A method for identifying curved beams based on the extension of line geometric characteristics

Abstract

The present invention relates to the technical field of arc-shaped beam recognition, and in particular to an arc-shaped beam recognition method based on the extension of line geometric characteristics. Laser scanning is used to generate point cloud data containing wall, ceiling and ground building structures, and after noise reduction and filtering, an accurate three-dimensional model is constructed. An edge detection algorithm is used to extract arc-shaped beam lines, and geometric parameters such as curvature, radian and arc length are normalized to improve the consistency of geometric recognition. Through a preset arc parameter library, the solution can accurately extract and mark arcs, effectively avoiding the problem of confusion between arc-shaped beams and other structures. In addition, a convolutional neural network is introduced for intelligent classification and prediction, and complex geometric features are captured through multi-layer convolution to improve the accuracy and robustness of recognition. Finally, the missing arc-shaped beam structure is supplemented by a geometric extension algorithm and mapped to a three-dimensional model to achieve complete visualization, solving the problem of missing visualization information of arc-shaped beams in traditional methods.

Description

Technical Field

[0001] The present invention relates to the technical field of arc-shaped beam recognition, and in particular to an arc-shaped beam recognition method based on the extension of line geometric characteristics. Background Art

[0002] With the rapid development of the construction industry, the widespread use of non-standard geometric forms, such as curved beams, in complex building structures has led to increasingly stringent requirements for their design, inspection, and construction precision. As a crucial element in buildings, curved beams, with their complex shapes, are crucial for supporting construction personnel in their design. However, traditional methods for identifying and inspecting curved beams often rely on manual measurement and comparison with design drawings, resulting in low efficiency and susceptible to human error.

[0003] Existing methods for processing curved beams with complex curvature variations have the following limitations: Inaccurate recognition of complex geometries: Curved beams typically have continuous, smooth curvature variations and are often connected to surrounding structures. Traditional geometric feature extraction methods struggle to accurately distinguish curved beams from other adjacent structures. In three-dimensional space, the local information of curved beams is complex, and existing line extraction algorithms often fail to effectively handle partially obscured or missing geometric information, resulting in an inability to visualize the complete curved beam structure. Summary of the Invention

[0004] To solve the above problems, the present invention provides a curved beam identification method based on the extension of line geometric characteristics. Through technical means such as laser scanning, geometric feature extraction, intelligent classification and geometric extension, the recognition accuracy and geometric integrity of curved beams are significantly improved.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for identifying curved beams based on the extension of line geometric characteristics comprises the following steps:

[0007] Scanning the interior of the building and obtaining an indoor three-dimensional model, extracting edge lines from the indoor three-dimensional model and segmenting individual lines, and normalizing the individual lines to obtain standardized line parameters;

[0008] By traversing the preset arc parameter library, the corresponding single lines whose standardized line parameters meet the preset arc parameters are screened and marked as arcs to be processed. The preset arc parameters include curvature, arc range and arc length;

[0009] Taking the arc to be processed as the center, the individual lines connecting the arc to be processed are obtained and combined with the arc to be processed to construct a beam recognition geometric model. The beam recognition geometric model is identified and classified based on the convolutional neural network, and the probability distribution of the points where the arc to be processed matches the curved beam is output;

[0010] Based on the probability distribution of the points matching the arc to be processed and the curved beam, the arc to be processed is supplemented and extended in the beam recognition geometric model to obtain the extended arc and remap it in the three-dimensional model for visualization and the curved beam position is calibrated by the extended arc.

[0011] Furthermore, scanning the interior of the building and obtaining the indoor three-dimensional model includes:

[0012] The building interior is scanned in all directions using laser scanning equipment to obtain point cloud data including wall, ceiling and ground structures. The point cloud data is then subjected to noise reduction and filtering to generate a 3D indoor model.

[0013] Furthermore, the extraction of edge lines and segmentation of individual lines from the indoor three-dimensional model includes the following steps:

[0014] Applying edge detection algorithms to the generated indoor 3D model, identifying edge lines of building structures such as walls, ceilings, and floors from the 3D model as initial lines;

[0015] Splits an initial line into individual lines based on the line's curvature and vertices.

[0016] Furthermore, the process of taking the arc to be processed as the center, obtaining the monomer lines connecting the periphery of the arc to be processed, and combining the monomer lines with the arc to be processed to construct the beam recognition geometric model includes the following steps:

[0017] Taking the geometric center of the arc to be processed as the base point, a spatial index algorithm is used to search for neighboring single lines in three-dimensional space whose distance to the arc to be processed is less than a preset distance threshold;

[0018] The neighboring individual lines are geometrically combined with the arc to be processed, and the connections of the individual lines are smoothed using the spline interpolation algorithm;

[0019] The connection errors between lines are dynamically adjusted through the error correction algorithm to generate a beam recognition geometric model.

[0020] Furthermore, the identification and classification of the beam recognition geometric model based on the convolutional neural network and the output of the probability distribution of the points where the arc to be processed matches the curved beam include the following steps:

[0021] The recognition geometric model is input into the convolutional neural network model, and the spatial connection relationship between the individual lines and adjacent lines in the geometric model is extracted through the convolution layer to generate a geometric model feature map;

[0022] Perform multi-layer convolution and pooling operations on the extracted geometric model feature map to fuse local geometric features at different scales to obtain a multi-scale fused geometric feature map;

[0023] The multi-scale fused geometric feature map is input into the fully connected layer, and the geometric features are classified by the Softmax activation function. The probability distribution of the matching between the arc to be processed and the curved beam structure is calculated, and the probability value of the point where each arc to be processed matches the curved beam in the beam recognition geometric model is output.

[0024] Furthermore, the formula of the convolutional neural network is as follows:

[0025]

[0026] Among them, z i，j，k is the probability distribution of the kth curved beam or non-curved structure at the (i, j) position of the final output; X i+m，j+n is the parameter set of the geometric feature map at position (i+m, j+n), which includes the standardized geometric parameters of the arc to be processed and its surrounding monomer lines; W m，n，k is the weight of the convolution kernel at position (m,n) corresponding to the kth curved beam or non-curved structure; b k is the bias term of the kth category; Softmax is the activation function; M and N are the height and width of the convolution kernel respectively.

[0027] Furthermore, the loss function formula of the convolutional neural network is as follows:

[0028]

[0029] Among them, L is the total loss function; N is the total number of samples; y i is the true label of the i-th sample; p(y i ) is the predicted probability of the convolutional neural network for the i-th sample; is the regularization term, W k is the weight matrix of the k-th convolution kernel; λ is the regularization coefficient; K is the total number of layers of the convolutional neural network.

[0030] Furthermore, the method of supplementing and extending the arc to be processed in the beam recognition geometric model based on the probability distribution of points matching the arc to be processed with the curved beam includes the following steps:

[0031] The probability mean of the probability distribution of the points matching the curved beam within the window is calculated by sliding the preset window size;

[0032] Determine the extension path and end point based on the probability mean and the preset probability threshold;

[0033] The arc to be processed is supplemented and extended according to the extended path and end point.

[0034] Furthermore, the process of obtaining the extended arc, remapping the extended arc in the three-dimensional model, performing visualization, and calibrating the position of the curved beam by the extended arc includes the following steps:

[0035] The arc data generated by the supplementary extension is mapped back to the global coordinates of the indoor three-dimensional model according to the spatial coordinate system;

[0036] Based on the mapped extended arcs, a visualization algorithm is applied to the 3D model to convert the arcs into a geometric display model through a graphics rendering engine;

[0037] Perform semantic calibration on the specific position of the curved beam in the geometric display model.

[0038] The present invention provides the following beneficial effects: It uses laser scanning to comprehensively scan a building interior, generating point cloud data encompassing walls, ceilings, and floor structures. Through noise reduction and filtering, it produces an accurate three-dimensional model. Compared to traditional methods that rely on manual measurement and comparison with design drawings, 3D scanning technology efficiently and accurately captures geometric information about building structures, avoiding recognition errors caused by human factors and ensuring data accuracy. Based on the 3D model, an edge detection algorithm is used to extract the initial lines of the curved beams and normalize them based on geometric parameters such as curvature, radian, and arc length. By standardizing geometric parameters, this solution ensures uniform processing of the geometric features of the curved beams and other adjacent structures, effectively improving geometric consistency during the recognition process and overcoming parameter mismatches in complex geometries. By establishing a preset arc parameter library, this solution traverses and extracts line features that meet the preset parameters, marking the arcs for processing. This step effectively avoids the shortcomings of traditional methods in identifying curved beams adjacent to other building structures. By comparing and accurately screening geometric parameters, accurate identification and separation of curved beams is achieved. The convolutional neural network (CNN) model is further introduced, and combined with the geometric model features, the matching degree between the arc to be processed and the curved beam is intelligently classified and predicted. Through multi-layer convolution operations and multi-scale feature fusion, the neural network model can better capture the feature changes in complex geometric forms, improve the accuracy and robustness of recognition, and significantly outperform the traditional fixed geometric rule algorithm. After the arc to be processed is matched with the curved beam, this scheme performs geometric extension based on the probability distribution output by the convolutional neural network to deal with the partial occlusion or missing problem of the curved beam in three-dimensional space, generate extended arcs, and remap them to the three-dimensional model to achieve visualization of the complete curved beam geometric structure, thereby overcoming the problem of incomplete curved beam recognition information in the existing technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of the steps of a curved beam identification method based on the extension of line geometric characteristics in the present invention.

[0040] Figure 2 This is a flow chart of the steps of obtaining a single line connecting the periphery of an arc to be processed and combining it with the arc to be processed to construct a beam recognition geometric model in the present invention. DETAILED DESCRIPTION

[0041] See also Figure 1-2 As shown, the present invention relates to a method for identifying curved beams based on the extension of line geometric characteristics, comprising the following steps:

[0042] Scanning the interior of the building and obtaining an indoor three-dimensional model, extracting edge lines from the indoor three-dimensional model and segmenting individual lines, and normalizing the individual lines to obtain standardized line parameters;

[0043] By traversing the preset arc parameter library, the corresponding single lines whose standardized line parameters meet the preset arc parameters are screened and marked as arcs to be processed. The preset arc parameters include curvature, arc range and arc length;

[0044] Taking the arc to be processed as the center, the individual lines connecting the arc to be processed are obtained and combined with the arc to be processed to construct a beam recognition geometric model. The beam recognition geometric model is identified and classified based on the convolutional neural network, and the probability distribution of the points where the arc to be processed matches the curved beam is output;

[0045] Based on the probability distribution of the points matching the arc to be processed and the curved beam, the arc to be processed is supplemented and extended in the beam recognition geometric model to obtain the extended arc and remap it in the three-dimensional model for visualization and the curved beam position is calibrated by the extended arc.

[0046] In some embodiments, a laser scanner first acquires three-dimensional point cloud data of a building interior. This point cloud data, presented as discrete coordinates in space, contains all geometric information about the building's surface. To ensure high accuracy in the three-dimensional model, the present invention employs a density- and distance-based point cloud denoising algorithm (e.g., a K-nearest-neighbor local weighted average denoising method) to remove noise points. A Gaussian filter is then applied to smooth the point cloud data, preserving key geometric features. This preprocessing step lays the data foundation for subsequent line extraction and analysis. The Canny edge detection algorithm is then applied to the processed three-dimensional model to extract the building's edge lines. The Canny algorithm calculates image gradients to identify areas with significant changes in curvature and, combined with a dual-thresholding technique, ensures the accuracy and robustness of the detection results. The extracted initial line information is then processed using a line segmentation algorithm to segment the complex building's curves into individual lines. This segmentation process is based on geometric feature changes, using the curvature change rate as a criterion. When the curvature change rate exceeds a preset threshold, the line is segmented into distinct individual lines. In order to ensure the uniformity of geometric information at different spatial scales, the present invention uses a normalization algorithm to standardize the geometric characteristics (such as curvature, radian and arc length) of each individual line. The system can map geometric features at different scales to the same distribution, so that subsequent processing can be carried out in a unified geometric space. The line parameters after standardization are input into the arc parameter library in the system. The arc parameter library stores the geometric characteristics of common arc beams. The present invention traverses the parameter library through a brute force search algorithm to find arc features that match the arc to be processed and marks them as arcs to be processed. After the arc marking is completed, the system further uses a spatial indexing algorithm, such as a KD tree or an octree, to retrieve the individual lines adjacent to the arc to be processed. The spatial indexing algorithm can efficiently handle the nearest neighbor search problem in high-dimensional space and ensure the spatial correlation between the arc to be processed and its adjacent lines. Next, the system combines these adjacent lines with the arc to be processed to construct a beam recognition geometric model. During the combination process, the spline interpolation algorithm is used to smooth the connection points of adjacent lines to ensure the continuity of the geometric model in curvature and spatial position, and to avoid geometric mutations or discontinuities. Based on the constructed geometric model, the system introduces a convolutional neural network (CNN) to intelligently classify the geometric model. CNN first extracts the local features of the geometric model, and uses the convolution kernel to slide on the feature map to calculate the geometric features of the local area. Through the superposition of multiple convolutional layers, CNN can extract the spatial connection relationship and local geometric features of the geometric model layer by layer to generate a high-dimensional feature map. Subsequently, the system reduces the dimensionality of the features through a pooling operation, generates a multi-scale fusion feature map, and calculates the probability distribution of the matching between the arc to be processed and the curved beam through a Softmax classifier. Based on the probability distribution output by the convolutional neural network, the present invention adopts a geometric extension algorithm based on spline curves to supplement and extend the arc to be processed.Specifically, the system uses the high-probability points identified by the convolutional neural network as the starting point for extension and generates new extended line segments through spline interpolation or Bezier curves. This process ensures that the extended lines remain smooth and continuous, conforming to the actual geometric characteristics of the curved beams in the building. After the extension is completed, the system remaps the extended arcs to the three-dimensional model. The mapping process uses a spatial coordinate mapping algorithm to ensure that the extended geometric information is accurately aligned with the global model of the building structure. After the three-dimensional model is updated, the system uses visual rendering technology to accurately display the extended curved beam geometric model, facilitating subsequent architectural design and personnel identification reference.

[0047] Furthermore, scanning the interior of the building and obtaining the indoor three-dimensional model includes:

[0048] The building interior is scanned in all directions using laser scanning equipment to obtain point cloud data including wall, ceiling and ground structures. The point cloud data is then subjected to noise reduction and filtering to generate a 3D indoor model.

[0049] It should be noted that a laser scanner performs a comprehensive scan of the building interior. This device emits laser pulses and measures the coordinates of each point within the building based on their reflection time, generating complete 3D point cloud data. This point cloud data comprehensively captures the geometry of every interior surface, including detailed information about walls, ceilings, floors, and other building structures. Laser scanning achieves millimeter-level resolution, enabling it to capture even subtle geometric variations in the building surface, which is particularly important for subsequent curved beam identification and geometric processing. After point cloud data acquisition, the system performs a series of preprocessing operations on the raw point cloud data. Due to the complex scanning environment within the building, the data acquisition process inevitably introduces noise and redundant information, such as invalid data points caused by lighting interference, scanning device errors, or reflective objects. To address this, the system first applies a point cloud denoising algorithm to the point cloud data. This algorithm identifies and removes outliers by calculating the distance difference between each data point and its neighboring points. Specifically, the system uses a statistical analysis method to analyze the neighborhood of each data point, marking points with inconsistent distance distribution with their neighbors as noise and removing them, thereby improving the overall quality of the point cloud data. After noise reduction, the system applies filtering to the denoised point cloud data. This filtering process further removes high-frequency errors from the point cloud data through smoothing, while preserving key geometric features. Commonly used filtering methods are Gaussian filtering or mean filtering, which perform a weighted average of adjacent data points in the point cloud to reduce the impact of random errors and ensure data smoothness and continuity. The filtered point cloud data more accurately reflects the building's true geometry, facilitating subsequent 3D model generation and geometric feature extraction. The system then performs geometric fitting on the denoised and filtered point cloud data to generate a 3D model of the building's interior. Since the point cloud data contains all surface information within the building, the system performs geometric analysis to fit these discrete point clouds into a continuous geometric surface model. This process utilizes surface reconstruction algorithms, such as triangulated meshing algorithms (e.g., Delaunay triangulation), to construct a complete 3D model by connecting the data points in the point cloud into a number of triangular facets. This model accurately depicts the geometric form of the building's interior structures, such as walls, ceilings, and floors.

[0050] Furthermore, the extraction of edge lines and segmentation of individual lines from the indoor three-dimensional model includes the following steps:

[0051] Applying edge detection algorithms to the generated indoor 3D model, identifying edge lines of building structures such as walls, ceilings, and floors from the 3D model as initial lines;

[0052] Splits an initial line into individual lines based on the line's curvature and vertices.

[0053] In some embodiments, the system first applies an edge detection algorithm based on the generated 3D indoor model. The core purpose of this algorithm is to extract significant geometric edge lines within the building from complex 3D data, particularly the edges of large structures such as walls, ceilings, and floors. To ensure edge detection accuracy, the system typically employs gradient-based edge detection techniques (such as the Canny edge detection algorithm), which calculates the rate of change of the model surface normal to identify areas with significant curvature variation. These areas often correspond to geometric boundaries within the building structure, such as corners, column-wall junctions, and ceiling angles. The multi-level thresholding technique used in Canny edge detection ensures noise suppression while capturing key boundaries within the building's geometry. After edge detection, the system identifies and extracts these edge lines and defines them as initial lines. These initial lines may contain complex geometric information and, due to the diversity of building structures, often exhibit a wide range of curvature variations. For example, the junction of a wall and ceiling may contain multiple angles. These geometric features can lead to uneven curvature variations, further increasing the complexity of data processing. To more accurately analyze and process these complex initial lines, the present invention uses curvature analysis and inflection point identification algorithms to segment the extracted initial lines. First, the system calculates the curvature values of each initial line at different locations. Curvature values reflect the degree of curvature of a line in three-dimensional space. In architectural geometry, locations with large changes in curvature often correspond to significant geometric features of the structure, such as corners or edge inflections. By analyzing the curvature variation patterns, the system locates key geometric points of the line—locations where the curvature variation exceeds a preset threshold. Combining the curvature variation analysis results, the system identifies inflection points within the initial line. These inflection points typically correspond to geometric corners within the building structure, such as the junction of a wall and ceiling. To ensure segmentation accuracy, the system uses each inflection point as a basis for line segmentation. Specifically, when a line's curvature variation reaches a certain level or a distinct inflection point appears, the system segments the initial line at that location. In this way, a relatively complex initial line is divided into multiple relatively simple individual lines. Each individual line has relatively simple geometric characteristics, typically exhibiting uniform curvature and a stable geometric form. The goal is to break down complex architectural geometry into more manageable basic units, facilitating subsequent geometric analysis, classification, and processing. For some curved beam structures, the segmented individual lines can more clearly express their local geometric characteristics, such as the curvature and radian of the curved beam.

[0054] Furthermore, the process of taking the arc to be processed as the center, obtaining the monomer lines connecting the periphery of the arc to be processed, and combining the monomer lines with the arc to be processed to construct the beam recognition geometric model includes the following steps:

[0055] Taking the geometric center of the arc to be processed as the base point, a spatial index algorithm is used to search for neighboring single lines in three-dimensional space whose distance to the arc to be processed is less than a preset distance threshold;

[0056] The neighboring individual lines are geometrically combined with the arc to be processed, and the connections of the individual lines are smoothed using the spline interpolation algorithm;

[0057] The connection errors between lines are dynamically adjusted through the error correction algorithm to generate a beam recognition geometric model.

[0058] In some embodiments, after identifying the arc to be processed, the system uses a spatial indexing algorithm to search for other lines in the three-dimensional model, using the geometric center of the arc to be processed as the base point. Specifically, spatial indexing algorithms often employ efficient data structures such as KD trees or octrees to handle proximity queries in high-dimensional space. Using these algorithms, the system can quickly identify individual lines whose distance from the arc to be processed is less than a preset threshold. These lines are considered candidate lines geometrically related to the arc to be processed. In practice, the geometric center of the arc to be processed is typically calculated based on its spatial position and geometric properties. By executing the spatial indexing algorithm, the system can identify the lines geometrically closest to this center point in three-dimensional space. These lines may be located on other parts of the curved beam or on architectural elements connecting the arc. To ensure the accuracy of the indexing results, the selection of a preset distance threshold is crucial. An excessively high threshold may introduce irrelevant geometric lines, while an excessively low threshold may result in omissions. Through experiments, the present invention has established an appropriate distance threshold in practical applications based on the geometric complexity of the building. Next, the system combines the neighboring individual lines obtained through the spatial index algorithm with the arc to be processed to form a preliminary geometric model. To ensure continuity and smoothness between the lines, the present invention uses a spline interpolation algorithm to smooth the line connections. Spline interpolation is a mathematical method commonly used in curve fitting. By calculating a smooth curve between interpolation points, it avoids abrupt changes or discontinuities at line connections. During this process, the spline interpolation algorithm considers the geometric parameters of the lines, including curvature and arc length, to generate a smooth transition curve, ensuring that the combined geometric model conforms to the actual curved beam structure. In actual architectural applications, curved beams have complex geometric characteristics, and curvature may vary with spatial position. Therefore, the spline interpolation process must ensure that the interpolation result is not only visually smooth but also mathematically differentiable. This means that the derivative of the interpolated curve should also change smoothly to avoid geometrically unreasonable sharp transitions. Furthermore, when processing longer arc combinations, the present invention adaptively adjusts the number of interpolation points based on the complexity of the lines to ensure a balance between interpolation curve accuracy and computational efficiency. After completing the initial geometric model assembly and interpolation, the system dynamically adjusts the geometric errors between lines using an error correction algorithm. Because lines in the building model may be affected by factors such as scanning accuracy and data acquisition errors, minor geometric errors are inevitable during the line assembly process. To ensure the accuracy of the final beam recognition geometric model, the present invention incorporates an error correction mechanism. This error correction algorithm analyzes the spatial deviations between lines and automatically adjusts the connection positions and angles to align with the actual building structure.During the error correction process, the system first calculates the offset and angle difference between the lines, and then uses a series of geometric transformation operations (such as translation and rotation) to accurately align the endpoints of the lines with the geometric positions of the arcs to be processed. At the same time, the error correction algorithm will also determine whether the overall curvature of the lines needs to be adjusted based on the actual building geometry. For cases with small errors, the system will adopt a minimum correction strategy to maintain the integrity of the original data as much as possible; for cases with large errors, the system will gradually eliminate significant errors between lines through iterative correction methods.

[0059] Furthermore, the identification and classification of the beam recognition geometric model based on the convolutional neural network and the output of the probability distribution of the points where the arc to be processed matches the curved beam include the following steps:

[0060] The recognition geometric model is input into the convolutional neural network model, and the spatial connection relationship between the individual lines and adjacent lines in the geometric model is extracted through the convolution layer to generate a geometric model feature map;

[0061] Perform multi-layer convolution and pooling operations on the extracted geometric model feature map to fuse local geometric features at different scales to obtain a multi-scale fused geometric feature map;

[0062] The multi-scale fused geometric feature map is input into the fully connected layer, and the geometric features are classified by the Softmax activation function. The probability distribution of the matching between the arc to be processed and the curved beam structure is calculated, and the probability value of the point where each arc to be processed matches the curved beam in the beam recognition geometric model is output.

[0063] In some embodiments, the constructed beam recognition geometric model is first used as input and imported into a convolutional neural network (CNN) for processing. This geometric model contains geometric information about the arc to be processed and its adjacent lines. The task of the CNN is to identify the degree of match between the arc to be processed and the curved beam structure by analyzing this geometric data. During this process, the CNN performs feature extraction on the input geometric model through a convolutional layer. The convolutional layer uses a sliding window to scan a local area of the entire geometric model and extract the spatial connectivity and geometric characteristics of the area, such as the angle between adjacent lines, curvature changes, and spatial distance. The role of the convolution kernel is to capture local features in the geometric model through weight learning. These features can reflect the interrelationships between lines and the continuity of the geometric form. After the convolution operation, the network generates a series of feature maps, which represent the feature expression of the geometric model in different local areas. To enhance the hierarchical expression of features, the system inputs the feature maps into multiple convolutional layers for further processing. Each convolution layer can capture geometric information at different scales. For example, shallower convolutional layers primarily capture local line details, such as sudden changes in curvature and angular features, while deeper convolutional layers are able to capture the overall spatial structure and macroscopic morphology. This multi-layer convolutional processing approach ensures that convolutional neural networks can not only identify local details of geometric models but also understand their global characteristics. After the convolution operation, the system performs a pooling operation on the extracted feature maps. Pooling reduces the size of the feature maps through downsampling, thereby reducing data dimensionality and computational complexity. Common pooling methods include max pooling and average pooling. The former retains the maximum value of the features in the local area, while the latter retains the average value of the features in the local area. Through pooling, convolutional neural networks can effectively extract the key features of the geometric model while minimizing redundant information. The pooled feature map represents the fusion of local geometric features at different scales, enabling the network to perform a global analysis of the spatial structure of the entire geometric model. Next, the multi-scale fused feature map, resulting from the multi-layer convolution and pooling operations, is input into the fully connected layer. The fully connected layer is the last step in the convolutional neural network, which is used to integrate the high-dimensional features extracted previously and map them to the output space. Specifically, the fully connected layer converts the feature map into a linear combination to obtain an output related to the target task. For the present invention, the output is the probability distribution of the matching between the arc to be processed and the curved beam. In the fully connected layer, the system converts the output result into a normalized probability value through the Softmax activation function. The Softmax function can convert the output of the network into a probability distribution for each category, ensuring that the sum of all probability values is equal to 1. In this way, the system can calculate the probability of each arc to be processed that it matches the curved beam. The output probability distribution represents the degree to which the arc to be processed matches the curved beam structure in the geometric model.Specifically, for each arc to be processed, the network outputs a probability value for its belonging to a curved beam. For example, if the probability value of a particular arc is close to 1, it indicates a very high match with a curved beam, while a lower probability value indicates that it may belong to another structure. In practice, the system will perform further processing based on these probabilities. For example, it may select arcs with probability values above a certain threshold as candidates for curved beams, or adjust the details of the geometric model based on the distribution of probability values.

[0064] Furthermore, the formula of the convolutional neural network is as follows:

[0065]

[0066] Among them, z i，j，k is the probability distribution of the kth curved beam or non-curved structure at the (i, j) position of the final output; X i+m，j+n is the parameter set of the geometric feature map at position (i+m, j+n), which includes the standardized geometric parameters of the arc to be processed and its surrounding monomer lines; W m，n，k is the weight of the convolution kernel at position (m,n) corresponding to the kth curved beam or non-curved structure; b k is the bias term of the kth category; Softmax is the activation function; M and N are the height and width of the convolution kernel respectively.

[0067] Specifically, Z i，j，k X represents the final output of the convolutional neural network, that is, the probability distribution value of the k-th type of structure (curved beam or non-curved structure) at position (i, j). This value represents the network's classification result for the current geometric model at a specific location. Specifically, during the recognition process, the network outputs the probability that each pixel or feature point belongs to a certain category. i+m，j+n The parameter set includes not only the geometric properties of the arc being processed, but also the normalized geometric parameters of its neighboring individual lines. These parameters may include geometric information such as curvature, arc angle, and arc length. Normalization allows for uniform comparison and analysis across different layers of the network. The convolution kernel is the core component of a convolutional neural network for feature extraction. Its weights are continuously adjusted during network training to capture local patterns within the geometric model. For example, the kernel weights help the network identify specific geometric features within a curved beam, such as continuous curves or connections between adjacent lines. The bias term adjusts the convolutional computation results, allowing the network to more flexibly capture characteristics from different categories during feature extraction and classification. For each category, the network uses a different bias value to balance the network output, enabling it to more accurately distinguish curved beams from other structures. The softmax function is a commonly used activation function in multi-classification tasks. It normalizes the network's raw output into a probability distribution, where the sum of the probabilities for all output categories equals 1.

[0068] Furthermore, the loss function formula of the convolutional neural network is as follows:

[0069]

[0070] Among them, L is the total loss function; N is the total number of samples; y i is the true label of the i-th sample; p(y i ) is the predicted probability of the convolutional neural network for the i-th sample; is the regularization term, W k is the weight matrix of the k-th convolution kernel; λ is the regularization coefficient; K is the total number of layers of the convolutional neural network.

[0071] Specifically, the role of the loss function is to measure the difference between the network's predicted results and the actual results, and to use this difference to guide the network's parameter adjustment and optimize the model's performance. The loss function in this invention consists of two main parts: classification loss - y i log(p(y i ))+(1-y i )log(1-p(y i )) and regularization term First, the classification loss measures the accuracy of the network's prediction for each example. For the curved beam recognition task, each example represents a curved line to be processed, and the network's task is to determine whether this arc is a curved beam. Each example has a true label (such as "curved beam" or "non-curved beam"). Based on the characteristics of the geometric model, the network outputs a predicted probability value, indicating the likelihood that the arc is a curved beam. The classification loss calculates the network's error by comparing the true label with the predicted probability. If the network's prediction is close to the true label, the loss is small; if the prediction differs significantly from the true label, the loss value increases. A larger loss indicates a less accurate prediction. Through this mechanism, the network continuously adjusts its internal parameters to minimize the loss, thereby improving the model's accuracy. For example, in the curved beam recognition task, if the true label of a particular arc is "curved beam," if the network predicts that the arc is a "curved beam" with a 90% probability, the loss value will be small because the prediction is close to the true label. However, if the network predicts only a 20% probability for the arc, the loss value will be large, prompting the network to adjust its weights during training to improve subsequent predictions. Secondly, the regularization term in the loss function is used to prevent the model from overfitting. Overfitting occurs when a model performs very well on the training data but performs poorly on new data. This is often caused by the model being too complex or overly dependent on the specific training data. To avoid this, the regularization term constrains the network's weight parameters, preventing them from becoming too large or too complex. By adding a penalty to the weights, the regularization term smooths the network's learning process and prevents overfitting to the training data. This ensures that the network not only performs well on the training data but also maintains good predictive ability on unknown new data. The strength of the regularization is controlled by a parameter called the regularization coefficient, which determines the degree of penalty applied to the weights. A large regularization coefficient forces the network to reduce the size of its weights, thereby improving generalization; a small coefficient allows the network's weights to adjust more freely. Through the design of this loss function, the convolutional neural network can effectively learn complex geometric features in the curved beam recognition task and avoid overfitting problems while maintaining high recognition accuracy.

[0072] Furthermore, the method of supplementing and extending the arc to be processed in the beam recognition geometric model based on the probability distribution of points matching the arc to be processed with the curved beam includes the following steps:

[0073] The probability mean of the probability distribution of the points matching the curved beam within the window is calculated by sliding the preset window size;

[0074] Determine the extension path and end point based on the probability mean and the preset probability threshold;

[0075] The arc to be processed is supplemented and extended according to the extended path and end point.

[0076] Specifically, the system first calculates the probability mean of the probability distribution of the points within the sliding window that match the curved beam. Specifically, after classification processing using a convolutional neural network, the model outputs a probability value for each geometric point matching the curved beam. To further analyze the local characteristics of these points, the system uses a sliding window technique to statistically analyze the probability distribution of these points. The sliding window size is preset and typically adjusted based on the curvature and geometric characteristics of the curved beam. The window captures fluctuations in local characteristics and analyzes the overall matching of the points within each region with the curved beam. Within the sliding window, the system calculates the average probability value of all points in the region, which is the probability mean. This method allows the system to better understand the overall characteristics of the local region. This is especially true when the matching probability of certain points may be low or fluctuate abnormally. The probability mean provides a smooth, global perspective. This operation is particularly important for curved beams with complex curvature variations, as the probability value of a single point may not fully reflect the geometric shape of the region. By smoothing the probability values, the system can avoid interference from local outliers, thereby achieving more reliable matching results. Next, based on the mean probability and a preset probability threshold, the system determines the extension path and endpoint. In real-world building models, curved beams may have missing data due to occlusion, scanning errors, or incomplete modeling. To automatically complete these missing data, the system first compares the mean probability calculated using a sliding window with a preset probability threshold. The probability threshold is a key criterion used by the system to determine whether a point can be considered part of a curved beam. If the mean probability in a region is higher than the threshold, it indicates a high degree of match between the points in that region and the curved beam. The system considers this region to be part of the curved beam and suitable for extension. The extension path is determined based on the curvature characteristics of the curved beam. The system analyzes the geometric curvature changes of the curve to be processed and infers the extension direction and path. During this process, the system combines existing geometric information to calculate how the extended portion should maintain curvature continuity with the known portion. For example, if the existing curve exhibits a large curvature change, the system ensures that the extended portion transitions smoothly in space, avoiding abrupt geometric turns. The endpoint of the extension path is determined based on further analysis of the probability values. As the arc extends, the system will gradually reduce the probability mean within the sliding window until the mean approaches the preset probability threshold lower limit. At this point, the system will assume that the extended part of the arc beam has reached the end and determine the end point position. Accurate determination of the end point is crucial to ensuring the geometric integrity of the arc beam. The system uses this mechanism to prevent the extended part from being too long or too short, ensuring that the completed arc beam can seamlessly connect with the existing structure. Finally, the system supplements and extends the arc to be processed based on the extension path and end point. In this step, the system uses a geometric interpolation algorithm (such as spline interpolation or Bezier curve interpolation) to generate smooth extended lines.An interpolation algorithm uses multiple key points along the extended path to generate a smooth curve that conforms to the curvature of the curved beam. This algorithm ensures that the newly generated curve not only matches the existing curved beam geometry but also exhibits a natural transition in space.

[0077] Furthermore, the process of obtaining the extended arc, remapping the extended arc in the three-dimensional model, performing visualization, and calibrating the position of the curved beam by the extended arc includes the following steps:

[0078] The arc data generated by the supplementary extension is mapped back to the global coordinates of the indoor three-dimensional model according to the spatial coordinate system;

[0079] Based on the mapped extended arcs, a visualization algorithm is applied to the 3D model to convert the arcs into a geometric display model through a graphics rendering engine;

[0080] Perform semantic calibration on the specific position of the curved beam in the geometric display model.

[0081] In some embodiments, the system first supplements the extended arc data and, using spatial coordinate mapping, reintegrates the extended portion into the global coordinates of the interior 3D model. Specifically, during the generation of the extended arc, the system uses an interpolation algorithm (such as spline interpolation or Bezier interpolation) to supplement the missing portions of the curved beam. This supplemented arc data exists in a local coordinate system. To accurately integrate it back into the 3D building model, the system requires a global coordinate transformation. During the mapping process, the system first determines the relationship between the global coordinate system in the 3D model and the local coordinate system of the extended arc. This relationship is typically described using a rotation matrix and a translation vector to ensure that the extended arc appears at the correct location in the 3D model. In a building, any offset in the 3D coordinates affects the integrity of the geometric structure. Therefore, geometric accuracy must be maintained during the mapping process to ensure that the extended arc is identical in position, orientation, and scale to the rest of the original curved beam. After the mapping is complete, the system processes the geometric information of the extended arc in the 3D model. Specifically, the system uses a graphics rendering engine to convert this geometric data into a displayable 3D geometric model. Graphics rendering is the core of the visualization process, transforming the mathematical representation of the extended arc into a visual geometric object. The rendering engine processes the arc's 3D geometry, lighting, material properties, and other characteristics to ensure a realistic display of the curved beam structure in the 3D view. During the visualization rendering process, the system generates a visual model of the arc based on the curvature, arc length, and spatial position of the curved beam and integrates it with the original building model. Through efficient graphics calculations, the rendering engine ensures that the display of the extended arc is consistent with the surrounding building structure, avoiding geometric distortion or display errors. For example, if the extended curved beam has complex curvature variations, the rendering engine can accurately represent its smooth transition curve while maintaining visual consistency in 3D space. Furthermore, to enhance visualization accuracy and realism, the system can incorporate detail enhancement techniques during the rendering process. For example, by analyzing the arc's curvature, the system can appropriately adjust the display accuracy of the arc to ensure that key geometric features are visually captured. After the rendering is complete, the user can view the curved beam from different angles in the 3D view to confirm that its geometric characteristics meet the design requirements. Finally, the system semantically calibrates the specific position of the extended curved beam within the 3D geometric model. Semantic calibration involves aligning the curved beam in the geometric model with its actual function and significance in the building. This semantic calibration allows the system to establish a clear association between geometric objects (such as curved beams) and their structural roles, facilitating subsequent construction design and structural analysis.

[0082] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary engineering technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for identifying curved beams based on the extension of line geometric characteristics, characterized in that: The following steps are involved: Scanning the interior of the building and obtaining an indoor three-dimensional model, extracting edge lines from the indoor three-dimensional model and segmenting individual lines, and normalizing the individual lines to obtain standardized line parameters; By traversing the preset arc parameter library, the corresponding single lines whose standardized line parameters meet the preset arc parameters are screened and marked as arcs to be processed. The preset arc parameters include curvature, arc range and arc length; Taking the arc to be processed as the center, the individual lines connecting the arc to be processed are obtained and combined with the arc to be processed to construct a beam recognition geometric model. The beam recognition geometric model is identified and classified based on the convolutional neural network, and the probability distribution of the points where the arc to be processed matches the curved beam is output; Based on the probability distribution of the points matching the arc to be processed and the curved beam, the arc to be processed is supplemented and extended in the beam recognition geometric model to obtain the extended arc and re-map it in the three-dimensional model for visualization and calibration of the curved beam position through the extended arc; The method of taking the arc to be processed as the center, obtaining the monomer lines connecting the periphery of the arc to be processed and combining them with the arc to be processed to construct the beam recognition geometric model includes the following steps: Taking the geometric center of the arc to be processed as the base point, a spatial index algorithm is used to search for neighboring single lines in three-dimensional space whose distance to the arc to be processed is less than a preset distance threshold; The neighboring individual lines are geometrically combined with the arc to be processed, and the connections of the individual lines are smoothed using the spline interpolation algorithm; The connection errors between lines are dynamically adjusted through the error correction algorithm to generate a beam recognition geometric model.

2. The arc beam identification method based on line geometric characteristics extension according to claim 1, characterized in that: Scanning the interior of a building and obtaining an indoor three-dimensional model includes: The building interior is scanned in all directions using laser scanning equipment to obtain point cloud data including wall, ceiling and ground structures. The point cloud data is then subjected to noise reduction and filtering to generate a 3D indoor model.

3. The arc beam identification method based on line geometric characteristics extension according to claim 1, characterized in that: The method of extracting edge lines from the indoor three-dimensional model and segmenting individual lines comprises the following steps: Applying edge detection algorithms to the generated indoor 3D model, identifying edge lines of building structures such as walls, ceilings, and floors from the 3D model as initial lines; Splits an initial line into individual lines based on the line's curvature and vertices.

4. The arc beam identification method based on line geometric characteristics extension according to claim 1, characterized in that: The method of identifying and classifying the beam recognition geometric model based on a convolutional neural network and outputting the probability distribution of the points where the arc to be processed matches the curved beam comprises the following steps: The recognition geometric model is input into the convolutional neural network model, and the spatial connection relationship between the individual lines and adjacent lines in the geometric model is extracted through the convolution layer to generate a geometric model feature map; Perform multi-layer convolution and pooling operations on the extracted geometric model feature map to fuse local geometric features at different scales to obtain a multi-scale fused geometric feature map; The multi-scale fused geometric feature map is input into the fully connected layer, and the geometric features are classified by the Softmax activation function. The probability distribution of the matching between the arc to be processed and the curved beam structure is calculated, and the probability value of the point where each arc to be processed matches the curved beam in the beam recognition geometric model is output.

5. The arc beam identification method based on line geometric property extension according to claim 4, characterized in that: The formula of the convolutional neural network is as follows: ； in, is the probability distribution of the kth curved beam or non-curved structure at the (i, j) position of the final output; The geometric feature map is The parameter set of the position contains the standardized geometric parameters of the arc to be processed and its surrounding single lines; is the weight of the convolution kernel at position (m,n) corresponding to the kth curved beam or non-arc structure; is the bias term for the kth category; is the activation function; M and N are the height and width of the convolution kernel respectively.

6. The arc beam identification method based on line geometric property extension according to claim 1, characterized in that: The loss function formula of the convolutional neural network is as follows: ； in, is the total loss function; is the total number of samples; is the true label of the i-th sample; is the predicted probability of the convolutional neural network for the i-th sample; is the regularization term, is the weight matrix of the k-th convolution kernel; is the regularization coefficient; K is the total number of layers of the convolutional neural network.

7. The arc beam identification method based on line geometric property extension according to claim 1, characterized in that: The method of supplementing and extending the arc to be processed in the beam recognition geometric model based on the point probability distribution of the arc to be processed and the curved beam includes the following steps: The probability mean of the probability distribution of the points matching the curved beam within the window is calculated by sliding the preset window size; Determine the extension path and end point based on the probability mean and the preset probability threshold; The arc to be processed is supplemented and extended according to the extended path and end point.

8. The arc beam identification method based on line geometric property extension according to claim 7, characterized in that: Obtaining the extended arc, remapping it in the three-dimensional model, performing visualization, and calibrating the curved beam position by the extended arc includes the following steps: The arc data generated by the supplementary extension is mapped back to the global coordinates of the indoor three-dimensional model according to the spatial coordinate system; Based on the mapped extended arcs, a visualization algorithm is applied to the 3D model to convert the arcs into a geometric display model through a graphics rendering engine; Perform semantic calibration on the specific position of the curved beam in the geometric display model.

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