimization objective is:

[0041] in, Let i be the weight of the i-th interior point. The residual function is defined according to the geometric task type. It is a point-level geometric loss.

[0042] This design fully integrates information from point-level geometric constraints, edge-level geometric consistency constraints, and spatial distribution constraints. By using a weight matrix to amplify the contribution of effective interior points and suppress the influence of interfering points, the solved geometric parameters more closely resemble the geometric patterns of the real scene. After the solution is completed, the optimal geometric model parameters are output. Combined with the final set of interior points, the geometric estimation of the image is completed.

[0043] This invention selects the following traditional geometric estimation methods as a comparison benchmark: RANSAC: Disables local optimization and serves as a baseline for evaluating the accuracy and stability of robust estimation. LO-RANSAC: Performs local optimization (such as iterative least squares) on the inlier set of the current best model, while refining the model parameters and inlier assignments; -RANSAC: Based on LO-RANSAC, it extends the local optimization stage by introducing truncated quadratic loss and setting an upper bound on the number of interior points; GC-RANSAC: Employs a graph cut energy minimization method, combining residual size and spatial coherence to achieve interior / exterior point partitioning, and then refines the model accordingly. PSC-RANSAC: Clusters matching pairs in displacement space to remove mismatches, and then refines the model parameters.

[0044] For the task of estimating the fundamental matrix and homography matrix, this paper uses the mean of pixel error. (Unit: pixels) and standard deviation (Unit: pixels) is used as the evaluation metric, and the improvement rate is defined. The performance improvement of the proposed method compared to the comparison method is quantified, and the improvement rate is calculated using the following formula:

[0045] For the relative pose estimation task, this paper uses rotation error. (Unit: degrees) and translation error (Unit: degrees) is used as the evaluation index, and the average error is defined. The improvement rate is calculated based on this average error. This is used to characterize the overall error level.

[0046] Figure 2 This paper summarizes the experimental results of six algorithms on three types of image geometric estimation tasks, with the best performance results highlighted in bold. Quantitative evaluation results of DLOSAC and five traditional methods on the three core geometric estimation tasks are also presented. Figure 2As shown, DLOSAC achieved the lowest mean error and minimum standard deviation in average performance across almost all tasks and in tests on individual datasets, comprehensively outperforming existing methods such as traditional RANSAC and LO-RANSAC. This result fully demonstrates the technical superiority of this invention: relying on the accurate encoding of endogenous neighborhood topology by Delaunay triangulation and the multi-dimensional loss collaborative design of edge-level geometric consistency constraints and spatial distribution regularization, it effectively captures the local structural correlations and global distribution uniformity between interior points, significantly improving its resistance to imaging noise, feature mismatches, and interior point clustering, maintaining stable and high-precision estimation in different scenarios. Even in complex scene tests, DLOSAC maintains a significant advantage, effectively avoiding the problem of traditional methods easily getting trapped in local optima or fitting bias, and controlling computational overhead while achieving higher accuracy, fully demonstrating its comprehensive technical advantages in accuracy, robustness, and efficiency.

[0047] Example: This invention provides an image geometric estimation method based on Delaunay triangulation-guided (DLOSAC). The implementation method will be specifically illustrated below using an indoor mobile robot visual localization scenario as an example. In this scenario, the robot, equipped with a monocular camera, acquires RGB images of the same room from different perspectives. It needs to estimate the homography matrix between the two images to calculate its pose and thus complete autonomous navigation. In this scenario, image matching is easily affected by changes in lighting, object occlusion, and repetitive furniture textures, resulting in a large number of mismatched points in the matched pairs. Furthermore, interior points tend to cluster in dense areas such as shelves and tables, and are sparsely distributed in open areas. Traditional methods struggle to balance geometric estimation accuracy and robustness. This method, through a complete process design including ORB feature extraction, initial matching pair generation, RANSAC inlier screening, topology construction, multi-dimensional loss calculation, weight optimization, and parameter refinement, not only inherits the core advantages of traditional estimation algorithms in resisting outlier interference and maintaining basic geometric stability, but also effectively solves the problems of insufficient coordination between geometric and spatial optimization, poor robustness in complex scenes, and difficulty in guaranteeing accuracy. It achieves the current best inlier screening and model refinement, and completes high-precision, highly robust image geometric parameter estimation, providing reliable support for robot pose calculation.

[0048] The known conditions (i.e., input variables) of this invention are: original RGB images (640×480 resolution) of the same scene from different perspectives acquired by the robot; the variable to be determined is: the optimal homography matrix between the two images. Fundamental matrix Relative pose Explanation of known conditions and variables to be solved: The two RGB images are the query image and reference image for the robot's current position, respectively, containing common indoor objects such as tables, shelves, and the floor; the fundamental matrix describes the epipolar constraints of the two images, the homography matrix represents the planar projection relationship, and the relative pose directly characterizes the camera's motion state; all three are core geometric parameters for robot pose calculation. Figure 1 As shown, the specific workflow of the image geometric estimation method guided by Delaunay triangulation is as follows: Step 1: ORB feature extraction, initial matching pair generation, and RANSAC inlier screening: First, the input query image and reference image (original RGB images) are processed by the ORB feature extractor: for each image, keypoints are extracted and corresponding descriptions are generated, resulting in the keypoint set and description set for the query image and the reference image. This process effectively preserves corner features of objects such as table edges and shelf corners, resisting feature distortion caused by changes in lighting. Then, the two sets of descriptions are input into the matcher, and an initial set of matching pairs is selected using a similarity metric. ,in , These are the homogeneous pixel coordinates of the matching points in the query image and the reference image, respectively. This represents the initial total number of matching pairs. In actual indoor mobile robot visual localization, after the robot moves a certain distance within the room, and after extraction and preliminary matching, an initial matching point set M of N=200 pairs is obtained. These matching points contain a large number of erroneous matches caused by repetitive textures on indoor shelves and reflections on the tabletop.

[0049] Based on the above initial set of matching pairs Initiate the classical RANSAC algorithm iteration: each iteration starts from... The smallest sample set is randomly selected from the data to generate model hypotheses. Set residual threshold Calculate all matching points relative to geometric residuals , will satisfy Matching points are determined to be interior points, and the number of interior points is counted using an indicator function.

[0050] in: The function is an indicator function; it takes the value 1 if the condition is true, and 0 otherwise. The iteration is repeated until the confidence criterion is met, at which point the optimal model hypothesis with the largest number of interior points is retained, and the initial interior point set is output. and the initial model In this example, this step quickly removes erroneous matching points that clearly violate the physical projection relationship by setting a residual threshold τ (3 pixels).

[0051] The optimal model is defined as:

[0052] This step, within the feasible region of parameters, quickly filters out a large number of outliers, providing high-quality foundational data for subsequent topology construction. In this example, after RANSAC initial screening, 53 inliers remain from the 200 matching points, forming the initial inlier set, Pinlier. However, these inliers are extremely unevenly distributed in the image space. 32 inliers are concentrated on the textured tabletop, while only 21 inliers representing distant walls and the ground are sparsely distributed. If these 50 points are used directly for geometric estimation, the dense points on the tabletop will lead to local overfitting, causing a severe tilt in the calculated robot pose.

[0053] Step 2: Encoding the neighborhood relations of interior points using Delaunay triangulation: The initial interior point set output in step one To process the target (in this example, the 53 selected 2D pixel coordinates, m=53), a Delaunay triangulation operation is performed. The core of this triangulation follows the "empty circumcircle property"—the circumcircle of any triangle contains only its three vertices. This property maximizes the minimum interior angle of all triangles, effectively avoiding the generation of degenerate triangles with narrow or obtuse angles, ensuring the uniformity and numerical stability of the triangular mesh, and solving the problems of uneven point distribution and high noise interference in indoor scenes. Simultaneously, Delaunay triangulation naturally induces graph structure, providing a solid foundation for topological graph construction. Furthermore, this step only triangulates the initially selected interior point set, rather than all original matching points, significantly reducing the computational cost of triangulation and ensuring the algorithm's efficiency. In the physical scenario of this example, this step connects 32 interior points clustered on the desktop with 21 interior points scattered on the ground and walls based on spatial proximity, so that the desktop area automatically forms a dense small-scale triangular mesh, while the open area forms a sparse large-scale triangular mesh, thereby explicitly depicting the local density differences and global non-uniformity of interior points in the image space.

[0054] The specific steps for Delaunay triangulation are as follows: 1. Initialize the point set bounding box: using the initial inlier set Based on the extreme coordinates of all points, a minimum bounding box is constructed to ensure that the bounding box completely covers all initial interior points, thus determining the effective range of the subdivision; 2. Construct a super triangle: Generate a super triangle whose three vertices must exceed the initial interior point set. The bounding box is constructed to ensure that all initial interior points are located inside the super triangle, serving as the initial mesh structure for subdivision; 3. Point-by-point insertion and local re-subdivision: Insert the interior points of the initial interior point set into the current triangular mesh one by one in random order. For each insertion point, perform the following operations: a. Traverse the current triangular mesh and locate the target triangle containing the insertion point; b. Connect the insertion point to the three vertices of the target triangle to divide the target triangle into three new sub-triangles; 4. Verification and adjustment of empty circumcircle property: Verify the empty circumcircle property of the newly generated sub-triangle and its adjacent triangles. If the circumcircle of an adjacent triangle contains the insertion point, delete the common edge of the adjacent triangle, reconnect the vertices to form a new triangle, and repeat this verification process until all triangles satisfy the empty circumcircle property. 5. Trim super triangle vertices: Traverse the final triangular mesh and delete all triangles that contain super triangle vertices. The remaining set of triangles is the Delaunay triangular mesh consisting only of the initial interior points.

[0055] Through the above steps, a Delaunay triangular mesh that satisfies the property of an empty circumcircle can be efficiently constructed, providing a high-quality geometric foundation for subsequent topology graph construction. At the same time, this partitioning process is only performed on the interior point set after the initial screening, which greatly reduces the computational overhead and ensures the efficiency of the algorithm.

[0056] A topology graph is constructed based on the final triangular mesh obtained from the above subdivision. , where vertex set edge set Adjacent vertices of the triangle Explicitly encoding the neighborhood topology between internal points provides accurate basis for the association of adjacent points in subsequent edge-level geometric consistency analysis, and also provides triangular geometric properties to support the calculation of spatial distribution loss.

[0057] Step 3: Construct a multi-dimensional loss function By integrating point-level geometric loss, edge-level geometric consistency loss, and spatial distribution loss to construct joint constraints, the limitations of traditional single-point residual constraints are overcome. The three types of losses complement each other and work synergistically to effectively solve the geometric estimation problem in complex indoor scenes. The specific calculation is as follows: (1) Point-level geometric loss ): As a fundamental constraint to ensure the core fitting accuracy of the model, the residuals are calculated based on the geometric task type: Fundamental matrix : (Polar constraint); homography matrix : (Projection constraints); Relative pose : (rigid body motion constraints, ); Point-level loss is the square of the residual: In this example, represents the square of the pixel distance between the corner point of the table projected through the currently assumed homography matrix H and the actual matching point, used to measure whether a single feature point conforms to the physical projection law. (2) Edge-level geometric consistency loss ): Based on the geometric characteristics of camera motion, this design addresses each edge in the topological graph. Define loss:

[0058] in: for and The pixel distance is normalized by the image diagonal length to ensure consistent weights across images of different resolutions. , These are the pixel lengths of the corresponding edges in the query image and the reference image, respectively. In the indoor scene of this example, when the camera is panned or rotated, the side lengths of adjacent points of rigid objects such as the edge of the shelf and the outline of the table should be consistent. Points that are mismatched or affected by occlusion will show significant deviations in side length. Introducing weights Strengthen the geometric consistency constraints on nearby interior points, as these interior points are more likely to have similar depths and their geometric relationships are more stable during camera movement. In contrast, distant interior points are more affected by perspective distortion, so the constraint weights should be appropriately reduced.

[0059] (3) Spatial distribution loss ): By quantifying the uniformity of the spatial distribution of interior points using the geometric properties of triangles, and suppressing local overfitting caused by interior point clustering, an area descriptor is first defined. and shape descriptors :

[0060]

[0061] in: For the first The number of adjacent triangles of each interior point can be obtained by traversing the triangulation results and counting them. For the first In this example, the area ATij of adjacent triangles formed by the inliers within the desktop dense clustering region is significantly smaller than the global average area, causing the area descriptor to... Increase; while the area of ​​adjacent triangles formed by interior points within sparse areas of the ground increases. Significantly larger than the global average area, which also causes the area descriptor to... Increase. Area descriptor The smaller the value, the closer the area of ​​the triangles adjacent to the interior point is to the global mean, and the more uniform the spatial distribution. The largest interior angle of the triangle (in radians). In this example, triangles formed by sparse interior points on the ground or wall often exhibit a long and narrow shape, with their largest interior angle approaching π, resulting in a shape descriptor... i increases significantly. Shape descriptor The smaller the value, the closer the triangle is to an equilateral triangle, the more stable the grid structure, and the better it solves the problem of triangle degradation caused by sparse points in open areas. The spatial distribution loss is the product of the two descriptors, which comprehensively reflects the spatial uniformity of the interior points: .

[0062] Step 4: Joint weight optimization, constructing the weight matrix: For each interior point First, calculate the average edge-level geometric consistency loss. and average spatial distribution loss Introducing a balance factor Integrate the two into a unified loss ,in Optimization weights are used to balance geometric consistency and spatial distribution, preventing any single constraint from excessively dominating the optimization process. The uniform loss is then converted into interior point weights using an exponential decay function. This function's properties result in exponentially higher weights for interior points with strong geometric consistency and uniform spatial distribution (such as continuous interior points along a table edge), while outliers or severely clustered interior points (such as outliers in densely packed shelving areas) are effectively weighted lower. Finally, a weight matrix is ​​constructed. .

[0063] The specific steps for joint weight optimization are as follows: Loss fusion: for each inlier For all its adjacent edges Take the arithmetic mean For all adjacent triangles Take the arithmetic mean The averaging operation weakens the interference of a single outlier edge or triangle on the overall loss.

[0064] in interior point The number of adjacent edges, This is a balancing factor used to precisely adjust the weighting of geometric consistency and spatial distribution in the optimization process. To ensure the model maintains stable performance across different scenarios, a sensitivity analysis is performed on it in this example, and the results are as follows. Figure 3 As shown, Selected in The reasonable value within the range is taken by default. This range of values ​​can effectively balance the contributions of the two types of constraints, avoiding one constraint from excessively dominating the optimization process. Furthermore, the error curve is smooth and stable within this range, indicating that the algorithm has low sensitivity to this hyperparameter.

[0065] Weight matrix construction: using an exponential decay function

[0066] in The scaling parameter controls the weight decay rate, balancing robustness and sensitivity. To balance the discriminative power and noise resistance of weight differences, a sensitivity analysis is performed in this example, with the following results. Figure 4 As shown, scaling parameters Used to adjust the weights of the proposed regularization term: The smaller the value, the more the regularization differences between samples are amplified, and the relative weight of points with larger residuals will increase significantly; conversely, the larger the value, the more the regularization differences between samples are amplified. The larger the value, the smoother the regularization differences between samples will be, and the weight of points with larger residuals will be reduced.

[0067] Selected in The reasonable value within the range is taken by default. This value allows for interior points with strong geometric consistency and uniform spatial distribution ( Smaller (those with lower) weights receive exponentially higher weights, becoming the core contributors to parameter estimation; while The weights of larger inliers (which may be mismatched inliers or cluster points) are significantly reduced, and their interference is effectively suppressed.

[0068] Constructing the weight matrix By using weighted differential modulation, effective interior points play a dominant role in subsequent parameter refinement, significantly suppressing the influence of interference points. This technique enhances the contribution of effective interior points through weighted modulation, thereby significantly suppressing the impact of interference points.

[0069] Construct a diagonal weight matrix based on the weights of all interior points. ( (where is the number of interior points). This matrix enables differentiated modulation of different interior points, allowing the topological constraints and loss constraints guided by Delaunay triangulation to be fully integrated into the subsequent parameter refinement process.

[0070] Step 5: Parameter refinement, output optimal geometric parameters The weight matrix constructed in step four Based on this, and combined with the point-level geometric loss from step three, the optimal geometric parameters are solved using weighted least squares. The optimization objective is:

[0071] In this example, the traditional unweighted least squares method assigns equal weights (i.e., the equivalent weights are all 1) to the aforementioned 53 initial interior points. This equalization process leads to the robot pose calculation result being overly dominated by the 32 desktop cluster interior points, causing local overfitting. However, after weighted optimization using the formula (9) of this invention, when resolving the homography matrix H, the weight wp of the 32 desktop cluster interior points drops to 0.15 after joint loss calculation, and the contribution of these interior points in the parameter solution process is significantly suppressed. In contrast, the 21 spatially uniform wall and ground interior points, with a weight wp as high as 0.9, highlight their dominant position in the model parameter fitting. This optimization objective deeply integrates multi-dimensional information such as point-level geometric constraints, edge-level geometric consistency constraints, and spatial distribution constraints. Through the weight matrix, it amplifies the contribution of effective interior points and suppresses the influence of interference points. At the same time, relying on the topological structure provided by Delaunay triangulation, it ensures that the parameter estimation process strictly conforms to the real distribution law of interior points in physical space. The above minimization problem is solved using a numerical optimization algorithm, iterating until the preset convergence condition is met.

[0072] After the solution is completed, the optimal geometric model parameters θ are output. The final interior point set completes the image geometric estimation process. The final output is a high-precision homography matrix θ. =H is fed back to the robot's underlying control system in real time, effectively eliminating positioning drift errors caused by local texture clustering, thus ensuring the autonomous navigation accuracy and robustness of the mobile robot in complex indoor environments. This optimization objective deeply integrates comprehensive information from point-level geometric constraints, edge-level geometric consistency constraints, and spatial distribution constraints. It amplifies the contribution of effective interior points and suppresses the influence of interfering points through a weight matrix. At the same time, relying on the topological structure of Delaunay triangulation, it ensures that the parameter estimation process closely matches the real spatial distribution pattern of interior points.

[0073] Based on the aforementioned experiments and examples, the image geometric estimation framework (DLOSAC) proposed in this invention, guided by Delaunay triangulation, overcomes the limitations of traditional methods by introducing Delaunay triangulation and combining geometric consistency and spatial distribution co-optimization. It significantly outperforms existing geometric estimation algorithms in terms of anti-imaging noise, feature mismatch capability, geometric parameter estimation accuracy, adaptability to complex scenes, and computational efficiency.

[0074] Although the present invention has been described above with reference to embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of the invention. In particular, as long as there is no structural conflict, the features in the disclosed embodiments can be combined with each other in any manner. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, the present invention is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. An image geometric estimation method guided by Delaunay triangulation, characterized in that, Includes the following steps: S1: Delaunay triangulation: the initial set of interior points obtained from the initial screening of random sampling consistency. Perform Delaunay triangulation to construct a topological graph. , For vertex set, It is a neighborhood edge set; the partition follows the "empty circumcircle property": the circumcircle of any triangle contains only its own three vertices; S2: Multi-dimensional loss function design: Innovatively define edge-level geometric consistency loss and spatial distribution loss, and construct constraints by combining classic point-level geometric loss; S3: Joint weight optimization: For each interior point First, calculate the average edge-level geometric consistency loss. and average spatial distribution loss Introducing a balance factor Integrate the two into a unified loss ,in Optimization weights are used to balance geometric consistency and spatial distribution, preventing any single constraint from excessively dominating the optimization process. The uniform loss is then converted into interior point weights, ensuring that interior points with strong geometric consistency and uniform spatial distribution receive higher weights, while outliers or severely clustered interior points are effectively weighted lower. Finally, a weight matrix is ​​constructed. , This represents the number of interior points; S4: Parameter Fine-tuning and Output: Based on the Weight Matrix The optimal geometric parameters are solved by weighted least squares. The optimization objective is to minimize the weighted residual sum. .

2. The image geometric estimation method based on Delaunay triangulation guided by claim 1, characterized in that, The specific steps for the Delaunay triangulation in S1 are as follows: Initialize the point set bounding box: with the initial inlier set Based on the extreme coordinates of all points, a minimum bounding box is constructed to ensure that the bounding box completely covers all initial interior points, thus determining the effective range of the subdivision; Construct a super triangle: Generate a super triangle whose three vertices coordinates must exceed the initial interior point set. The bounding box is constructed to ensure that all initial interior points are located inside the super triangle, serving as the initial mesh structure for subdivision; Point-by-point insertion and local repartitioning: Insert the interior points of the initial interior point set into the current triangular mesh one by one in a random order. For each insertion point, perform the following operations: Traverse the current triangular mesh and locate the target triangle containing the insertion point; Connect the insertion point to the three vertices of the target triangle and divide the target triangle into three new sub-triangles. Empty circumcircle property verification and adjustment: Perform empty circumcircle property verification on the newly generated sub-triangle and its adjacent triangles. If the circumcircle of an adjacent triangle contains the insertion point, delete the common edge of the adjacent triangle, reconnect the vertices to form a new triangle, and repeat this verification process until all triangles satisfy the empty circumcircle property. Trim super triangle vertices: Traverse the final triangular mesh, delete all triangles containing super triangle vertices, and the remaining set of triangles is the Delaunay triangular mesh consisting only of the initial interior points.

3. The image geometric estimation method based on Delaunay triangulation guided by claim 1, characterized in that, The specific steps for designing the multi-dimensional loss function in S2 are as follows: Point-level geometric loss : As a fundamental constraint to ensure the core fitting accuracy of the model, the residuals are calculated based on the geometric task type: Fundamental matrix : Polar constraints; homography matrix : Projection constraints; Relative pose : Rigid body motion constraints ; Point-level loss is the square of the residual: ; Edge-level geometric consistency loss : Based on the geometric characteristics of camera motion, this design addresses each edge in the topological graph. Redefining loss: ； in: for and The pixel distance is normalized by the image diagonal length to ensure consistent weights across images of different resolutions. , These are the pixel lengths of the corresponding edges in the query image and the reference image, respectively. When the camera rotates, the edge lengths of correctly matched edges remain consistent, while mismatches will result in significant deviations in length. When the camera pans, the edge lengths of points within close proximity are more likely to remain consistent due to similar depths, while the edge lengths of points within distant proximity may be inconsistent due to differences in depth. Introducing weights Strengthen the geometric consistency constraints of near interior points, as these interior points are more likely to have similar depths, and their geometric relationships are more stable during camera movement. In contrast, far interior points are more affected by perspective distortion, so the constraint weights should be appropriately reduced. Spatial distribution loss : By quantifying the uniformity of the spatial distribution of interior points using the geometric properties of triangles, and suppressing local overfitting caused by interior point clustering, an area descriptor is first defined. and shape descriptors : ； ； in: For the first The number of adjacent triangles of each interior point can be obtained by traversing the triangulation results and counting them. For the first The area of ​​each adjacent triangle, area descriptor The smaller the value, the closer the area of ​​the triangles adjacent to the interior point is to the global mean, and the more uniform the spatial distribution. The largest interior angle of the triangle, shape descriptor The smaller the value, the closer the triangle is to an equilateral triangle, and the more stable the grid structure. The spatial distribution loss is the product of the two descriptors, which comprehensively reflects the spatial uniformity of the interior points: 。 4. The image geometric estimation method based on Delaunay triangulation guided by claim 1, characterized in that, The specific steps for joint weight optimization in S3 are as follows: Loss fusion: for each inlier For all its adjacent edges Take the arithmetic mean For all adjacent triangles Take the arithmetic mean The averaging operation weakens the interference of a single outlier edge or triangle on the overall loss. ； This is a balancing factor used to adjust the weight ratio of geometric consistency and spatial distribution in the optimization process. Weight matrix construction: using an exponential decay function: ； Will Convert to interior point weights, so that Smaller interior point weights rise rapidly. Larger interior point weights decrease slowly while constructing a weight matrix. By using weighted differential modulation, effective interior points play a dominant role in subsequent parameter refinement, while the influence of interference points is significantly suppressed.

5. The image geometric estimation method based on Delaunay triangulation guided by claim 1, characterized in that, The specific steps for parameter fine-tuning and output in S4 are as follows: Based on the weight matrix The optimal parameters are solved by weighted least squares. The optimization objective is: ； in, Let i be the weight of the i-th interior point. The residual function is defined according to the geometric task type. It is a point-level geometric loss.

Images