Method and system for generating scrap steel material taking point based on point cloud

Abstract

The invention provides a scrap steel material taking point generation method and system based on point cloud. The method comprises the steps that S1, three-dimensional point cloud data of a scrap steel warehouse area are obtained in real time through a laser radar; s2, performing rasterization processing on the three-dimensional point cloud data to generate discretized grid point cloud data; s3, matching a corresponding material taking rule according to the type of the material, wherein the material taking rule comprises at least one of layered material taking according to high priority, preferential material taking according to flatness and preferential segmented material taking according to distance; s4, on the basis of the matched material taking rule, density and surface gradient feature information of candidate material taking points in the grid point cloud data are calculated; and S5, screening a target material taking position according to the density and surface gradient feature information, generating a recommended material taking point set, and outputting a material taking point with the highest priority. According to the method, the material taking task recommendation problem of the unmanned crown block of the waste steel storage yard is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of material transportation and data processing, and in particular to a method and system for generating scrap steel material reclaiming points based on point clouds. Background Art

[0002] As a "green resource," scrap steel is indispensable for reducing production costs, alleviating environmental burdens, and promoting sustainable development. With technological advancements, its recycling rate and application scope will continue to expand, becoming a core pillar of the steel industry's transformation.

[0003] Scrap steel yards are metal storage areas responsible for supplying raw materials to electric furnaces and converters. These yards are complex processes, operate in harsh environments, and require high labor intensity. With the increasing automation of industry, steel companies are increasingly demanding automated and intelligent scrap processing. This requires a method that can accurately determine scrap material reclaim points to automate and accurately process scrap lifting and other operations, improving production efficiency and quality. Advances in laser scanning technology, sensor technology, and computer performance have made the acquisition of point cloud data more convenient, efficient, and accurate, providing a technical foundation for point cloud-based scrap material reclaim point generation methods.

[0004] The patent document (patent number: CN201910695156.9) discloses a train loading and distributing system and method based on an unmanned grab trolley mode. The system uses the grab trolley to dynamically scan the wagons of trains entering the depot to obtain laser scanning data. Based on the laser scanning data, the system generates a three-dimensional image of the train wagons to be loaded. The system records the movement position of the grab trolley, generates point-to-point distribution operation commands, executes the distribution operation commands, and records the weight of each material drop point. The grab trolley's grab weight is obtained in real time, and the amount of material dropped by each grab is recorded in the three-dimensional wagon image data. Based on the three-dimensional wagon image data, a loading model is generated. Based on the amount of material dropped by each grab, the system calculates whether the total amount of material loaded on the train to be loaded reaches the rated load. If so, loading is terminated; if not, loading is continued. However, the patent mentions that the material type in the operation scenario is single and the material surface can be considered continuous. For scrap steel, due to the varying hardness and softness, it is impossible to use a single rule to recommend grab points to ensure the amount of material to be loaded. Summary of the Invention

[0005] In view of the defects in the prior art, the purpose of the present invention is to provide a method and system for generating scrap steel material collection points based on point cloud.

[0006] The method for generating scrap steel material reclaiming points based on point cloud provided by the present invention includes:

[0007] Step S1: Obtaining three-dimensional point cloud data of the scrap steel storage area in real time through laser radar;

[0008] Step S2: performing rasterization processing on the three-dimensional point cloud data to generate discretized raster point cloud data;

[0009] Step S3: matching corresponding material picking rules according to the type of material, wherein the material picking rules include at least one of picking by high priority layer, picking by flatness priority, and picking by distance priority segmentation;

[0010] Step S4: Based on the matched material collection rules, the density and surface inclination characteristic information of the candidate material collection points in the grid point cloud data are calculated;

[0011] Step S5: Filter target material extraction positions according to the density and surface inclination characteristic information, generate a set of recommended material extraction points, and output the material extraction point with the highest priority.

[0012] Preferably, the rasterization process includes:

[0013] Set the total length of the grid map_height, the total width map_width, the starting addresses startx and starty, and the grid size size;

[0014] Traverse the lidar data point set pts i ∈{(x1,y1,z1),...(xn,yn,zn)};

[0015] Calculate the grid row and column coordinates corresponding to each data point using the following formula:

[0016]

[0017] Among them, pt_row and pt_col represent the row and column coordinates of the grid, pts i (x i ), pts i (y i ), pts i (z i ) represents the x, y, and z coordinates of the current data point i; pt_z represents the z value of the current grid.

[0018] Preferably, the high-priority hierarchical material collection rule includes: sorting the grid point cloud data from large to small according to the z value, screening candidate points; calculating the point cloud density and surface inclination of each candidate point, wherein: the point cloud density is determined by counting the ratio of the number of points in the voxel to the voxel volume; the surface inclination is calculated by fitting the angle between the local plane normal vector and the horizontal plane normal vector; and preferentially selecting candidate points with a density greater than a preset threshold and an inclination less than a preset threshold as target material collection positions;

[0019] The flatness-prioritized material collection rule includes: dividing the grid point cloud data into regions, calculating the normal vector consistency of points in each region; fitting a local plane using a k-nearest neighbor algorithm, and calculating the average value or variance of the normal vector angle in the neighborhood; selecting the region with high normal vector consistency or small variance as the target material collection location;

[0020] The distance-priority segmented material picking rule includes: determining the material picking direction based on the position information of the receiving trolley provided by the warehouse management system; intercepting point cloud data in the specified area, and screening candidate points based on density and surface inclination characteristics; and giving priority to selecting the candidate point closest to the receiving trolley as the target material picking position.

[0021] Preferably, the density calculation includes: defining a neighborhood area within the suction cup projection range with the candidate point as the center; counting the number of point clouds in the neighborhood and calculating the point cloud density within a unit volume; if the density exceeds a preset threshold, it is marked as a valid candidate point.

[0022] Preferably, the surface inclination calculation includes: fitting the plane equation and extracting the plane normal vector using the least squares method for the point cloud within the neighborhood of the candidate point, and calculating the angle θ between it and the horizontal plane normal vector; if θ is less than a preset threshold, it is marked as a valid candidate point.

[0023] The point cloud-based scrap steel material collection point generation system provided by the present invention includes:

[0024] Module M1: Use LiDAR to obtain real-time 3D point cloud data of the scrap steel storage area;

[0025] Module M2: performing rasterization processing on the three-dimensional point cloud data to generate discretized raster point cloud data;

[0026] Module M3: Matching corresponding material picking rules according to the type of material, wherein the material picking rules include at least one of picking by high priority layer, picking by flatness priority, and picking by distance priority segmentation;

[0027] Module M4: Based on the matching material collection rules, calculate the density and surface inclination characteristic information of the candidate material collection points in the grid point cloud data;

[0028] Module M5: Filter the target material extraction position according to the density and surface inclination characteristic information, generate a set of recommended material extraction points, and output the material extraction point with the highest priority.

[0029] Preferably, the rasterization process includes:

[0030] Set the total length of the grid map_height, the total width map_width, the starting addresses startx and starty, and the grid size size;

[0031] Traverse the lidar data point set pts i ∈{(x1,y1,z1),...(xn,yn,zn)};

[0032] Calculate the grid row and column coordinates corresponding to each data point using the following formula:

[0033]

[0034] Among them, pt_row and pt_col represent the row and column coordinates of the grid, pts i (x i ), pts i (y i ), pts i (z i ) represents the x, y, and z coordinates of the current data point i; pt_z represents the z value of the current grid.

[0035] Preferably, the high-priority hierarchical material collection rule includes: sorting the grid point cloud data from large to small according to the z value, screening candidate points; calculating the point cloud density and surface inclination of each candidate point, wherein: the point cloud density is determined by counting the ratio of the number of points in the voxel to the voxel volume; the surface inclination is calculated by fitting the angle between the local plane normal vector and the horizontal plane normal vector; and preferentially selecting candidate points with a density greater than a preset threshold and an inclination less than a preset threshold as target material collection positions;

[0036] The flatness-prioritized material collection rule includes: dividing the grid point cloud data into regions, calculating the normal vector consistency of points in each region; fitting a local plane using a k-nearest neighbor algorithm, and calculating the average value or variance of the normal vector angle in the neighborhood; selecting the region with high normal vector consistency or small variance as the target material collection location;

[0037] The distance-priority segmented material picking rule includes: determining the material picking direction based on the position information of the receiving trolley provided by the warehouse management system; intercepting point cloud data in the specified area, and screening candidate points based on density and surface inclination characteristics; and giving priority to selecting the candidate point closest to the receiving trolley as the target material picking position.

[0038] Preferably, the density calculation includes: defining a neighborhood area within the suction cup projection range with the candidate point as the center; counting the number of point clouds in the neighborhood and calculating the point cloud density within a unit volume; if the density exceeds a preset threshold, it is marked as a valid candidate point.

[0039] Preferably, the surface inclination calculation includes: fitting the plane equation and extracting the plane normal vector using the least squares method for the point cloud within the neighborhood of the candidate point, and calculating the angle θ between it and the horizontal plane normal vector; if θ is less than a preset threshold, it is marked as a valid candidate point.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The present invention uses laser radar to perform three-dimensional modeling of materials, discretizes material information through rasterization processing, regularizes manual material picking experience, calculates the local density and surface inclination information of the materials, generates a suitable target picking position, and solves the problem of recommending picking tasks for unmanned overhead cranes in scrap steel yards. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0043] Figure 1 This is a schematic diagram of rasterization processing;

[0044] Figure 2a and Figure 2b This is a schematic diagram of taking materials by high priority layer;

[0045] Figure 3 This is a flow chart of the material taking rule according to high priority layer;

[0046] Figure 4a and Figure 4b Schematic diagram of material selection based on flatness priority;

[0047] Figure 5 This is a flow chart of the rule for taking materials in priority according to flatness;

[0048] Figure 6 This is a schematic diagram of taking materials by distance priority;

[0049] Figure 7 This is a flow chart of the material taking rule based on distance priority;

[0050] Figure 8 Flowchart of the method for generating scrap steel material picking points based on point clouds. DETAILED DESCRIPTION

[0051] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0052] Example

[0053] like Figure 8The present invention provides a method for generating scrap steel material picking points based on point clouds. It uses laser radar to obtain material data in the scrap steel storage area in real time, and establishes three-dimensional spatial information of the material pile through rasterization processing; according to the material type, the corresponding picking rules are matched, the density and surface inclination feature information of the picking candidate points are calculated, and a suitable target picking position is generated.

[0054] The specific implementation process is as follows:

[0055] The scrap crane uses electromagnetic suction cups to transfer scrap materials such as crushed material, silicon steel sheets, and slag. A laser radar installed on the crane monitors the crane's position in real time, generating a 3D point cloud of the scrap material. By applying 3D point cloud data processing technology based on different material reclaiming rules, the crane calculates the appropriate reclaiming position and recommends appropriate reclaiming tasks for the unmanned scrap crane.

[0056] LiDAR: A sensor that uses the ToF principle to achieve long-distance ranging;

[0057] Point cloud: a collection of spatial data points;

[0058] Overhead crane: A type of bridge crane that runs on rails;

[0059] Receiving trolley: a transport vehicle for transferring materials;

[0060] wms: warehouse management system.

[0061] The method for generating scrap steel material collection points based on point cloud includes:

[0062] Step 1: Rasterize the reservoir area point cloud data.

[0063] The step 1 comprises the following steps:

[0064] Step 1.1: Given the total grid length map_height, total width map_width, grid starting address startx, starty and grid size size, obtain the lidar data pts returned by the material i ∈{(x1,y1,z1),...(xn,yn,zn)};

[0065] Step 1.2: Traverse the lidar data and assign grid values ​​according to the following rules:

[0066]

[0067] Among them, pt_row and pt_col are the row and column coordinates of the grid, pts i (x i ), pts i (y i ), ptsi (z i ) represents the x, y, and z coordinates of the current data point i; pt_z represents the z value of the current grid. Generate the rasterized material point cloud data map_points, such as Figure 1 shown.

[0068] Step 2: Match the corresponding material collection rules.

[0069] Due to the different shapes of materials, such as rectangular shaped packing blocks, they are stacked randomly. When the suction cup is lowered normally, the surface of the packing blocks will block the suction cup from falling, resulting in less contact surface between the packing blocks and the suction cup. In addition, the large weight of the packing blocks leads to a small amount of suction in a single suction. To solve this problem, according to the characteristics of different materials, corresponding picking rules are set. By matching the materials with the picking rules, the single suction amount of the materials can be increased. The specific picking rules are classified as follows:

[0070] 1) Take materials by high priority layer

[0071] According to the grid data, candidate points are recommended according to the z value from large to small, such as Figure 2a and Figure 2b According to the target point generation algorithm, the characteristic information of the point cloud (point cloud density, surface inclination) is calculated to generate the target material position. The specific process is as follows: Figure 3 shown.

[0072] The point cloud density is obtained as follows:

[0073] Assume that the point cloud dataset is P t ={p t1 , p t2 ,…,p tn}, where p ti =(xi, yi, zi) is the spatial coordinate of the i-th point. We define the side length of a voxel as v, with point p t The voxel coordinates (u i , v i , w i ) can be calculated by the following formula:

[0074]

[0075] Then, by counting each unique (u i , v i , w i ) The number of points corresponding to the combination can be used to obtain the point cloud density within each voxel. u,v,w Represents the number of points within a voxel (u, v, w), then the point cloud density ρ u,v,w It can be expressed as:

[0076]

[0077] The surface inclination is calculated as follows:

[0078] For each point p in the point cloud ti , select the k nearest neighbor points P around it ti , k={p ti 1, p ti 2, ..., p ti k}, and then use the least squares method to fit a plane ax+by+cz+d=0 so that the sum of the squares of the distances from these points to the plane is minimized.

[0079] Let n = (a, b, c) be the normal vector of the fitted plane, and its unit normal vector Assume that the normal vector of the reference plane is (corresponding to the horizontal plane), then point p ti The surface inclination θ at i It can be obtained by calculating the angle between two normal vectors. The formula is as follows:

[0080]

[0081] 2) Prioritize material selection based on flatness

[0082] like Figure 4a and Figure 4b As shown in the figure, according to the grid data, the material pile information in the specified area is obtained, and the surface flatness value of the material point cloud is calculated based on the flatness algorithm. The material is screened according to the flatness value, and then the target point is generated to generate the target material position. The specific process is as follows Figure 5 shown.

[0083] The flatness is obtained as follows:

[0084] Estimate the normal vector of the target point. Use the points in the neighborhood to fit a plane. The normal vector of the plane is the normal vector of the point. Use the least squares method to fit the points in the local neighborhood to obtain the plane equation ax + by + cz + d = 0, and then obtain the normal vector.

[0085] Determine the local neighborhood of each target point. Use k-nearest neighbor search or radius search method, assuming that k nearest neighbor points N = {N1, N2, ..., N k}, calculate the normal vector of point P With each neighbor point N i Normal vector The angle θ i , can be obtained through the vector dot product formula calculate.

[0086] Count the changes in the angle. Calculate the mean or variance of the cosine of the angle. The closer the mean is to 1, the more consistent the normal vector direction is, and the smoother the surface is. The smaller the variance is, the less change in the normal vector angle is, and the smoother the surface is.

[0087] Furthermore, combined with the material taking efficiency, according to the position of the receiving trolley in the material grid, the material taking rules provided are as follows:

[0088] 3) Prioritize material picking by distance

[0089] For grid data, WMS gives the material taking direction according to the position of the receiving trolley in the material grid, such as Figure 6 As shown, the material pile information in the specified area is obtained. According to the target point generation algorithm, the same as the classification rule 1) is expressed, the feature information of the point cloud (point cloud density, surface inclination) is calculated, and the target material position is generated. The specific process is as follows Figure 7 shown.

[0090] Step 3: Using the suction cup's xy plane projection range as the target point neighborhood, calculate the feature information of the point cloud: data density, material surface inclination, and generate candidate points, as described in classification rule 1).

[0091] The step 3 comprises the following steps:

[0092] Step 3.1: Receive the material to be taken plane area (x_start, y_start), (x_end, y_end) sent by WMS, further intercept the target point cloud data through this area, and mark it according to the following rules:

[0093]

[0094] Among them, 1 means to retain the point, and 0 means to delete the point; pt label Indicates the current grid identifier; pt x ,pt y Indicates the x and y coordinates of the current grid.

[0095] Step 3.2: Take the material point cloud marked as 1 as the center point (pt_centerx, pt_centery), count the point cloud data within the range of the suction cup length and width, and calculate the point cloud density pt_density within this range;

[0096] Step 3.3: Use the material point cloud marked as 1 as the center point (pt_centerx, pt_centery) to calculate the inclination information pt_angle of the material surface within the length and width of the suction cup;

[0097] Step 3.4: Traverse all point clouds marked as 1 to obtain density and surface tilt information;

[0098] Step 3.5: Further screen the generated candidate material points according to the following rules;

[0099]

[0100] pts_tartget represents the candidate point; pt i _density represents the neighborhood density of the grid point; pt i _angle represents the inclination angle of the stockpile surface near the grid point.

[0101] Among them, the density threshold density_threshold and the surface inclination threshold angle_threshold are marked as 1, indicating the final set of recommended sampling points. If the set is not empty, the sampling points in the set are prioritized by density and surface inclination, and the sampling point with the highest priority is selected as the final recommended point. If the set is empty, it means that there are currently no suitable points to recommend, and the sampling range needs to be readjusted and step 3 repeated.

[0102] Those skilled in the art will appreciate that, in addition to implementing the system, device, and various modules provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, embedded microcontrollers, and the like by logically programming the method steps. Therefore, the system, device, and various modules provided by the present invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; the modules for implementing various functions can also be considered both software programs for implementing the method and structures within the hardware component.

[0103] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A method for generating scrap steel material collection points based on point cloud, characterized in that: include: Step S1: Obtaining three-dimensional point cloud data of the scrap steel storage area in real time through laser radar; Step S2: performing rasterization processing on the three-dimensional point cloud data to generate discretized raster point cloud data; Step S3: matching corresponding material picking rules according to the material type, wherein the material picking rules include at least one of picking by high priority layer, picking by flatness priority, and picking by distance priority segmentation; Step S4: Based on the matched material collection rules, the density and surface inclination characteristic information of the candidate material collection points in the grid point cloud data are calculated; Step S5: Filter target material extraction positions according to the density and surface inclination characteristic information, generate a set of recommended material extraction points, and output the material extraction point with the highest priority.

2. The method for generating scrap steel material collection points based on point cloud according to claim 1, characterized in that: The rasterization process includes: Set the total length of the grid map_height, the total width map_width, the starting addresses startx and starty, and the grid size size; Traverse the lidar data point set pts i ∈{(x1,y1,z1),...(xn,yn,zn)}; Calculate the grid row and column coordinates corresponding to each data point using the following formula: Among them, pt_row and pt_col represent the row and column coordinates of the grid, pts i (x i ), pts i (y i ), pts i (z i ) represents the x, y, and z coordinates of the current data point i; pt_z represents the z value of the current grid.

3. The method for generating scrap steel material collection points based on point cloud according to claim 2, characterized in that: The high-priority hierarchical material collection rule includes: sorting the grid point cloud data from large to small according to the z value, screening candidate points; calculating the point cloud density and surface inclination of each candidate point, wherein: the point cloud density is determined by counting the ratio of the number of points in the voxel to the voxel volume; the surface inclination is calculated by fitting the angle between the local plane normal vector and the horizontal plane normal vector; and preferentially selecting candidate points with a density greater than a preset threshold and an inclination less than a preset threshold as target material collection positions; The flatness-prioritized material collection rule includes: dividing the grid point cloud data into regions, calculating the normal vector consistency of points in each region; fitting a local plane using a k-nearest neighbor algorithm, and calculating the average value or variance of the normal vector angle in the neighborhood; selecting the region with high normal vector consistency or small variance as the target material collection location; The distance-priority segmented material picking rule includes: determining the material picking direction based on the position information of the receiving trolley provided by the warehouse management system; intercepting point cloud data in the specified area, and screening candidate points based on density and surface inclination characteristics; and giving priority to selecting the candidate point closest to the receiving trolley as the target material picking position.

4. The method for generating scrap steel material collection points based on point cloud according to claim 1, characterized in that: The density calculation includes: defining a neighborhood area within the suction cup projection range with the candidate point as the center; counting the number of point clouds in the neighborhood and calculating the point cloud density within a unit volume; if the density exceeds a preset threshold, it is marked as a valid candidate point.

5. The method for generating scrap steel material collection points based on point cloud according to claim 1, characterized in that: The surface inclination calculation includes: fitting the plane equation and extracting the plane normal vector using the least squares method for the point cloud within the candidate point neighborhood, and calculating the angle θ between the plane equation and the horizontal plane normal vector; if θ is less than a preset threshold, it is marked as a valid candidate point.

6. A scrap steel material collection point generation system based on point cloud, characterized in that: include: Module M1: Use LiDAR to obtain real-time 3D point cloud data of the scrap steel storage area; Module M2: performing rasterization processing on the three-dimensional point cloud data to generate discretized raster point cloud data; Module M3: Matching corresponding material picking rules according to the type of material, wherein the material picking rules include at least one of picking by high priority layer, picking by flatness priority, and picking by distance priority segmentation; Module M4: Based on the matching material collection rules, calculate the density and surface inclination characteristic information of the candidate material collection points in the grid point cloud data; Module M5: Filter the target material extraction position according to the density and surface inclination characteristic information, generate a set of recommended material extraction points, and output the material extraction point with the highest priority.

7. The point cloud-based scrap steel material collection point generation system according to claim 6, characterized in that: The rasterization process includes: Set the total length of the grid map_height, the total width map_width, the starting addresses startx and starty, and the grid size size; Traverse the lidar data point set pts i ∈{(x1,y1,z1),...(xn,yn,zn)}; Calculate the grid row and column coordinates corresponding to each data point using the following formula: Among them, pt_row and pt_col represent the row and column coordinates of the grid, pts i (x i ), pts i (y i ), pts i (z i ) represents the x, y, and z coordinates of the current data point i; pt_z represents the z value of the current grid.

8. The point cloud-based scrap steel material collection point generation system according to claim 7, characterized in that: The high-priority hierarchical material collection rule includes: sorting the grid point cloud data from large to small according to the z value, screening candidate points; calculating the point cloud density and surface inclination of each candidate point, wherein: the point cloud density is determined by counting the ratio of the number of points in the voxel to the voxel volume; the surface inclination is calculated by fitting the angle between the local plane normal vector and the horizontal plane normal vector; and preferentially selecting candidate points with a density greater than a preset threshold and an inclination less than a preset threshold as target material collection positions; The flatness-prioritized material collection rule includes: dividing the grid point cloud data into regions, calculating the normal vector consistency of points in each region; fitting a local plane using a k-nearest neighbor algorithm, and calculating the average value or variance of the normal vector angle in the neighborhood; selecting the region with high normal vector consistency or small variance as the target material collection location; The distance-priority segmented material picking rule includes: determining the material picking direction based on the position information of the receiving trolley provided by the warehouse management system; intercepting point cloud data in the specified area, and screening candidate points based on density and surface inclination characteristics; and giving priority to selecting the candidate point closest to the receiving trolley as the target material picking position.

9. The point cloud-based scrap steel material collection point generation system according to claim 6, characterized in that: The density calculation includes: defining a neighborhood area within the suction cup projection range with the candidate point as the center; counting the number of point clouds in the neighborhood and calculating the point cloud density within a unit volume; if the density exceeds a preset threshold, it is marked as a valid candidate point.

10. The point cloud-based scrap steel material collection point generation system according to claim 6, characterized in that: The surface inclination calculation includes: fitting the plane equation and extracting the plane normal vector using the least squares method for the point cloud within the candidate point neighborhood, and calculating the angle θ between the plane equation and the horizontal plane normal vector; if θ is less than a preset threshold, it is marked as a valid candidate point.

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