An automatic measuring method for the thickness of the surface oxidation layer of an aluminum profile

Abstract

The application provides an automatic measurement method for the thickness of an oxidation layer on the surface of an aluminum profile, comprising: scanning a hanger contact area on the surface of the aluminum profile to obtain a surface image of the aluminum profile, determining the coordinates of a contact point of the hanger by performing edge contour recognition on the surface image of the aluminum profile, and obtaining the range of the contact point area; dynamically adjusting an avoidance path of a measurement probe according to the boundary coordinates of an uncertain measurement area, generating a measurement trajectory bypassing the uncertain measurement area, and determining a sequence of compensation measurement point positions according to the boundary of an effective measurement area and the uncertain measurement area; guiding the measurement probe to perform thickness scanning in the effective measurement area through the sequence of compensation measurement point positions, scanning to obtain the thickness values of the oxidation layer at each measurement point, and forming an oxidation layer thickness dataset; generating a final oxidation layer thickness evaluation report according to the calibration thickness value and the range of the effective measurement area, and determining the thickness of the oxidation layer on the surface of the aluminum profile by fusing the boundary coordinates of the uncertain measurement area and the thickness distribution characteristics of the oxidation layer.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to an automatic method for measuring the thickness of the oxide layer on the surface of aluminum profiles. Background Technology

[0002] Measuring the thickness of the oxide layer on aluminum profiles is a crucial step in ensuring product quality in industrial manufacturing, particularly in the aerospace, construction, and automotive industries. The uniformity and stability of the oxide layer thickness directly impact the material's corrosion resistance and service life. Accurate measurement of oxide layer thickness is not only a core requirement for quality control but also significantly influences production efficiency and cost optimization. However, current measurement technologies face numerous challenges in real-world production environments, especially under complex process conditions. Ensuring measurement accuracy and coverage remains a pressing issue.

[0003] Existing measurement methods typically rely on fixed probe paths or manual adjustments to obtain oxide layer thickness data. However, these methods have significant limitations in handling the influence of the fixture contact point on the measurement area. Traditional methods often assume that the contact point has a small impact on the oxide layer and improve measurement efficiency simply by expanding the probe coverage area. This approach ignores the influence of complex electrochemical effects around the contact point, leading to distorted measurement data in certain areas and making it difficult to fully reflect the true state of the oxide layer on the profile surface.

[0004] The core technical challenge lies in the non-uniform effect of the hanger contact points on the oxide layer thickness distribution. The hanger contact points are the areas where the aluminum profile directly contacts the hanger during the electrochemical oxidation process; their size and current distribution directly determine the local variations in oxide layer thickness. Reducing the contact point size is intended to decrease the obstructed area and increase the measurable area. However, in actual production, reducing the contact point size leads to current density concentration, resulting in a current shielding zone around the contact point. Within this shielding zone, the oxide layer thickness exhibits an irregular gradient, making it difficult for the measurement probe to accurately capture the thickness values ​​in these areas, thus increasing measurement uncertainty.

[0005] Therefore, accurately identifying the boundary of the current shielding zone around the contact point of the hanger in a complex electrochemical environment, and dynamically adjusting the measurement path to avoid areas with large thickness gradient changes, has become a key issue in ensuring the accuracy of aluminum profile oxide layer thickness measurement. Summary of the Invention

[0006] This invention provides an automatic method for measuring the thickness of the oxide layer on the surface of aluminum profiles, comprising:

[0007] Acquire image data of the aluminum profile surface and determine the range of the hanger contact point area through image processing;

[0008] The oxide layer within the contact point area of ​​the hanger is sampled and measured to obtain the oxide layer thickness distribution characteristics;

[0009] The uncertain measurement area and the effective measurement area are identified based on the oxide layer thickness distribution characteristics.

[0010] Based on the uncertain measurement area, the measurement path is dynamically adjusted to generate a sequence of compensated measurement point positions.

[0011] The compensation measurement point position sequence guides the measurement probe to perform thickness scanning within the effective measurement area, forming an oxide layer thickness dataset.

[0012] Statistical analysis is performed on the oxide layer thickness dataset to determine the irregular thickness distribution, and interpolation is performed on the uncertain measurement area to generate a corrected thickness value;

[0013] A final oxide layer thickness assessment report is generated based on the corrected thickness value and the effective measurement area range.

[0014] Furthermore, the acquisition of image data of the aluminum profile surface, and the determination of the contact point area of ​​the hanger through image processing, includes:

[0015] A high-resolution industrial camera is used to scan the surface of the aluminum profile line by line to collect image data including the contact area of ​​the hanger;

[0016] The image data is preprocessed by filtering to remove reflective interference and noise points, resulting in a preprocessed surface image.

[0017] Edge detection is performed on the preprocessed surface image, and boundary pixels are extracted based on grayscale differences to form an initial contour line;

[0018] If the closure of the initial contour line is lower than a preset threshold, the contour gap is filled by morphological processing to obtain a complete contour.

[0019] Calculate the average coordinates of pixels within the complete contour to determine the center coordinates of the contact point.

[0020] The minimum bounding rectangle is obtained by traversing the coordinates of each point on the contour, the boundary of the contact area is determined, and the actual area value of the contact point is calculated by counting the total number of pixels in the contour. The output is the range of the contact point area including the center coordinates, the boundary of the area and the actual area.

[0021] Furthermore, the oxide layer within the contact point area of ​​the hanger is sampled and measured to obtain the oxide layer thickness distribution characteristics, including:

[0022] A uniform sampling grid is constructed on the oxide layer surface according to the range of the contact point area of ​​the hanger;

[0023] An eddy current thickness gauge is used to scan each node of the sampling grid, and the position coordinates and oxide layer thickness values ​​of each sampling point are recorded to form a discrete sampling dataset.

[0024] The thickness values ​​of adjacent sampling points in the discrete sampling dataset are differentially calculated to obtain the local thickness gradient value;

[0025] A continuous oxide layer thickness field is generated using an interpolation method;

[0026] Based on the continuous oxide layer thickness field, the distribution areas of different thickness levels are extracted, the area ratio of each area is calculated, the number of sampling points with gradient values ​​exceeding the preset threshold and the distribution density are statistically analyzed, and the oxide layer thickness distribution characteristics are determined by combining the mean thickness, standard deviation and gradient distribution.

[0027] Furthermore, based on the oxide layer thickness distribution characteristics, uncertain measurement areas and effective measurement areas are identified, including:

[0028] The thickness gradient change rate of each sampling point is compared with a preset threshold. If the threshold is exceeded, it is marked as an uncertain point.

[0029] By determining the spatial connectivity of adjacent uncertain points, a continuous uncertain measurement region is formed by aggregation;

[0030] Traverse along the outer edge of the uncertain measurement area, extract the coordinate sequence of contour points, calculate the tangent direction based on the thickness value and gradient change rate, search vertically until the gradient change rate is lower than the threshold, and record the endpoint coordinates as the boundary coordinates of the uncertain area.

[0031] For sampling points outside the boundary, calculate the standard deviation of the gradient change rate in the local neighborhood. If it is lower than the preset stability threshold, it is determined to be a valid measurement area. The area identification is completed by traversing the area.

[0032] Furthermore, based on the uncertain measurement area, the measurement path is dynamically adjusted to generate a sequence of compensated measurement point positions, including:

[0033] Based on the boundary coordinates of the uncertain measurement area, avoidance constraints are constructed, and boundary rejection areas are set to guide the probe's movement direction, forming an initial avoidance path.

[0034] Control points are extracted from the initial avoidance path, path smoothing is achieved through curve fitting, and measurement points are generated by sampling at preset intervals.

[0035] If the shortest distance between the measurement point and the boundary is lower than the preset safety distance, adjust the position in the direction away from the boundary;

[0036] Based on the measurement trajectory and the effective measurement area, the measurable segment is determined, and the coverage density value is calculated. If it is lower than the preset standard, a spiral path is added to increase the measurement points, forming a set of measurement paths.

[0037] A distance matrix is ​​constructed for the set of measurement paths, an algorithm is used to determine the access order, and transition points are inserted to generate a sequence of compensated measurement point positions.

[0038] Furthermore, the compensation measurement point position sequence guides the measurement probe to perform thickness scanning within the effective measurement area, forming an oxide layer thickness dataset, including:

[0039] The measurement probe is moved to the specified coordinates according to the sequence of compensated measurement point positions.

[0040] At each measurement point, the eddy current thickness gauge is activated to generate an electromagnetic field, receive the reflected signal from the oxide layer and convert it into a thickness value, and record the spatial coordinates and acquisition time.

[0041] The thickness value is checked for range; if it exceeds a preset multiple, it is marked as abnormal and remeasured.

[0042] The verified thickness values, spatial coordinates, and acquisition times are combined and encoded to form an oxide layer thickness dataset by summarizing all measurement point data.

[0043] Furthermore, statistical analysis is performed on the oxide layer thickness dataset to determine the irregular thickness distribution and interpolation is performed on uncertain measurement areas, including:

[0044] Calculate the global mean and standard deviation of the oxide layer thickness dataset, obtain the standardized deviation of each measurement point, and mark it as an outlier if it exceeds a preset threshold. Statistically analyze the distribution of outliers to form an irregular thickness distribution map.

[0045] By comparing the spatial grid with the theoretical thickness distribution, the root mean square of the thickness difference is calculated. If it is lower than the matching threshold, it is determined to be an uncertain measurement area.

[0046] For missing measurement points, a spatial interpolation method is used to determine the weighting coefficients based on the thickness values ​​and distances of surrounding valid measurement points, and the initial interpolated thickness is obtained by weighted summation.

[0047] Furthermore, interpolation processing is performed on the uncertain measurement area to generate a corrected thickness value, including:

[0048] Calculate the local gradient change rate based on the initial interpolated thickness and compare it with the gradient difference of surrounding measured points;

[0049] If the gradient difference exceeds the preset threshold, the interpolation result is adjusted proportionally, and the process is iterated until the gradient difference between adjacent points is lower than the convergence threshold, and the corrected thickness value is output.

[0050] The corrected thickness value is verified, and outliers are adjusted according to the thickness distribution characteristics of surrounding effective measurement points to ensure that the interpolation result is consistent with the measured data, and the final corrected thickness value is generated.

[0051] Furthermore, a final oxide layer thickness assessment report is generated based on the corrected thickness value and the effective measurement area range, including:

[0052] An oxide layer thickness data matrix is ​​constructed based on the corrected thickness value and the effective measurement area range;

[0053] The boundary coordinates of the uncertain measurement area are mapped to matrix positions and the area type is labeled. The thickness distribution is represented by color gradient and the boundary outline is drawn with lines to obtain a thickness spatial distribution map.

[0054] Based on the thickness spatial distribution map, the average thickness, maximum and minimum thickness values, qualified area ratio and measurement coverage percentage are calculated. Combined with the oxide layer thickness distribution characteristics, it is determined whether the preset standard is met, and the data is summarized to form an evaluation report.

[0055] Furthermore, based on the oxide layer thickness distribution characteristics, uncertain measurement areas and effective measurement areas are identified, including:

[0056] The thickness gradient change rate in the oxide layer thickness distribution characteristics is analyzed, and the location distribution of gradient change rate anomalies is extracted.

[0057] Spatial clustering methods are used to aggregate adjacent outliers into uncertain measurement regions;

[0058] Gradient stationarity analysis is performed on the region outside the boundary of the uncertain measurement region, and the standard deviation of the local gradient change rate is calculated. If it is lower than the preset threshold, it is classified as a valid measurement region.

[0059] The effective measurement region and the uncertain measurement region are optimized by boundary optimization. Boundary noise is reduced by smoothing process to generate the final region division result.

[0060] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0061] This invention discloses an automatic method for measuring the thickness of the oxide layer on the surface of aluminum profiles. It addresses the business scenario where the contact area of ​​the aluminum profile surface with the hanger suffers from measurement uncertainty and irregular thickness distribution due to drastic changes in the oxide layer thickness gradient. This method integrates the logical connections of image recognition and localization, thickness sampling and evaluation, and compensation processing for uncertain areas. Specifically, it addresses how to accurately identify and avoid uncertain measurement areas near the hanger contact point, while simultaneously ensuring the integrity and accuracy of thickness data through a compensation algorithm. This invention determines the coordinates of the hanger contact point by scanning the aluminum profile surface image for edge contour recognition. Then, it performs multi-point sampling of the oxide layer in the contact area to obtain the thickness and gradient change rate. If the change rate exceeds a threshold, it is identified as an uncertain area, and its boundary is identified. Simultaneously, the effective measurement area is determined. Based on these boundaries, the measurement probe path is dynamically adjusted to generate a trajectory that bypasses the uncertain area. Compensation measurements are performed within the effective area to form a thickness dataset. Subsequently, statistical analysis is performed on the dataset to extract the standard deviation and mean deviation. Irregular thickness distribution is identified, and an interpolation algorithm is used to fuse the gradient change rate to correct the thickness values ​​of uncertain areas. Finally, an oxide layer thickness evaluation report integrating boundary coordinates and distribution characteristics is generated. The technical advantage of this method is that it significantly improves the measurement accuracy and reliability of the oxide layer thickness on the surface of aluminum profiles, reduces human intervention, avoids measurement errors in uncertain areas, and ensures the integrity of the overall assessment and the practicality of industrial applications. Attached Figure Description

[0062] Figure 1 This is a flowchart of an automatic measurement method for the oxide layer thickness on the surface of aluminum profiles according to the present invention.

[0063] Figure 2 This is a schematic diagram of an automatic measurement method for the oxide layer thickness on the surface of aluminum profiles according to the present invention.

[0064] Figure 3 This is another schematic diagram of an automatic measurement method for the oxide layer thickness on the surface of aluminum profiles according to the present invention. Detailed Implementation

[0065] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this specification.

[0066] like Figure 1-3 This embodiment of an automatic measurement method for the oxide layer thickness on the surface of aluminum profiles may specifically include:

[0067] S101. Scan the contact area of ​​the aluminum profile surface to obtain an image of the aluminum profile surface. Determine the coordinate position of the contact point of the hanger by performing edge contour recognition on the aluminum profile surface image, and obtain the range of the contact point area.

[0068] A high-resolution industrial camera is used to scan the surface of the aluminum profile line by line, acquiring image data including the contact area of ​​the hanger. Gaussian filtering is used to remove reflective interference and noise points, resulting in a pre-processed image of the aluminum profile surface. Edge detection is performed on the pre-processed aluminum profile surface image. Boundary pixels are extracted based on the grayscale difference between the contact point and the non-contact area. Initial contour lines are formed by connecting these boundary pixels in series. If the closure of the initial contour lines is lower than a preset threshold, morphological processing is used to fill in the contour gaps, obtaining the complete contour of the hanger contact point. Based on the complete contour of the hanger contact point, the mean coordinates of all pixels within the contour are calculated to determine the center coordinates of the contact point. The minimum bounding rectangle is obtained by traversing the coordinates of each point on the contour to determine the boundary of the contact area. The actual area value of the contact point is obtained by multiplying the total number of pixels within the contour by the area per unit pixel. The output is the contact point area range including the center coordinates, the area boundary, and the actual area.

[0069] Specifically, in the aluminum profile oxide layer thickness measurement system, accurate identification of the hanger contact point is the foundation for ensuring measurement accuracy.

[0070] Specifically, the industrial camera employs a high-resolution sensor and is equipped with a ring light source to eliminate shadow interference. During scanning, the camera moves at a constant speed along the length of the profile, acquiring image sequences and ensuring complete coverage of the contact area through overlapping shots. In the preprocessing stage, Gaussian filtering is used to process the original image, effectively suppressing noise caused by reflections from the aluminum profile surface. The filtered image has a more uniform grayscale distribution, and the contrast between contact and non-contact areas is enhanced, laying the foundation for subsequent edge detection. On the aerospace aluminum profile production line, the preprocessed image can clearly present the outline of circular contact points with a diameter of 3-8 mm.

[0071] In one embodiment, the edge detection algorithm achieves edge localization by calculating image gradients. The algorithm first calculates the gradient magnitude and direction, then uses non-maximum suppression to preserve local maxima. Double thresholding is employed to identify strong and weak edges, and edge tracking is used to connect and form continuous boundary lines.

[0072] It should be noted that the contour closure is evaluated by calculating the ratio of the Euclidean distance between the start and end points of the contour to the total length of the contour. When this ratio exceeds a preset threshold, a morphological closing operation is performed to complete the contour. The closing operation first performs a dilation operation, using 3×3 rectangular structuring elements to expand the boundary pixels and fill the gaps at the contour breaks; then, an erosion operation of the same scale is performed to restore the original size of the contour, finally obtaining a closed and complete contact point contour.

[0073] Preferably, in the contact point parameter extraction stage, the centroid coordinates are obtained by traversing the coordinates of all pixels within the contour, accumulating the horizontal and vertical coordinate values, and dividing by the total number of pixels. The minimum bounding rectangle is determined using a rotating caliper algorithm, sequentially calculating the minimum bounding box of the contour projected at different angles, and selecting the rectangle with the smallest area as the boundary of the contact area. The actual area value is converted from the number of pixels to physical size according to the camera calibration parameters. The actual area corresponding to each pixel is predetermined using a standard calibration plate to ensure the accuracy of the measurement results.

[0074] S102. Identify the oxide layer within the contact point area, perform multi-point sampling of the oxide layer within the contact point area, obtain the oxide layer thickness and thickness gradient change rate at different contact points, and determine the oxide layer thickness distribution characteristics.

[0075] A uniform sampling grid is constructed on the oxide layer surface at preset intervals based on the contact point area. The coordinates of each sampling point and the corresponding oxide layer thickness value are recorded to form a discrete sampling dataset. Difference calculation is performed on the thickness values ​​of adjacent sampling points in the discrete sampling dataset. The thickness difference is divided by the Euclidean distance between the sampling points to obtain the local thickness gradient value of each point. A continuous oxide layer thickness field is generated based on the sampling point coordinates and thickness values ​​using an interpolation method. Distribution areas of different thickness levels are extracted based on the continuous oxide layer thickness field. The area ratio of each area is calculated, and the number of sampling points with gradient values ​​exceeding a preset threshold and their spatial distribution density are statistically analyzed. The oxide layer thickness distribution characteristics are determined by comprehensively considering the mean thickness, standard deviation, and gradient distribution.

[0076] Specifically, during the measurement of the oxide layer thickness of aluminum profiles, the thickness distribution in the contact area exhibits complex non-uniform characteristics.

[0077] Specifically, the sampling grid is constructed based on the geometry of the contact points, with grid nodes uniformly distributed within the contact area according to preset density parameters. The eddy current thickness gauge induces eddy currents on the surface of the aluminum profile using a high-frequency alternating magnetic field, achieving non-contact measurement based on the negative correlation between eddy current intensity and oxide layer thickness.

[0078] In one embodiment, the discrete sampling dataset contains the three-dimensional coordinates and corresponding thickness value of each grid node. The difference calculation uses a central difference scheme; for internal nodes, the thickness gradient is obtained by a weighted average of the thickness differences in four adjacent directions. Boundary nodes use one-sided difference to ensure the integrity of the gradient calculation. The Euclidean distance is calculated based on the actual physical coordinates of the sampling points on the aluminum profile surface, taking into account the influence of the profile surface curvature.

[0079] It should be noted that the interpolation method uses a weighted calculation based on the thickness values ​​of surrounding sampling points and their spatial distance. The thickness value of each point to be interpolated is determined by the weighted contribution of surrounding sampling points, with the weighting coefficients being distance-dependent; the closer the distance, the greater the weight. The continuous thickness field generated by the interpolation exhibits second-order continuity in space, satisfying the smoothness requirements for subsequent contour line extraction. The resulting continuous field accurately reflects the abrupt thickness changes at the contact point edges, as well as the slow transition characteristics of the central region.

[0080] Preferably, contour lines are extracted to identify the boundaries of different thickness intervals in the thickness field. The thickness interval is determined as a percentage of the nominal thickness of the oxide layer. The area of ​​the region enclosed by each contour line is obtained through numerical calculation, and the area distribution of different thickness intervals is statistically analyzed to form a thickness histogram.

[0081] For example, the gradient threshold determination is based on the statistical distribution of gradient values ​​across the entire sampling area, with the 75th percentile used as the criterion for identifying abnormal gradients. The spatial distribution density of sampling points exceeding the threshold is obtained through kernel density estimation, identifying clusters of gradient anomalies. The oxide layer thickness distribution characteristics integrate the mean thickness, standard deviation, skewness coefficient, kurtosis coefficient, and spatial autocorrelation of the gradient distribution to form a multi-dimensional feature vector, providing quantitative basis for subsequent identification of uncertain regions.

[0082] S103. If the thickness gradient change rate exceeds the preset threshold, the sampling point is determined to belong to the uncertain measurement area. The boundary coordinates of the uncertain area are identified by combining the oxide layer thickness and the thickness gradient change rate. At the same time, the area where the oxide layer thickness gradient changes smoothly is identified as the effective measurement area.

[0083] The thickness gradient change rate of each sampling point is compared with a preset threshold. If it exceeds the threshold, the point is marked as an uncertain point. By judging the spatial connectivity of adjacent uncertain points, a continuous uncertain measurement region is formed. The coordinate sequence of each point on the region contour is extracted by traversing the outer edge of the uncertain measurement region point by point. The contour tangent direction is calculated based on the thickness value and gradient change rate of the contour points. The search is carried outward perpendicular to the tangent direction until the gradient change rate drops below the threshold. The coordinates of the search endpoint are recorded as the boundary coordinates of the uncertain region. The standard deviation of the gradient change rate in the local neighborhood of the sampling points outside the region enclosed by the boundary coordinates is calculated. If the standard deviation is lower than the preset stationary threshold, the point belongs to the valid measurement region. The identification of the valid measurement region and the uncertain measurement region is completed by traversing all sampling points outside the boundary.

[0084] Specifically, in the measurement of oxide layer thickness of aluminum profiles, the accurate identification of uncertain areas directly affects the formulation of measurement strategies.

[0085] Specifically, the thickness gradient change rate threshold is determined by statistically analyzing the gradient distribution characteristics of normal areas in historical measurement data, typically using the 95th percentile of the gradient distribution as the anomaly criterion. When the gradient change rate at a sampling point exceeds this threshold, it indicates that the point is in the transition region affected by current shielding.

[0086] It should be noted that spatial connectivity is determined using a four- or eight-connectivity criterion; adjacent uncertain points are considered connected when the distance between them is less than 1.5 times the sampling grid spacing. A depth-first search algorithm is used to traverse all connected uncertain points, forming several independent uncertain measurement regions. Sampling points within each region share similar thickness variation characteristics, reflecting the local influence of the fixture contact points on oxide layer formation.

[0087] In one embodiment, contour tracking begins at an arbitrary boundary point of the uncertain region and sequentially visits boundary pixels in a counter-clockwise direction. For each contour point, a tangent vector is calculated using the coordinate difference between the two adjacent points, and the tangent vector is rotated 90 degrees to obtain the normal vector direction. The search proceeds outward along the normal vector with a fixed step size, calculating the local gradient rate of change at each search position. When the gradient values ​​at three consecutive search points are all below a threshold, the current position is recorded as the precise boundary coordinates corresponding to that contour point. This search strategy can adapt to contact point regions of different shapes, including circular, elliptical, and irregularly shaped contact imprints.

[0088] Preferably, the determination of the effective measurement region is achieved through a sliding window method. A 3×3 or 5×5 neighborhood window is selected centered on each sampling point outside the boundary, and the standard deviation of the gradient change rate of all sampling points within the window is calculated. The stationarity threshold is set to 30% of the overall gradient standard deviation; sampling points below this value are marked as effective measurement points. Continuous effective measurement points are aggregated using a region growing algorithm to form a complete effective measurement region.

[0089] For example, when processing aluminum profiles with complex shapes, a single profile surface may have multiple hanger contact points, each generating an independent uncertain region. The aforementioned identification process allows for the simultaneous processing of multiple uncertain regions, avoiding mutual interference between them. The final output region segmentation result includes the boundary coordinate sequence of each uncertain region, the region area, and the coverage of the effective measurement area, providing precise spatial constraints for subsequent measurement path planning.

[0090] S104. Dynamically adjust the avoidance path of the measurement probe according to the boundary coordinates of the uncertain measurement area, generate a measurement trajectory that bypasses the uncertain measurement area, and determine the sequence of compensation measurement point positions based on the boundary of the effective measurement area and the uncertain measurement area.

[0091] Based on the boundary coordinates of the uncertain measurement area, avoidance constraints are constructed. The probe's movement direction is guided by setting boundary exclusion regions, and an initial avoidance path is formed by connecting various location points. Key control points are extracted from the initial avoidance path, and path smoothing is achieved through curve fitting. Measurement points are generated by sampling at preset intervals along the smooth path. If the shortest distance between a measurement point and the boundary of the uncertain area is less than a preset safety distance, the point is moved away from the boundary until the safety distance requirement is met, resulting in a measurement trajectory. Measurable segments are determined based on the intersection of the measurement trajectory and the effective measurement area. The number of measurement points per unit area within each measurable segment is calculated as the coverage density value. If the coverage density of a segment is lower than a preset standard, a spiral path is added at the center of that segment to increase the number of measurement points, forming a set of measurement paths. A distance matrix is ​​constructed for all measurement points in the measurement path set. The nearest neighbor algorithm is used to determine the access order. Transition points are inserted between adjacent measurement points based on the probe's maximum speed and acceleration constraints, generating a compensated measurement point position sequence containing coordinates and order.

[0092] Specifically, in the path planning for measuring the oxide layer thickness of aluminum profiles, the design of the avoidance mechanism directly determines the feasibility and efficiency of the measurement.

[0093] Specifically, the potential energy field is constructed based on an analogy with electric field theory. Each boundary point of the uncertain region is considered a point source carrying the same charge, generating a repulsive potential field in the measurement space. The potential energy value is calculated using Coulomb's law, which states that the potential energy is inversely proportional to the square of the distance. The potential energy coefficient is dynamically adjusted according to the importance of the uncertain region. When the measuring probe is located in a certain spatial position, the repulsive forces generated by all boundary points are vector-superimposed to form a resultant force, and the direction of the resultant force points in the direction of the fastest decrease in the potential energy gradient.

[0094] It should be noted that the attractive and repulsive forces at the target point work together to form a composite potential field. The attractive force adopts a linear model, and its intensity is proportional to the distance from the probe to the target point, ensuring that the probe can move towards the target position while avoiding obstacles. At each location in the potential field, the instantaneous movement direction of the probe is determined by calculating the potential energy gradient, and the continuous direction vectors form the initial avoidance path. This method can adaptively handle uncertain regions of different shapes and sizes, including convex, concave, and complex regions with holes.

[0095] In one embodiment, the path smoothing process first identifies key feature points in the initial path. Curvature calculation employs a discrete three-point circular arc method, determining a local arc by using three adjacent path points; the reciprocal of the arc radius is the curvature value at that point. When the curvature exceeds a preset threshold, the point is marked as a turning point. For straight segments, a sampling point is selected at fixed intervals as a control point to ensure that the Bézier curve accurately approximates the original path. The cubic Bézier curve is defined by four control points: the start and end points remain unchanged, while the two middle control points are adjusted according to the tangent direction and curvature magnitude, ensuring the curve maintains continuity of the first and second derivatives at connection points. Path smoothing is achieved through curve fitting, ensuring the curve remains continuous at connection points, eliminating sharp turns and oscillations, resulting in smoother probe movement and reducing the impact of mechanical vibration on measurement accuracy.

[0096] Preferably, the safety distance of the measurement point takes into account several factors. The probe of the eddy current thickness gauge has a certain physical size, typically 5-10 mm in diameter, and the safety distance should be at least greater than the probe radius. Furthermore, the electromagnetic field distribution near the boundary of the uncertain region is uneven; getting too close can cause measurement signal distortion. The safety distance also includes tolerance for positioning errors, ensuring that even with slight positioning deviations, the probe will not enter the uncertain region. When a measurement point is detected to violate the safety distance constraint, it moves in the opposite direction of the line connecting that point to the nearest boundary point, with the movement step gradually increasing until the constraint condition is met.

[0097] For example, a gridding method is used to assess the coverage density. The effective measurement area is divided into a uniform square grid, with the grid size matching the spatial scale of oxide layer thickness. The number of measurement points within each grid is counted, and the result is divided by the grid area to obtain the local coverage density. For areas with insufficient density, a spiral provides an efficient filling solution. The polar equation of the spiral is r = a + bθ, where parameter a determines the initial radius and b controls the pitch. The spiral starts from the geometric center of the sparse region and expands outward until it reaches the region boundary or meets the density requirements. The advantage of the spiral path is that it can cover a two-dimensional region with continuous movement, avoiding frequent starts, stops, and turns.

[0098] Understandably, optimizing the access order is crucial for reducing measurement time. A distance matrix records the Euclidean distance between any two measurement points; the matrix's symmetry reduces computation by half. The nearest neighbor algorithm starts from an arbitrary starting point and selects the nearest unvisited point as the next target. While this greedy strategy doesn't guarantee global optimality, it quickly yields satisfactory results in practical applications, especially when measurement points are relatively evenly distributed. Furthermore, the probe's kinematic constraints include maximum speed, maximum acceleration, and minimum turning radius. Between adjacent measurement points, if the straight-line distance divided by the maximum speed is less than the acceleration / deceleration time, a transition point needs to be inserted. The location of the transition point is determined through trapezoidal velocity planning to ensure smooth transitions during acceleration, constant speed, and deceleration. For turning maneuvers, when the angle between two adjacent path segments is less than a preset value, a circular arc transition is inserted at the corner, with the arc radius not less than the probe's minimum turning radius.

[0099] In one possible implementation, the entire path planning process employs a hierarchical strategy. First, a global path is rapidly generated at coarse resolution, followed by fine-tuning in local areas. This approach balances computational efficiency and path quality, making it particularly suitable for handling the complex surfaces of large aluminum profiles. The final output sequence of compensated measurement point locations includes not only 3D coordinates but also the normal vector information for each point, suggested measurement parameters, and expected measurement uncertainties, providing comprehensive guidance for subsequent data acquisition and processing.

[0100] S105. The measurement probe is guided to perform thickness scanning within the effective measurement area by compensating for the measurement point position sequence. The oxide layer thickness values ​​of each measurement point are obtained by scanning, forming an oxide layer thickness dataset.

[0101] The measurement probe is sequentially moved to designated coordinates according to the sequence of compensated measurement point positions. At each measurement point, the eddy current thickness gauge is activated to generate a high-frequency electromagnetic field, receive the oxide layer reflection signal, and convert it into a thickness value. Simultaneously, the spatial coordinates and acquisition time of that point are recorded. The thickness value is then checked for range. If the value exceeds a preset multiple of the nominal oxide layer thickness, it is marked as abnormal, and the measurement is repeated at that location. The checked thickness value, spatial coordinates, and acquisition time are combined and encoded, and all measurement point data are aggregated to form an oxide layer thickness dataset.

[0102] Specifically, in the actual measurement of the oxide layer thickness of aluminum profiles, the sequence of compensated measurement points provides accurate spatial guidance information.

[0103] Specifically, each measurement point contains three-dimensional coordinates and a suggested probe attitude angle. The controller drives the stepper motor to achieve precise positioning based on these parameters.

[0104] It should be noted that the working principle of the eddy current thickness gauge is based on the law of electromagnetic induction. A high-frequency oscillation circuit generates an alternating current of 10-100kHz, which induces eddy currents on the surface of the aluminum profile through the probe coil. The oxide layer acts as an insulator, hindering the propagation of eddy currents, and its thickness is positively correlated with the degree of eddy current attenuation. The voltage signal induced by the receiving coil is amplified, detected, and converted from analog to digital, ultimately mapped to a thickness value.

[0105] Preferably, data verification employs a dual mechanism. Range verification is based on the nominal thickness of the oxide layer, typically set to a reasonable range of 0.5 to 2 times the nominal value. Continuity verification checks the thickness difference between adjacent measurement points; if it exceeds a preset gradient threshold, an anomaly marker is triggered. For measurement points marked as an anomaly, the system automatically performs three repeated measurements at that location, taking the median as the final value.

[0106] For example, the data encoding adopts a structured format, with each record containing the measurement point number, spatial coordinates, thickness value, acquisition time, and quality identifier. The summarized oxide layer thickness dataset is stored according to spatial location index, which facilitates subsequent statistical analysis and visualization processing.

[0107] S106. Perform statistical analysis on the oxide layer thickness dataset, extract the standard deviation and mean deviation of the thickness values ​​to determine the irregular distribution of thickness, identify uncertain measurement areas by comparing the characteristics of the irregular thickness distribution with the oxide layer thickness distribution, use a compensation algorithm to interpolate the uncertain measurement areas, and determine the corrected thickness value by fusing the thickness gradient change rate.

[0108] For the oxide layer thickness dataset, the global mean and standard deviation are calculated. The thickness value of each measurement point is subtracted from the mean and divided by the standard deviation to obtain the standardized deviation. Points with deviations exceeding a preset threshold are marked as outliers. The distribution of outliers per unit area is statistically analyzed to form a thickness irregularity distribution map. This thickness irregularity distribution map is compared with the theoretical thickness distribution under a standard oxidation process using a spatial grid. The root mean square of the thickness difference within the corresponding grid is calculated as the similarity coefficient. Regions with similarity coefficients below a preset matching threshold are identified as uncertain measurement regions, and the coordinates of missing measurement points within these regions are extracted. For missing measurement points, a spatial interpolation method is used to determine the weight coefficients of each point based on the thickness values ​​and spatial distances of surrounding valid measurement points. A weighted sum is then used to obtain the initial interpolated thickness of the missing point. Based on this initial interpolated thickness, the local gradient change rate is calculated. The difference between this gradient and the gradients of surrounding measured points is compared. If the difference exceeds a threshold, the interpolation result is adjusted proportionally. This process is iterated until the gradient difference between adjacent points is less than a convergence threshold, and the corrected thickness value is output.

[0109] Specifically, in the post-processing stage of aluminum profile oxide layer thickness data, statistical analysis revealed the inherent laws of thickness distribution.

[0110] Specifically, the standardized deviation was calculated using the Z-score method in statistics. The thickness value at each measurement point was subtracted from the global average, and then divided by the standard deviation to obtain a dimensionless deviation index. When the absolute value of the deviation exceeded 2.5, it indicated that the thickness value at that point deviated from the normal distribution by more than the 99% confidence interval and was marked as a statistical outlier. The spatial clustering of these outliers was obtained through kernel density estimation, forming a continuous density distribution map that visually reflects the spatial characteristics of thickness irregularities.

[0111] It should be noted that the theoretical thickness distribution is established based on statistical modeling of a large amount of historical production data. Under standard anodizing process conditions, the oxide layer thickness at various locations on the aluminum profile surface follows a specific spatial distribution pattern, which is influenced by the current density distribution, solution flow state, and profile geometry. The theoretical distribution was obtained through finite element simulation combined with experimental verification, forming a reference template containing the expected thickness value and allowable deviation. When comparing the spatial mesh, the measured distribution map and the theoretical distribution map are divided into square meshes of the same size, and the thickness difference within each mesh reflects the degree of local deviation.

[0112] In one embodiment, the similarity coefficient calculation considers not only the absolute thickness difference but also a gradient consistency factor. For each grid cell, the square of the difference between the measured thickness and the theoretical thickness is calculated, along with the cosine of the angle between their gradient directions. The similarity coefficient is defined as a weighted combination of the root mean square of the difference and the gradient consistency factor, with the weighting coefficient dynamically adjusted according to measurement accuracy requirements. When the similarity coefficient is below 0.7, it indicates that the measured thickness distribution in that region deviates significantly from theoretical expectations, requiring the reconstruction of thickness data using interpolation methods.

[0113] For example, the core of Kriging interpolation lies in the construction and solution of the semivariogram. The semivariogram describes the variation of spatial correlation with distance. The empirical semivariogram is obtained by calculating the average of the squared thickness differences between measurement point pairs at different distances. Commonly used theoretical semivariogram models include the spherical model, the exponential model, and the Gaussian model. The model parameters are determined by fitting the model using the least squares method. The spherical model is suitable for cases where the correlation decreases rapidly within a specific distance. Its expression includes three parameters: nugget value, sill value, and range. The nugget value reflects measurement error and micro-variability, the sill value represents the overall degree of variability, and the range defines the effective range of spatial correlation.

[0114] Preferably, the Kriging equations are constructed based on the principles of unbiased estimation and minimizing the estimation variance. Assume there are n valid measurement points surrounding the point to be interpolated, each assigned a weight λi, where the weights satisfy the unbiased constraint condition that the sum of the weights equals 1. The constrained optimization problem is transformed into a system of linear equations to be solved using the Lagrange multiplier method. The coefficient matrix of the equations consists of the semi-variogram values ​​between the measurement points, and the right-hand vector contains the semi-variogram values ​​between the point to be interpolated and each measurement point. Solving the equations yields the optimal weights for each measurement point, and the weighted sum gives the interpolation thickness. This method not only provides the interpolation estimate but also the estimation variance, used to evaluate the reliability of the interpolation results. Furthermore, the gradient iterative correction process ensures the spatial continuity of the interpolation results. The initial interpolation thickness is calculated using the finite difference method to obtain the local gradient, which is compared with the gradients of the surrounding measured points. The gradient difference is evaluated using the vector norm; when the Euclidean distance of the gradient vector exceeds a preset threshold, a correction mechanism is triggered. The correction amount is proportional to the gradient difference, and the proportionality coefficient is determined empirically, typically between 0.3 and 0.5. After each iteration, the gradient is recalculated and convergence is evaluated. Convergence criteria include the thickness change between adjacent iterations being less than 0.1 micrometers or the gradient difference being less than a preset precision.

[0115] Understandably, the convergence of the iterative process is closely related to the quality of the initial interpolation. Kriging interpolation provides a good initial estimate and typically converges within 3-5 iterations. For complex, uncertain regions, more iterations may be required. To prevent oscillations, a relaxation factor is introduced, and the new interpolation result is a weighted average of the previous iteration value and the calculated value.

[0116] In one possible implementation, the entire data processing flow employs a modular processing strategy, dividing the surface of large aluminum profiles into multiple processing units. Each unit independently performs statistical analysis and interpolation correction, with boundary areas using overlapping processing to ensure continuity. The final corrected thickness value not only fills in measurement blind spots but also eliminates the influence of outlier measurements, providing a complete and reliable data foundation for oxide layer quality assessment. Through this comprehensive processing method, accurate thickness distribution information can be obtained even in difficult-to-measure areas such as fixture contact points, increasing measurement coverage from the original 85% to nearly 100%.

[0117] S107. Generate the final oxide layer thickness assessment report based on the corrected thickness value and the effective measurement area range, and determine the oxide layer thickness on the aluminum profile surface by integrating the boundary coordinates of the uncertain measurement area and the oxide layer thickness distribution characteristics.

[0118] An oxide layer thickness data matrix is ​​constructed based on the corrected thickness values ​​and the effective measurement area. The boundary coordinates of uncertain measurement areas are mapped to the corresponding positions in the matrix and the area type is labeled. The thickness value distribution is represented by a color gradient, and the boundary contours are drawn with lines to obtain an oxide layer thickness spatial distribution map. Based on the oxide layer thickness spatial distribution map, the average thickness, maximum and minimum thickness values, the proportion of areas with thicknesses within the acceptable range, and the percentage of the measured area to the total area are calculated. Combining the oxide layer thickness distribution characteristics, it is determined whether the preset quality standards are met. All data are summarized to form an aluminum profile surface oxide layer thickness evaluation report.

[0119] Specifically, the oxide layer thickness data matrix is ​​constructed using a two-dimensional array structure, with row and column indices corresponding to the physical coordinates of the aluminum profile surface. Each matrix element stores the thickness value at that location. For uncertain measurement areas, in addition to the thickness value, an area type identifier is added to distinguish between measured values, interpolated values, and boundary points.

[0120] In one embodiment, the color gradient mapping uses a rainbow spectrum, with the minimum thickness value corresponding to blue, the maximum to red, and intermediate values ​​determined by linear interpolation. Boundary contour lines are drawn using solid black lines with a line width of 2 pixels to ensure clear visibility against a colored background. The resolution of the spatial distribution map is determined based on the measurement density, typically 1-5 pixels per millimeter.

[0121] It should be noted that quality standards are determined based on industry norms and customer requirements. The oxide layer thickness of aerospace-grade aluminum profiles is typically required to be within the range of 8-12 micrometers, with a pass rate of over 95%. When calculating coverage, the sum of the actual measured and interpolated areas is divided by the total area of ​​the profile. Coverage below 90% must be specifically noted in the report.

[0122] Preferably, the evaluation report adopts a structured format, including four parts: basic information, statistical summary, distribution chart, and quality conclusion. The basic information records the profile batch, specifications, and measurement time; the statistical summary lists the various numerical indicators; the distribution chart visually displays the spatial distribution of thickness; and the quality conclusion provides the pass / fail determination and improvement suggestions.

[0123] The above description is merely a preferred embodiment of one or more embodiments of this specification and is not intended to limit the scope of one or more embodiments of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments of this specification should be included within the protection scope of one or more embodiments of this specification.

Claims

1. An automatic method for measuring the thickness of the oxide layer on the surface of aluminum profiles, characterized in that, include: Acquire image data of the aluminum profile surface and determine the range of the hanger contact point area through image processing; A uniform sampling network is constructed on the oxide layer surface according to the range of the contact point area of ​​the hanger; An eddy current thickness gauge is used to scan the nodes of the sampling network point by point, and the position coordinates and oxide layer thickness values ​​of each sampling point are recorded to form a discrete sampling dataset. The thickness values ​​of adjacent sampling points in the discrete sampling dataset are differentially calculated to obtain the local thickness gradient value; A continuous oxide layer thickness field is generated using an interpolation method; Based on the continuous oxide layer thickness field, the distribution areas of different thickness levels are extracted, the area ratio of each area is calculated, the number of sampling points with gradient values ​​exceeding the preset threshold and the distribution density are counted, and the oxide layer thickness distribution characteristics are determined by combining the thickness mean, standard deviation and gradient distribution. Based on the oxide layer thickness distribution characteristics, the thickness gradient change rate of each sampling point is compared with a preset threshold. If the threshold is exceeded, it is marked as an uncertain point. By determining the spatial connectivity of adjacent uncertain points, a continuous uncertain measurement region is formed by aggregation; Traverse along the outer edge of the uncertain measurement area, extract the coordinate sequence of contour points, calculate the tangent direction based on the thickness value and gradient change rate, search vertically until the gradient change rate is lower than the threshold, and record the endpoint coordinates as the boundary coordinates of the uncertain area. Calculate the standard deviation of the gradient change rate in the local neighborhood of the sampling points outside the boundary. If it is lower than the preset stability threshold, it is determined to be a valid measurement area. Traverse the area to complete the area identification and identify uncertain measurement areas and valid measurement areas. Based on the uncertain measurement area, the measurement path is dynamically adjusted to generate a sequence of compensated measurement point positions; The compensation measurement point position sequence guides the measurement probe to perform thickness scanning within the effective measurement area, forming an oxide layer thickness dataset. Statistical analysis is performed on the oxide layer thickness dataset to determine the irregular thickness distribution, and interpolation is performed on the uncertain measurement area to generate a corrected thickness value; A final oxide layer thickness assessment report is generated based on the corrected thickness value and the effective measurement area range.

2. The automatic measurement method for the oxide layer thickness of aluminum profiles as described in claim 1, characterized in that, The acquisition of image data of the aluminum profile surface, and the determination of the contact point area of ​​the hanger through image processing, includes: A high-resolution industrial camera is used to scan the surface of the aluminum profile line by line to collect image data including the contact area of ​​the hanger; The image data is preprocessed by filtering to remove reflective interference and noise points, resulting in a preprocessed surface image. Edge detection is performed on the preprocessed surface image, and boundary pixels are extracted based on grayscale differences to form an initial contour line; If the closure of the initial contour line is lower than a preset threshold, the contour gap is filled by morphological processing to obtain a complete contour. Calculate the average coordinates of pixels within the complete contour to determine the center coordinates of the contact point. The minimum bounding rectangle is obtained by traversing the coordinates of each point on the contour, the boundary of the contact area is determined, and the actual area value of the contact point is calculated by counting the total number of pixels in the contour. The output is the range of the contact point area including the center coordinates, the boundary of the area and the actual area.

3. The automatic measurement method for the oxide layer thickness of aluminum profiles as described in claim 1, characterized in that, Based on the uncertain measurement area, the measurement path is dynamically adjusted to generate a sequence of compensated measurement point positions, including: Based on the boundary coordinates of the uncertain measurement area, avoidance constraints are constructed, and boundary rejection areas are set to guide the probe's movement direction, forming an initial avoidance path. Control points are extracted from the initial avoidance path, path smoothing is achieved through curve fitting, and measurement points are generated by sampling at preset intervals. If the shortest distance between the measurement point and the boundary is lower than the preset safety distance, adjust the position in the direction away from the boundary; Based on the measurement trajectory and the effective measurement area, the measurable segment is determined, and the coverage density value is calculated. If it is lower than the preset standard, a spiral path is added to increase the measurement points, forming a set of measurement paths. A distance matrix is ​​constructed for the set of measurement paths, an algorithm is used to determine the access order, and transition points are inserted to generate a sequence of compensated measurement point positions.

4. The automatic measurement method for the oxide layer thickness of aluminum profiles as described in claim 1, characterized in that, The compensated measurement point position sequence guides the measurement probe to perform thickness scanning within the effective measurement area, forming an oxide layer thickness dataset, including: The measurement probe is moved to the specified coordinates according to the sequence of compensated measurement point positions. At each measurement point, the eddy current thickness gauge is activated to generate an electromagnetic field, receive the reflected signal from the oxide layer and convert it into a thickness value, and record the spatial coordinates and acquisition time. The thickness value is checked for range; if it exceeds a preset multiple, it is marked as abnormal and remeasured. The verified thickness values, spatial coordinates, and acquisition times are combined and encoded to form an oxide layer thickness dataset by summarizing all measurement point data.

5. The automatic measurement method for the oxide layer thickness of aluminum profiles as described in claim 1, characterized in that, Statistical analysis was performed on the oxide layer thickness dataset to determine the irregular thickness distribution and interpolation was performed on uncertain measurement areas, including: The global mean and standard deviation of the oxide layer thickness dataset are calculated, and the standardized deviation of each measurement point is obtained. If the deviation exceeds the preset threshold, it is marked as an outlier. The distribution of outliers is statistically analyzed to form a thickness irregularity distribution map. By comparing the spatial grid with the theoretical thickness distribution, the root mean square of the thickness difference is calculated. If it is lower than the matching threshold, it is determined to be an uncertain measurement area. For missing measurement points, a spatial interpolation method is used to determine the weighting coefficients based on the thickness values ​​and distances of surrounding valid measurement points, and the initial interpolated thickness is obtained by weighted summation.

6. The automatic measurement method for the oxide layer thickness of aluminum profiles as described in claim 1, characterized in that, Interpolation processing is performed on the uncertain measurement area to generate a corrected thickness value, including: Calculate the local gradient change rate based on the initial interpolated thickness and compare it with the gradient difference of surrounding measured points; If the gradient difference exceeds the preset threshold, the interpolation result is adjusted proportionally, and the process is iterated until the gradient difference between adjacent points is lower than the convergence threshold, and the corrected thickness value is output. The corrected thickness value is verified, and outliers are adjusted according to the thickness distribution characteristics of surrounding effective measurement points to ensure that the interpolation result is consistent with the measured data, and the final corrected thickness value is generated.

7. The automatic measurement method for the oxide layer thickness of aluminum profiles as described in claim 1, characterized in that, A final oxide layer thickness assessment report is generated based on the corrected thickness value and the effective measurement area, including: An oxide layer thickness data matrix is ​​constructed based on the corrected thickness value and the effective measurement area range; The boundary coordinates of the uncertain measurement area are mapped to matrix positions and the area type is labeled. The thickness distribution is represented by color gradient and the boundary outline is drawn with lines to obtain a thickness spatial distribution map. Based on the thickness spatial distribution map, the average thickness, maximum and minimum thickness values, qualified area ratio and measurement coverage percentage are calculated. Combined with the oxide layer thickness distribution characteristics, it is determined whether the preset standard is met, and the data is summarized to form an evaluation report.

8. The automatic measurement method for the oxide layer thickness of aluminum profiles as described in claim 1, characterized in that, Identifying uncertain measurement areas and effective measurement areas based on the oxide layer thickness distribution characteristics includes: The thickness gradient change rate in the oxide layer thickness distribution characteristics is analyzed, and the location distribution of gradient change rate anomalies is extracted. Spatial clustering methods are used to aggregate adjacent outliers into uncertain measurement regions; Gradient stationarity analysis is performed on the region outside the boundary of the uncertain measurement region, and the standard deviation of the local gradient change rate is calculated. If it is lower than the preset threshold, it is classified as a valid measurement region. The effective measurement region and the uncertain measurement region are optimized by boundary optimization. Boundary noise is reduced by smoothing process to generate the final region division result.

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