Two-line sub-pixel intersection positioning method based on robust estimation and local refinement

Abstract

This invention discloses a method for locating the sub-pixel intersection point of two straight lines based on robust estimation and local refinement, comprising the following steps: S10, defining the Region of Interest (ROI) and extracting sub-pixel edges at multiple scales; S20, initial fitting of the straight lines based on robust estimation; S30, refining the intersection region and assessing uncertainty. This invention achieves intersection point location accuracy superior to the pixel level; significantly reduces the impact of abnormal edge points, missing local edges, and interference near the intersection point on the location results; has a high degree of automation, reducing reliance on manual parameter adjustments; and can output the intersection point coordinates while providing an estimate of its location uncertainty, providing a decision-making basis for downstream applications.

Description

Technical Field

[0001] This invention belongs to the field of machine vision positioning technology, and relates to a method for locating the sub-pixel intersection of two straight lines based on robust estimation and local refinement. Background Technology

[0002] In the field of industrial machine vision inspection, the extraction of straight line features and the accurate localization of their intersections is a fundamental and crucial task. Its applications are extremely wide-ranging, including: locating the intersections of pads and traces in PCB board inspection; locating alignment marks (usually "L" or "+" shapes) on glass substrates in LCD panel manufacturing; determining the intersections of baselines in the visual measurement of mechanical parts to calculate angles or centers; and estimating vehicle attitude based on the vanishing points of lane line intersections in autonomous driving. The accuracy of intersection localization directly affects the accuracy of subsequent measurements, alignment, and control.

[0003] Existing machine vision-based methods for locating the intersection of two straight lines typically follow a basic process of "edge detection -> line fitting -> intersection finding". The most similar implementations include methods based on Hough transform, methods based on least squares line fitting, and methods based on chain code tracing and line segment aggregation.

[0004] Existing technical solution 1: A line detection and intersection method based on the standard Hough transform (SHT). The Hough transform is a classic algorithm for line detection. Its core idea is to map collinear points in the image space to a peak point in the parameter space (such as the ρ-θ space in polar coordinates). For each edge point in the image... It satisfies the following equation in the parameter space: ,in It is the distance from the origin to the line. It is the angle between the normal to the straight line and the x-axis. By accumulating parameters in the parameter space and performing peak detection, the main straight lines in the image can be extracted. The parameters of the two straight lines are then obtained. and Then, the coordinates of their intersection point This can be obtained by solving the following system of equations: ; The solution is: ; The advantage of this method lies in its robustness to noise and partial edge point loss. However, its disadvantages are also significant: firstly, its accuracy is limited. The accuracy of the Hough transform is affected by the parameter space quantization interval (…). Due to limitations, smaller intervals mean higher computational and storage overhead, creating a trade-off between accuracy and efficiency. Secondly, sub-pixel edge information cannot be directly utilized. Hough transform is typically performed on pixel-level edge maps, sacrificing the accuracy gains that sub-pixel localization might offer. Finally, in complex backgrounds or multi-line scenes, peak detection in parameter space is easily interfered with, leading to false positives or false negatives, and it is difficult to accurately correlate edge segments belonging to the same physical line.

[0005] Existing technical solution two: A line fitting and intersection method based on least squares (LS). This method first extracts the set of edge points belonging to the two lines using an edge detection algorithm (such as the Canny operator), denoted as... and Then, for each point set, a line fit is performed using the least squares method. For the point set... Fitted straight line The parameters are obtained by minimizing the sum of squared residuals. The solution is obtained. Its analytical solution is: ; Obtain the equations of the two lines. and Then, the coordinates of the intersection point were obtained by solving a system of linear equations: ; This method is computationally efficient and achieves higher accuracy than the Hough transform. However, its core drawback lies in its extreme sensitivity to outliers. The objective function of the least squares method is... The norm means that any edge point deviating from the principal line (potentially due to noise, local defects, or interference from neighboring features) will have a quadratic effect on the fitting result, causing the fitted line to shift and leading to significant errors in intersection point localization. Furthermore, this method relies on accurate point set segmentation, meaning that edge points must be correctly assigned to their corresponding lines beforehand. This step is inherently difficult and error-prone when image quality is poor or when edge points in the line intersection area are mixed.

[0006] Existing technical solution three: A method based on chain code tracking and line segment aggregation. This method first performs chain code tracking on the binarized edge image to obtain a series of continuous edge contours. Then, it uses a line segment approximation algorithm (such as the Douglas-Peucker algorithm) or splits the contours into several short line segments, and then aggregates them based on collinearity and proximity between the line segments to finally form a line segment representing a long straight line. The intersection of two line segments is the desired line segment. This method can directly obtain the endpoints of the line segments and has good performance for detecting short line segments or polylines. However, its disadvantages are: the process is complex, and its stability depends on the parameters of multiple steps (such as the chain code tracking direction and the line segment aggregation threshold). More importantly, its positioning accuracy is limited by the pixel-level accuracy of the initial edge, and the line segment aggregation process may introduce new errors. For industrial applications requiring sub-pixel-level accuracy, this method is often difficult to meet the requirements.

[0007] Through in-depth analysis of the above-mentioned existing technical solutions, we can clearly summarize their common key shortcomings in achieving high-precision and high-robust positioning of the intersection of two straight lines: 1. Accuracy bottleneck: Hough transform is limited by parameter quantization; least squares method and chain code method are mostly based on pixel-level edges, which fail to make full use of image information to achieve sub-pixel level positioning accuracy.

[0008] 2. Insufficient robustness: Least squares method is sensitive to outliers; Hough transform is easily disturbed in complex scenes; the performance of all methods will significantly decrease when the edges of straight lines are missing, there are breaks, or the edge points of intersection regions are contaminated with each other.

[0009] 3. Low level of automation and intelligence: Existing methods typically require manual setting of numerous parameters (such as the high and low thresholds of the Canny operator, the quantization interval of the Hough transform, and the tolerance of line segment aggregation), and lack the ability to assess the uncertainty (confidence) of the final intersection point location result. Users cannot know the reliability of this intersection point coordinate under the current image quality. Summary of the Invention

[0010] The purpose of this invention is to provide a high-precision localization method for the intersection of two straight lines based on the fusion of sub-pixel edge guidance and robust estimation. This invention aims to overcome the limitations of pixel-level accuracy, improve robustness under non-ideal imaging conditions, and endow the intersection localization results with quantifiable reliability. Specific objectives include: achieving intersection localization accuracy superior to pixel-level accuracy; significantly reducing the impact of abnormal edge points, missing local edges, and interference near the intersection on the localization results; high automation, reducing reliance on manual parameter adjustments; and the ability to output intersection coordinates while providing an estimate of their localization uncertainty, thus providing a decision-making basis for downstream applications.

[0011] To address the above problems, the technical solution of this invention is a method for locating the sub-pixel intersection of two straight lines based on robust estimation and local refinement, comprising the following steps: S10, Region of Interest (ROI) definition and multi-scale sub-pixel edge extraction; S20, initial linear fit based on robust estimation; S30, Cross-regional refinement and uncertainty assessment.

[0012] Preferably, step S10 includes the following steps: S11, Region of Interest (ROI) definition; S12, multi-scale edge enhancement; S13, sub-pixel edge point positioning.

[0013] Preferably, S11 specifically includes: defining a Region of Interest (ROI) for each line to be detected, where different ROIs have overlapping areas near their intersections.

[0014] Preferably, S12 specifically includes: constructing a multi-scale image space using a Gaussian pyramid for the image within each ROI, and performing edge enhancement filtering at different scales.

[0015] Preferably, step S13 specifically includes: performing sub-pixel level edge point localization at the selected optimal scale or by fusing multi-scale information, using a sub-pixel localization method based on gray-scale moments, i.e., for each pixel-level edge point... We take its neighborhood and locate the center position of the edge by calculating the first moment of the gray-level distribution within the neighborhood. Let the pixel coordinates in the neighborhood be Its grayscale value Then the sub-pixel edge point coordinates Calculated using the following formula: ; in, It is an extremely small constant to prevent division by zero errors, and the output is a set of two sub-pixel edge points. and .

[0016] Preferably, step S20 uses a random sampling consensus algorithm for initial line fitting. The steps for achieving consistency in random sampling include: S21, Random Sampling: From Two points are randomly selected from the data to determine a straight line model; S22, Consensus Set Construction: Calculate the distance from all points in the point set to the straight line. Set a distance threshold , distance less than The points are included in the consensus set of the model; S23, Model Evaluation: Record the size of the consensus set of the current model; S24, Iteration: Repeat the above steps N times, where N is determined adaptively by the ratio of interior points or a preset value; S25, Optimal Model Selection: Select the linear model with the largest consensus set, and use all points within that consensus set to refit the final linear equation using the least squares method. ,in , used for normalization; This represents the offset of the line relative to the coordinate system. Similarly, for point sets By performing a random sampling consistency fit, the linear equation is obtained. .

[0017] Preferably, step S30 specifically includes the following steps: S31, refine the region definition, using the theoretical intersection points obtained from the initial fitting. Define a refined ROI centered on [the target group]. S32, Local edge point re-extraction and attribution determination; S33, weighted least squares refined fitting; S34, final intersection point calculation: Solve the refined system of straight line equations to obtain the final sub-pixel intersection point coordinates. ; S35, Intersection Uncertainty Assessment.

[0018] Preferably, S32 specifically includes: Within the refined ROI, high-precision sub-pixel edge point extraction is performed again to obtain a dense set of local edge points. ; for For each point in the matrix, calculate its distance to the two initial fitted lines. and distance and ; Based on the principle of closest distance, it is determined to belong to a straight line. or straight line The point sets are denoted as follows: and .

[0019] Preferably, S33 specifically includes: right and Weighted least squares fitting is performed separately to obtain local linear models, using Gaussian weights based on the distance from the point to the initially fitted line: ;in, It is the distance from the k-th point to its corresponding initially fitted line. It is a parameter that controls the rate of weight decay; This weighting function assigns higher weights to points closer to the initially fitted line, for a point set. and their weights Weighted least squares fitted line The objective function is to minimize ; Its analytical solution is: By using weighted least squares fitting, two refined line equations were obtained. .

[0020] Preferably, S35 specifically includes: Assuming the refined linear parameters If there is uncertainty, and its covariance matrix is ​​known or can be estimated, then the intersection point... covariance matrix It can be approximated using the error propagation formula: ; in, The coordinates of the intersection point Regarding the parameters of the two lines The Jacobian matrix, i.e., the first-order partial derivative matrix, It is a block diagonal covariance matrix composed of the uncertainties of the parameters of two straight lines; The overall positioning uncertainty of the intersection point is represented by the root mean square error of its coordinates: ; Should The value is output as a confidence index of the intersection point positioning accuracy.

[0021] The present invention has at least the following beneficial effects: 1. Positioning accuracy reaches sub-pixel level: Starting from the bottom edge detection, gray-scale moment sub-pixel positioning technology is adopted, which breaks through the pixel-level limitation and provides high-precision input for the entire process, making the final intersection positioning accuracy much higher than that of traditional methods.

[0022] 2. Extremely robust: The introduction of RANSAC for initial line fitting can effectively resist interference from outliers, noise, and missing local edges, ensuring that a correct line model can be obtained even when the image quality is not ideal.

[0023] 3. Local refinement improves the accuracy of the core area: By focusing on a small area near the intersection and performing distance-weighted refinement fitting, the local edge information that contributes the most to the intersection location is utilized to the maximum extent, while further suppressing the mutual interference of the intersection area, making the intersection coordinates themselves more accurate.

[0024] 4. Uncertainty Quantification Capability: This invention is the first to systematically introduce an uncertainty assessment model based on error propagation theory into the intersection point positioning process. The output confidence index... This enables downstream systems to know the reliability of the current positioning results, providing key data support for confidence-based decision-making, adaptive re-detection, or quality traceability, a function that existing technologies do not possess at all.

[0025] 5. High level of automation and intelligence: The methodology and process are standardized, and parameters (such as the number of RANSAC iterations and weight function parameters) are well-defined. The sensitivity of the image is relatively low, reducing the workload of manual debugging. The entire process, from coarse to fine, adaptively utilizes image information, demonstrating a high degree of intelligence. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the steps of the sub-pixel intersection point localization method for two straight lines based on robust estimation and local refinement according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the refined ROI of the two-line sub-pixel intersection point localization method based on robust estimation and local refinement in an embodiment of the present invention. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0028] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0029] See Figure 1 The flowchart of an embodiment of the method of the present invention includes the following steps: S10, Region of Interest (ROI) definition and multi-scale sub-pixel edge extraction; S20, initial linear fit based on robust estimation; S30, Cross-regional refinement and uncertainty assessment.

[0030] S10 includes the following steps: S11, Region of Interest (ROI) Definition: Based on prior knowledge, the user or upper-layer system defines a loose ROI for each line to be detected. These two ROIs overlap near their intersection. This step significantly reduces the amount of data processed subsequently and initially isolates irrelevant background.

[0031] S12, Multi-scale Edge Enhancement: For the image within each ROI, a Gaussian pyramid is used to construct a multi-scale image space. Edge enhancement filtering is performed at different scales, such as using derivative filters (e.g., Sobel) or more advanced filters (e.g., eigenvalue analysis based on the Hessian matrix to enhance linear structures). This helps capture edge information at different levels of blur, providing a more stable foundation for subsequent sub-pixel calculations.

[0032] S13, Sub-pixel edge point localization; At the selected optimal scale or by fusing multi-scale information, sub-pixel level edge point localization is performed using a gray-moment-based sub-pixel localization method, i.e., for each pixel-level edge point... We take its neighborhood and locate the center position of the edge by calculating the first moment of the gray-level distribution within the neighborhood. Let the pixel coordinates in the neighborhood be Its grayscale value Then the sub-pixel edge point coordinates Calculated using the following formula: ; in, It is an extremely small constant to prevent division by zero errors, and the output is a set of two sub-pixel edge points. and .

[0033] Directly on subpixel sets and Even using the least squares method, interference from outliers still exists. Therefore, this invention introduces the Random Sample Consensus (RANSAC) algorithm for robust initial line fitting.

[0034] S20 uses a random sampling consensus algorithm for initial linear fitting. The steps for achieving consistency in random sampling include: S21, Random Sampling: From Two points are randomly selected from the data to determine a straight line model; S22, Consensus Set Construction: Calculate the distance from all points in the point set to the straight line. Set a distance threshold , distance less than The points are included in the consensus set of the model; S23, Model Evaluation: Record the size of the consensus set of the current model; S24, Iteration: Repeat the above steps N times, where N is determined adaptively by the ratio of interior points or a preset value; S25, Optimal Model Selection: Select the linear model with the largest consensus set, and use all points within that consensus set to refit the final linear equation using the least squares method. ,in , used for normalization; This represents the offset of the line relative to the coordinate system. Similarly, for point sets By performing a random sampling consistency fit, the linear equation is obtained. RANSAC can efficiently and robustly estimate the correct linear model from a set of points containing outliers.

[0035] S30 is the core innovation of this invention. The initially fitted straight line is based on the point set within the entire ROI, but the accuracy of intersection point localization is most sensitive to the edge quality of the region near the intersection point. This stage aims to refine the intersection point using local information near the intersection region and evaluate its uncertainty.

[0036] See Figure 2 This is a schematic diagram of the refined ROI, showing the refined region defined centered on the initial fitting intersection point, and the determination of the attribution of local edge points within the region. S30 specifically includes the following steps: S31, refine the region definition, using the theoretical intersection points obtained from the initial fitting. Define a refined ROI centered on [the target group]. S32, Local edge point re-extraction and attribution determination; within the refined ROI, high-precision sub-pixel edge point extraction is performed again to obtain a dense set of local edge points. ; for For each point in the matrix, calculate its distance to the two initial fitted lines. and distance and ; Based on the principle of closest distance, it is determined to belong to a straight line. or straight line The point sets are denoted as follows: and .

[0037] S33, weighted least squares refined fitting; for and Weighted least squares fitting is performed separately to obtain local linear models, using Gaussian weights based on the distance from the point to the initially fitted line: ;in, It is the distance from the k-th point to its corresponding initially fitted line. It is a parameter that controls the rate of weight decay; This weighting function assigns higher weights to points closer to the initially fitted line, for a point set. and their weights Weighted least squares fitted line The objective function is to minimize ; Its analytical solution is: By using weighted least squares fitting, two refined line equations were obtained. .

[0038] S34, final intersection point calculation: Solve the refined system of straight line equations to obtain the final sub-pixel intersection point coordinates. ; S35, Intersection Uncertainty Assessment. Assume refined linear parameters. If there is uncertainty, and its covariance matrix is ​​known or can be estimated, then the intersection point... covariance matrix It can be approximated using the error propagation formula: ; in, The coordinates of the intersection point Regarding the parameters of the two lines The Jacobian matrix, i.e., the first-order partial derivative matrix, It is a block diagonal covariance matrix composed of the uncertainties of the parameters of two straight lines; The overall positioning uncertainty of the intersection point is represented by the root mean square error of its coordinates: ; Should The value is output as a confidence index of the intersection point positioning accuracy.

[0039] The scope of protection of this invention is defined by the appended claims, and its core innovation and key protection points are as follows: 1. A three-stage intersection localization framework of "multi-scale sub-pixel edge extraction -> robust initial fitting -> local refinement": protecting the overall technical route and process design.

[0040] 2. Robust initial line fitting using the RANSAC algorithm in line intersection point localization: Specifically, RANSAC is applied to address the line model deviation problem caused by outliers in intersection point localization.

[0041] 3. Intersection refinement method based on local refinement of ROI and weighted least squares (WLS): The specific technical solution is to protect the refinement region defined with the initial fitting intersection point as the center, and to perform WLS fitting within the region based on the Gaussian weights of the distance from the point to the initial fitting line, so as to achieve the refinement of intersection point coordinates.

[0042] 4. Introduce an uncertainty assessment model based on error propagation theory in intersection point localization: Utilize the uncertainty of the straight-line parameters, propagate through the Jacobian matrix, and calculate the covariance matrix of the intersection point coordinates and the final localization confidence. The complete method.

[0043] 5. Subpixel edge point extraction technology based on grayscale moment applied to line intersection point positioning: This paper protects the specific application of this subpixel technology as a preprocessing step in the front-end of high-precision intersection point positioning.

[0044] 6. A complete visual positioning system for the intersection of two straight lines, including output with uncertainty: a complete automated system implementation scheme from image acquisition and ROI setting to the final output of high-precision intersection coordinates and their confidence level.

[0045] In specific embodiments, the following alternative solutions can be implemented without departing from the core concept of the present invention: Alternatives to subpixel edge extraction methods: The gray-scale moment method can be replaced by a fitting method, such as fitting a quadratic curve or spline function to the gray-scale profile in the normal direction of the pixel-level edge points, and using its extreme points as the subpixel edge positions.

[0046] Robust estimation alternatives: RANSAC can be replaced by other robust regression algorithms, such as M-estimation, which reduces the impact of outliers by using a robust loss function (such as Huber loss), and is typically solved by iterative reweighted least squares (IRLS).

[0047] Alternatives to the weight function design: The Gaussian weight function can be replaced with other monotonically decreasing functions, such as inverse distance weights. Alternatively, the Tukey double-weighted function can be used, which has a better suppression effect on extreme outliers.

[0048] An alternative to the uncertainty propagation model: For cases where the Jacobian matrix is ​​difficult to calculate analytically, the Monte Carlo simulation method can be used. This involves sampling multiple times from the posterior distribution of the line parameters, calculating the coordinates of the corresponding intersection points, and then using the statistical variance of these intersection point samples to estimate the uncertainty.

[0049] Application scenario expansion: The core concept of this method—"coarse positioning -> robust model estimation -> local refinement -> uncertainty assessment"—can be extended to the positioning of other geometric features, such as the high-precision positioning of the intersection of circles, the tangent point of a line and a circle, and corner points (which can be regarded as the intersection of two edges).

[0050] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for locating the sub-pixel intersection point of two straight lines based on robust estimation and local refinement, characterized in that, Includes the following steps: S10, Region of Interest (ROI) definition and multi-scale sub-pixel edge extraction; S20, initial linear fit based on robust estimation; S30, Cross-regional refinement and uncertainty assessment.

2. The method according to claim 1, characterized in that, S10 includes the following steps: S11, Region of Interest (ROI) definition; S12, multi-scale edge enhancement; S13, sub-pixel edge point positioning.

3. The method according to claim 2, characterized in that, S11 specifically includes: defining a Region of Interest (ROI) for each line to be detected, with different ROIs having overlapping areas near their intersections.

4. The method according to claim 3, characterized in that, S12 specifically includes: for the image within each ROI, constructing a multi-scale image space using a Gaussian pyramid, and performing edge enhancement filtering at different scales.

5. The method according to claim 4, characterized in that, S13 specifically includes: performing sub-pixel level edge point localization at the selected optimal scale or by fusing multi-scale information, using a sub-pixel localization method based on gray-scale moments, that is, for each pixel-level edge point... We take its neighborhood and locate the center position of the edge by calculating the first moment of the gray-level distribution within the neighborhood. Let the pixel coordinates in the neighborhood be Its grayscale value Then the sub-pixel edge point coordinates Calculated using the following formula: ； in, It is an extremely small constant to prevent division by zero errors, and the output is a set of two sub-pixel edge points. and .

6. The method according to claim 5, characterized in that, S20 uses a random sampling consensus algorithm for initial linear fitting. The steps for achieving consistency in random sampling include: S21, Random sampling: from Two points are randomly selected from the data to determine a straight line model; S22, Consensus Set Construction: Calculate the distance from all points in the point set to the straight line. Set a distance threshold , distance less than The points are included in the consensus set of the model; S23, Model Evaluation: Record the size of the consensus set of the current model; S24, Iteration: Repeat the above steps N times, where N is determined adaptively by the ratio of interior points or a preset value; S25, Optimal Model Selection: Select the linear model with the largest consensus set, and use all points within that consensus set to refit the final linear equation using the least squares method. ,in , used for normalization; This represents the offset of the line relative to the coordinate system. Similarly, for point sets By performing a random sampling consistency fit, the linear equation is obtained. .

7. The method according to claim 6, characterized in that, S30 specifically includes the following steps: S31, refine the region definition, using the theoretical intersection points obtained from the initial fitting. Define a refined ROI centered on [the target group]. S32, Local edge point re-extraction and attribution determination; S33, weighted least squares refined fitting; S34, final intersection point calculation: Solve the refined system of straight line equations to obtain the final sub-pixel intersection point coordinates. ; S35, Intersection Uncertainty Assessment.

8. The method according to claim 7, characterized in that, Specifically, S32 includes: Within the refined ROI, high-precision sub-pixel edge point extraction is performed again to obtain a dense set of local edge points. ; for For each point in the matrix, calculate its distance to the two initial fitted lines. and distance and ; Based on the principle of closest distance, it is determined to belong to a straight line. or straight line The point sets are denoted as follows: and .

9. The method according to claim 8, characterized in that, Specifically, S33 includes: right and Weighted least squares fitting is performed separately to obtain local linear models, using Gaussian weights based on the distance from the point to the initially fitted line: ;in, It is the distance from the k-th point to its corresponding initially fitted line. It is a parameter that controls the rate of weight decay; This weighting function assigns higher weights to points closer to the initially fitted line, for a point set. and their weights Weighted least squares fitted line The objective function is to minimize ; Its analytical solution is: By using weighted least squares fitting, two refined line equations were obtained. .

10. The method according to claim 1, characterized in that, Specifically, S35 includes: Assuming the refined linear parameters If there is uncertainty, and its covariance matrix is ​​known or can be estimated, then the intersection point... covariance matrix It can be approximated using the error propagation formula: ; in, The coordinates of the intersection point Regarding the parameters of the two lines The Jacobian matrix, i.e., the first-order partial derivative matrix, It is a block diagonal covariance matrix composed of the uncertainties of the parameters of two straight lines; The overall positioning uncertainty of the intersection point is represented by the root mean square error of its coordinates: ； Should The value is output as a confidence index of the intersection point positioning accuracy.

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