A color lamp geometric feature recognition method based on a graph neural network

Abstract

The present application relates to a kind of based on the color light geometric feature identification method of graph neural network, comprising: the key vertex screening of color light is perceived driving, obtains key vertex set;Based on the key vertex set, the connection probability modeling of multi-head attention guide is carried out, and the connection probability between vertex pair is predicted;Based on the connection probability between vertex pair, the adaptive perception classification of triangular facet is carried out, and the final triangular face set of color light geometric feature retention is obtained.The present application provides an effective solution for the high-fidelity simplification of complex cultural heritage three-dimensional model, and realizes good balance between compression rate and feature retention.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cultural heritage digitization, and in particular to a colored lamp geometric feature recognition method based on a graph neural network. BACKGROUND

[0002] Polygon mesh model is the core data basis in the fields of cultural heritage digitization, virtual reality and three-dimensional visualization. The key attributes such as geometric fidelity, topological consistency and rendering efficiency of the polygon mesh model directly determine the practicability of the three-dimensional model. With the continuous progress of three-dimensional reconstruction and high-precision scanning technology, high-quality modeling of complex cultural entities has gradually become a reality. As a representative of Chinese Zigong colored lamps with strong decoration, such cultural heritage objects become one of the most challenging targets in three-dimensional digitization and lightweight modeling due to their dense structure, rich texture and frequent curvature changes.

[0003] In practical applications, models such as Zigong colored lamps usually contain millions of triangular faces and are extremely detailed. If directly used in real-time rendering or immersive display environment, it is easy to cause frame rate drop and interaction delay, which seriously limits its application potential in virtual restoration and interactive visualization. To overcome the performance bottleneck brought by high-complexity models, mesh simplification algorithms have become an important part of digital geometry processing. Among them, the classic quadratic error metric (QEM) algorithm is widely used due to its high efficiency and reasonable error control ability. However, the traditional QEM method uses a unified error metric mechanism, which is often not sensitive to local structural features. Especially in high-curvature, hollow structure and complex decoration areas, simplification often leads to structural degradation and loss of key details.

[0004] In order to improve the feature preservation ability of complex cultural heritage models, in recent years, researchers have proposed various improvement strategies, such as enhanced QEM algorithm combined with curvature and normal constraints, multi-level LOD framework for maintaining structure, and differentiable simplification process integrating deep learning. Although these methods have achieved certain success on standard benchmark datasets, they still face challenges in real cultural heritage scenarios, especially in accurately identifying visually sensitive areas and maintaining structural consistency during simplification. In addition, many existing researches lack clear distinction in the evaluation of sampling and simplification, resulting in ambiguous experimental levels and insufficient clarity in comparative analysis. SUMMARY

[0005] The purpose of the present application is to propose a color lamp geometric feature recognition method based on a graph neural network to solve the problems existing in the prior art. The present application combines geometric perception features and deep learning technology, takes structure-sensitive point sampling as the core, constructs a saliency score function through curvature and normal perturbation, dynamically models the topological connection probability between vertices using a multi-head graph attention mechanism, and proposes a triangle patch-level adaptive classifier based on geometric and perceptual consistency, thereby improving the feature region preservation ability and overall structural integrity of complex cultural heritage models (such as Zigong color lamps), and exhibiting better structural adaptability, generalization ability and engineering practical value.

[0006] To achieve the above purpose, the present application provides the following solutions:

[0007] A color lamp geometric feature recognition method based on a graph neural network, comprising:

[0008] Key vertex screening for perception-driven color lamps to obtain a key vertex set;

[0009] Based on the key vertex set, connection probability modeling guided by multi-head attention is performed, and the connection probability between vertex pairs is predicted;

[0010] Based on the connection probability between the vertex pairs, adaptive perception classification of the triangular patches is performed to obtain a final triangular face set that preserves the geometric features of the color lamp.

[0011] Optionally, the key vertex screening for perception-driven color lamps to obtain a key vertex set comprises:

[0012] The local mean curvature and the rate of change of the vertex normal direction of each color lamp vertex are calculated and normalized to obtain the saliency score of the fixed point;

[0013] Based on the saliency score, the key vertices in the structure-sensitive region are selected by enhanced farthest point sampling to obtain the key vertex set.

[0014] Optionally, the key vertices in the structure-sensitive region are selected by enhanced farthest point sampling, comprising:

[0015] Step 1. Randomly select a vertex from the input vertex set as the initial sampling vertex;

[0016] Step 2. In each iteration, select a vertex from the set of vertices that have not been sampled, which is farthest from the current set of sampled vertices and has a saliency score greater than a predetermined score threshold, and add it to the sampling set ;

[0017] Step 3. Repeat step 2 until the number of vertices in the sampling vertex set reaches a predetermined target number .

[0018] Optionally, based on the set of key vertices, multi-head attention-guided connection probability modeling is performed, and the connection probability between vertex pairs is predicted, including:

[0019] Based on the set of key vertices, an initial sparse adjacency graph is constructed using the k-nearest neighbor strategy;

[0020] For each key vertex, construct a rich feature representation that integrates geometric and perceptual attributes;

[0021] A multi-head graph attention mechanism is introduced based on the initial sparse adjacency graph, and combined with the rich feature representation, the probability of connection between vertex pairs is dynamically predicted.

[0022] Optionally, dynamically predicting the probability of connections between vertex pairs includes:

[0023] Calculate the connection weight of the h-th attention head for any pair of connected vertices;

[0024] Through the The connection weights generated by each attention point are averaged and aggregated to obtain the final connection weights.

[0025] Based on the final connection weights, the connection probabilities between vertices are obtained using the Sigmoid function.

[0026] Optionally, the rich features are represented as:

[0027]

[0028] in, To enrich feature representation, As vertex The three-dimensional coordinate position, It is the normal vector. These are the normalized vertex mean curvature and the rate of change of the normal, respectively.

[0029] Optionally, the connection weight of the h-th attention head is:

[0030]

[0031] in, Let h be the connection weight of the h-th attention head. and They are the first The feature transformation matrix and attention weight parameters of each attention head, denoted as follows: This indicates a feature concatenation operation. It is a non-linear activation function. As vertex In the neighbor set in the initial graph, k is the number of neighbors used to construct the initial adjacency graph (i.e. k in the k-NN graph), is the index of the current central vertex, is a certain neighbor vertex of the vertex.

[0032] Optionally, based on the connection probability between the vertex pairs, adaptive perceptual classification of triangular facets is carried out, and the final triangular facet set is obtained, comprising:

[0033] Based on the connection probability between the vertex pairs, an initial candidate triangular facet set is generated;

[0034] For the initial candidate triangular facet set, a feature representation of each candidate triangular facet is constructed; wherein the feature representation of the candidate triangular facet includes: the geometric shape of the triangle, the vertex saliency and the local topological feature;

[0035] The feature representation of the candidate triangular facet is input into a preset triangular facet classifier to obtain a retention probability of the candidate triangular facet;

[0036] The candidate triangular facet with a retention probability greater than a preset retention probability threshold is retained as the final triangular facet set.

[0037] Optionally, generating the initial candidate triangular facet set based on the connection probability between the vertex pairs comprises:

[0038] For any three vertices in the vertex set, if the vertex pair connection probability between the corresponding three vertices exceeds a preset connection threshold, an initial candidate triangular facet is formed.

[0039] The beneficial effects of the present application are:

[0040] The present application combines geometric perceptual features and deep learning technology, takes structure-sensitive point sampling as the core, constructs a saliency scoring function through curvature and normal perturbation, dynamically models the topological connection probability between vertices using a multi-head graph attention mechanism, and proposes a triangular facet-level adaptive classifier based on geometric and perceptual consistency, which improves the feature region preservation ability and overall structural integrity of complex cultural heritage models (such as Zigong colored lanterns), and exhibits better structural adaptability, generalization ability and engineering practical value. BRIEF DESCRIPTION OF DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0042] Figure 1 A framework schematic diagram of a color lamp geometric feature recognition method based on a graph neural network according to an embodiment of the present application;

[0043] Figure 2 A model quality evaluation graph of a Nian model at different simplification rates according to an embodiment of the present application;

[0044] Figure 3 A model quality evaluation graph of a Snake model at different simplification rates according to an embodiment of the present application;

[0045] Figure 4 A model quality evaluation graph of a Rabbit model at different simplification rates according to an embodiment of the present application;

[0046] Figure 5 A Chamfer distance comparison graph of various sampling methods at different simplification rates according to an embodiment of the present application; wherein (a) is a Nian model, (b) is a Cauldron model, (c) is a Rabbit model, and (d) is a Snake model;

[0047] Figure 6 A schematic diagram of a perception-driven key vertex screening and GNN-guided mesh simplification algorithm according to an embodiment of the present application;

[0048] Figure 7 A schematic diagram of a triangle patch adaptive classification algorithm based on perception features according to an embodiment of the present application. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of the present application.

[0050] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0051] The embodiment proposes a color lamp geometric feature recognition method based on a graph neural network, which comprises:

[0052] The key vertex screening of the color lamp is driven by perception to obtain a key vertex set;

[0053] Based on the key vertex set, multi-head attention-guided connection probability modeling is performed, and the connection probability between vertex pairs is predicted;

[0054] Based on the connection probability between the vertex pairs, adaptive perceptual classification of triangular facets is performed to obtain a final triangular facet set that retains the color lamp geometric features. The triangular facet set is a three-dimensional model that retains geometric features after simplification, and the three-dimensional model is expressed in the form of a triangular facet set.

[0055] Specifically, high-complexity three-dimensional meshes often contain dense decorative details and complex structural features in cultural heritage digitization, which brings significant challenges to efficient simplification while retaining key geometric information. This embodiment proposes a feature-aware salient point sampler (FASP) that integrates graph neural networks (GNN) and quadratic error metrics (QEM) for feature-aware key point sampling and mesh simplification in cultural heritage three-dimensional models such as Zigong color lamps. The FASP framework includes the following three stages: vertex saliency modeling, structure-aware key point sampling, and graph-guided connection modeling and triangular facet classification. The architecture of the framework is shown in Figure 1 Specifically, FASP first calculates vertex saliency scores by combining local curvature and normal perturbation, and selects structure-sensitive key vertices through enhanced farthest point sampling; then, a multi-head graph attention network is used to predict the connection probability between key vertices and generate a structure-aware adjacency graph; finally, an adaptive triangular facet classifier evaluates the facet retention probability based on the joint evaluation of geometric features and saliency features, and realizes differential simplification of visually sensitive areas. Experiments were conducted on the Zigong color lamp dataset and the TOSCA benchmark dataset, and the results showed that FASP significantly improved the geometric fidelity index (Hausdorff distance reduced by 28.9%, Chamfer distance reduced by 22.7%) while maintaining computational efficiency. This framework provides an effective solution for high-fidelity simplification of complex cultural heritage three-dimensional models, achieving a good balance between compression ratio and feature retention.

[0056] Further, the key vertex set is obtained by performing perceptual-driven key vertex screening on the color lamp, including:

[0057] The local mean curvature and the rate of change of the vertex normal direction are calculated for each vertex of the color lamp and normalized to obtain the saliency score of the fixed point;

[0058] Based on the saliency score, key vertices in the structure-sensitive region are selected through enhanced farthest point sampling to obtain the key vertex set.

[0059] Specifically, in this embodiment, the perceptual-driven key vertex screening includes:

[0060] The cultural heritage lantern model usually contains a large number of hollow decorative patterns, sharp edges and dense local details, which play a key role in the overall visual effect. However, traditional mesh simplification methods (such as QEM) ignore the special structure of visually sensitive areas in the model during simplification, which easily leads to the destruction or loss of important visual features. To overcome this problem, the embodiment proposes a perception-driven vertex selection method based on local geometric features and deep learning, which accurately locates and retains the key vertices in the visually salient areas of the lantern model, thereby improving the visual fidelity of the simplified model.

[0061] In particular, given an input triangular mesh model , where, represents a set of vertices, represents a set of edges, represents a set of triangular faces. First, a geometric saliency score function of the vertex is constructed to automatically identify the vertex set that has an important influence on the visual structure. Two important geometric indicators are selected, namely the local mean curvature of the vertex and the normal direction variation rate, which respectively depict the local geometric features and the surface normal variation characteristics of the vertex.

[0062] First, for each vertex , its local mean curvature is calculated:

[0063]

[0064] where, represents a set of one-ring neighbors of the vertex , and the weight coefficient takes the commonly used cotangent weight to ensure the stability of the curvature estimation. The area with high mean curvature usually corresponds to the visually sensitive areas such as hollow boundaries, sharp edges or carved decorations.

[0065] Secondly, the variation rate of the normal direction of the vertex is calculated to capture the area with a sharp change in the surface normal:

[0066]

[0067] where, represents the unit normal vector of the vertex , which is calculated by the weighted average of the normal vectors of its adjacent triangular faces. This indicator has high sensitivity to areas with carved decorations, sharp corners and hollow structures.

[0068] In order to utilize the above two indicators for visual saliency evaluation at the same time, the curvature and normal variation are normalized and then combined to construct the perception saliency score function of the vertex :

[0069]

[0070] wherein, are the normalized curvature and normal variation, respectively, and the weight factor controls the relative importance of the two geometric features. In experiments, we usually set to balance the contributions of curvature and normal variation to visual saliency.

[0071] To further realize end-to-end differentiable training, a Gumbel-Softmax soft sampling strategy is introduced, which enables the sampling process to adaptively select the vertices and maintain differentiability. In a specific implementation, let denote the input vertex set, be the saliency score vector, be the number of target sampled vertices, be the final sampled vertex set, then the specific operation steps of the enhanced farthest point sampling (FPS) algorithm are as follows:

[0072] 1. Randomly select a vertex from the input vertex set as the initial sampling vertex;

[0073] 2. In each iteration, select the vertex with the highest saliency score from the set of vertices that have not been sampled and that are farthest from the current set of sampled vertices, and add it to the sampling set;

[0074] Repeat step 2 until the number of vertices in the sampling vertex set reaches the target number .

[0075] The formal description of this sampling process is as follows:

[0076] ;

[0077] The enhanced FPS algorithm takes into account both the spatial distribution of vertices and the geometric saliency score, ensuring that the key vertices sampled are uniformly distributed in space while having high geometric feature saliency, thereby more effectively preserving important structural features in the visual sensitive regions of the model.

[0078] Through the above vertex screening mechanism that combines high-dimensional feature representation, curvature information, and normal variation, the perception-driven key vertex selection method proposed in this embodiment can accurately locate and preserve the visual sensitive regions in the color lamp model, providing a high-quality structural basis for subsequent mesh simplification and topology modeling, and further achieving more accurate and visually friendly mesh simplification results. The perception-driven key vertex selection and GNN-guided mesh simplification algorithm is as follows: Figure 6As shown.

[0079] Furthermore, based on the set of key vertices, multi-head attention-guided connection probability modeling is performed, and the connection probability between vertex pairs is predicted, including:

[0080] Based on the set of key vertices, an initial sparse adjacency graph is constructed using the k-nearest neighbor strategy;

[0081] For each key vertex, construct a rich feature representation that integrates geometric and perceptual attributes;

[0082] A multi-head graph attention mechanism is introduced based on the initial sparse adjacency graph. Combined with the rich feature representation, the probability of connection between vertex pairs is dynamically predicted. Specifically, the rich feature representation that integrates geometric and perceptual attributes determines the subsequent use of the multi-head graph attention mechanism to calculate the correlation between the vertex and other vertices, thereby dynamically determining the level of connection probability between them.

[0083] Furthermore, dynamically predicting the probability of connections between vertex pairs includes:

[0084] Calculate the connection weight of the h-th attention head for any pair of connected vertices;

[0085] Through the The connection weights generated by each attention head are averaged and aggregated to obtain the final connection weights; where h represents one of the multiple attention heads (index), and H represents the total number of attention heads (hyperparameter).

[0086] Based on the final connection weights, the connection probabilities between vertices are obtained using the Sigmoid function.

[0087] Specifically, in this embodiment, the multi-head attention-guided connection probability modeling includes the following:

[0088] After the key vertices are selected, it is necessary to further construct an accurate connection structure to clarify the topological relationships between the key vertices, thereby forming a mesh structure with visual fidelity. However, since cultural heritage lantern models often contain complex hollow patterns, boundaries with drastic curvature changes, and fine local structures, traditional distance or static adjacency relationships are difficult to accurately describe their topological characteristics. Therefore, this embodiment proposes a connection probability modeling method based on multi-head graph attention to dynamically learn and predict the topological connection relationships between vertices, and more accurately capture the true structure of visually sensitive areas.

[0089] Initial graph structure based on key vertices:

[0090] First, given the set of key vertices obtained above through perception-driven vertex filtering. An initial sparse adjacency graph is constructed using the k-Nearest Neighbor (k-NN) strategy. The specific steps are as follows:

[0091] For each vertex Define its space nearest Using 10 vertices as initial neighbors, an initial graph structure is formed:

[0092]

[0093] in, Represents the relationship with vertex P i The set of the k nearest vertices by Euclidean distance. This step ensures both local sparsity and topological connectivity of the initial connections.

[0094] Vertex feature construction and fusion:

[0095] To effectively capture the visual complexity of local regions of the model, for each vertex Construct rich feature representations and integrate their geometric and perceptual attributes:

[0096]

[0097] in, As vertex The three-dimensional coordinate position, It is the normal vector. These are the normalized vertex mean curvature and normal rate of change, as defined in the previous section. This fused feature can comprehensively characterize the local geometry and visual sensitivity of each vertex.

[0098] Multi-head graph attention mechanism models connection probabilities:

[0099] A multi-head graph attention mechanism is introduced based on the initial k-NN graph to dynamically predict and optimize the probabilities of connections between vertices. For any pair of connected vertices... , The formula for calculating the connection weights of each attention head is as follows:

[0100]

[0101] in, Let h be the connection weight of the h-th attention head. and They are the first The feature transformation matrix and attention weight parameters of each attention head, denoted as follows: This indicates a feature concatenation operation. is a nonlinear activation function, is a vertex is a neighbor set in the initial graph.

[0102] Through this mechanism, the model can dynamically adjust the connection weight according to the local features, highlight the topological relationship of the visual sensitive area, and reduce the attention degree to the unimportant structure.

[0103] Next, the connection weight generated by the attention head is averaged and aggregated to obtain the final connection weight:

[0104]

[0105] Finally, the connection probability between the vertices is obtained by using the Sigmoid function:

[0106]

[0107] Unsupervised end-to-end training and inference process:

[0108] During the training process, the geometric reconstruction error is optimized in an unsupervised end-to-end manner to ensure that the predicted connection probability is consistent with the real visual structure. In addition, structure sparsity and local connectivity constraints are imposed to ensure the effectiveness and visual fidelity of the predicted connection structure.

[0109] In the inference stage, the connection probability is processed by thresholding to determine the final topological relationship between the vertices, and then a complete simplified mesh topology structure is generated.

[0110] Through the above connection probability modeling method based on the multi-head attention mechanism, the precise connection structure modeling of the visual sensitive area in the cultural heritage lantern model is realized, effectively improving the visual quality and structural integrity of the final simplified model. This dynamic and adaptive connection prediction strategy can more accurately capture the local topological features of complex decorative structures, thereby ensuring the efficiency of mesh simplification while achieving higher visual fidelity and topological accuracy.

[0111] Further, based on the connection probability between the vertex pairs, adaptive perceptual classification of triangular patches is performed to obtain the final triangular face set, including:

[0112] Based on the connection probability between the vertex pairs, an initial candidate triangular patch set is generated;

[0113] For the initial candidate triangular patch set, a feature representation of each candidate triangular patch is constructed; wherein the feature representation of the candidate triangular patch includes: the geometric shape of the triangle, the vertex saliency and the local topological features;

[0114] ​The feature representation of the candidate triangular facet is input into a preset triangular facet classifier to obtain a retention probability of the candidate triangular facet.

[0115] The candidate triangular facet with a retention probability greater than a preset retention probability threshold is retained as the final triangular facet set.

[0116] Further, generating an initial candidate triangular facet set based on the connection probability between the vertex pairs includes:

[0117] For any three vertices in the vertex set, if the connection probabilities of the corresponding three edges all exceed a preset connection threshold, an initial candidate triangular facet is formed.

[0118] Specifically, in the embodiment, the adaptive perceptual classification of the triangular facet specifically includes:

[0119] After the connection structure between the vertices is determined, the next step is to determine the triangular facet set to be retained to ensure that the simplified mesh model can effectively reduce the complexity and completely retain the topological structure of the visually critical area. However, the visually sensitive area of the lantern model usually has a complex geometric structure and topological property, and the traditional method such as the facet screening strategy based on a fixed threshold or static rules often has difficulty in achieving good visual fidelity. Therefore, a perceptual-driven adaptive triangular facet classification method is proposed to realize accurate differential simplification of the visually sensitive area and the non-sensitive area.

[0120] Generation of the triangular facet candidate set:

[0121] First, according to the vertex connection probability predicted by the multi-head attention mechanism in the last section, an initial candidate triangular facet set is generated. Specifically, for any three vertices in the vertex set , if the connection probabilities of the corresponding three edges all exceed a preset threshold , an initial candidate triangular facet is formed:

[0122]

[0123] The threshold is determined by balancing the mesh reconstruction accuracy and visual fidelity in the experiment. This step ensures that the candidate facets have good connectivity and preliminary reasonableness in geometry and topology.

[0124] Geometric and perceptual feature representation of the facet:

[0125] In order to effectively determine whether the triangular facet should be retained, the feature representation of each candidate triangular facet is further constructed, specifically including the geometric shape of the triangular, the vertex saliency and the local topological feature:

[0126] ​

[0127] where 1, is the geometric feature of triangle, including area, normal direction difference and internal angle variance; is the average of saliency score of three vertices of triangle; is the average of edge connection probability of three vertices of triangle.

[0128] The fusion feature above can comprehensively reflect the properties of each candidate triangle in multiple dimensions, such as geometric shape, visual saliency and topological connectivity.

[0129] Design and training of adaptive perceptual classifier

[0130] On this basis, a triangle face patch classifier based on perceptual feature driving is designed to adaptively predict the retention probability of candidate triangle face patches. Specifically, a lightweight multilayer perceptron (MLP) is used as the classifier:

[0131]

[0132] where is the Sigmoid activation function, and the output is the retention probability of the candidate triangle face patch.

[0133] During the training process, the objective function is optimized end-to-end in an unsupervised manner, which is composed of geometric reconstruction error, fidelity constraint of visually sensitive regions and structural sparsity constraint:

[0134]

[0135] where represents the reconstruction geometry error (e.g. Chamfer distance or Hausdorff distance); represents the vertex and structure fidelity constraint of visually salient regions; is the structural sparsity constraint to control the degree of mesh simplification; the parameter , are weight coefficients, and the best values are determined by hyperparameter optimization in the experiment to balance visual quality and mesh complexity.

[0136] Patch classification and final mesh generation strategy:

[0137] In the inference stage, the prediction results of the classifier are used to generate the final mesh structure. Specifically, a retention probability threshold is set. For candidate triangle face patches that meet the condition , they are included in the final retained triangle face patch set :

[0138]

[0139] Retained probability threshold The application requirements can be adjusted to achieve the desired trade-off between mesh simplification rate and visual quality.

[0140] The adaptive triangle classification algorithm based on perceptual features is as shown in Figure 7

[0141] Through the above-mentioned adaptive classification mechanism based on geometric perceptual features, the method proposed in the embodiment can accurately realize the differentiated triangle retention of visual sensitive areas and non-sensitive areas, significantly improve the visual fidelity and topological integrity of the hollow decorative patterns and sharp corners in the cultural heritage lantern model, and thus effectively overcome the limitations of traditional mesh simplification methods.

[0142] The embodiment proposes a feature-aware mesh simplification framework FASP (Feature-Aware Salient Point Sampler) that integrates saliency-driven point sampling, graph neural network (GNN)-based topology modeling, and adaptive triangle classification. Specifically, FASP calculates vertex saliency scores by combining local curvature and normal perturbation, and selects structure-sensitive key vertices with the help of enhanced farthest point sampling. A multi-head graph attention network further predicts the connection probability between these key vertices to generate a structure-aware adjacency graph. Finally, an adaptive triangle classification algorithm evaluates the triangle retention probability based on geometric and saliency features, and realizes differentiated simplification of visually sensitive areas.

[0143] The embodiment conducts experiments on the Zigong lantern real scene dataset and the TOSCA benchmark dataset, systematically evaluates the representativeness and spatial uniformity of the sample point set in the sampling stage, and the global structure reconstruction and feature retention performance in the simplification stage. The results show that FASP can effectively maintain key geometric structures and visual consistency under high compression rate, significantly outperforming classic QEM and mainstream sampling methods.

[0144] The main contributions of the embodiment are as follows:

[0145] A novel FASP (Feature-Aware Salient Point Sampler) framework is proposed, which combines multi-scale geometric features (curvature and normal perturbation) with structure-aware scores to accurately select key points in visually sensitive areas of complex cultural heritage models, laying the foundation for high-fidelity simplification.

[0146] A multi-head graph attention mechanism guided topology modeling and adaptive triangle classification method is designed, which can explicitly model vertex connection probability and triangle retention probability during simplification, effectively improving geometric fidelity and structural consistency.​

[0147] System experiments are carried out on Zigong lantern dataset and TOSCA benchmark dataset to evaluate the performance of FASP in point sampling uniformity, feature region coverage, simplified geometry consistency and feature edge preservation, respectively. Experimental results show that FASP can still maintain the key structure and visual consistency of complex cultural models at high compression rate, and the overall performance is better than existing mainstream methods.

[0148] The following experiments are also carried out in this embodiment:

[0149] The proposed feature-aware keypoint sampling and mesh simplification method (FASP) is systematically evaluated through a series of quantitative and qualitative experiments. All experiments are carried out on Zigong lantern real-scene scanning dataset and standard TOSCA public dataset. FASP is compared with classic quadratic error metric (QEM) algorithm and common sampling strategies in detail to verify the effectiveness and superiority of FASP in geometry fidelity and visual sensitive area preservation.

[0150] The feature-aware keypoint sampling and simplification method (FASP) proposed in this embodiment is evaluated through a series of quantitative and qualitative experiments. First, the point sampling module is compared with several baseline strategies, including random sampling, uniform sampling and traditional farthest point sampling. Then, the simplification performance of the proposed framework on general benchmark models and personalized cultural heritage models (such as Zigong lantern dataset) is compared with the classic QEM algorithm.

[0151] Two representative datasets are used in this embodiment to comprehensively evaluate FASP:

[0152] Zigong lantern dataset: This dataset contains high-fidelity three-dimensional mesh models collected from real Zigong lantern exhibition pieces, with rich decorative details, dense high-curvature regions and hollow structures, suitable for evaluating simplification performance in cultural heritage scenarios.

[0153] TOSCA dataset: As a widely used standard test set, it contains 80 high-resolution three-dimensional mesh models, covering nine types of shapes such as people, animals and artificial objects. This dataset provides diverse geometric complexity to verify the cross-domain generalization ability of the method.

[0154] The Zigong lantern dataset is used as the main training and evaluation dataset, and the TOSCA dataset is used as the auxiliary verification set. All experiments are carried out on NVIDIA RTX 4070 GPU. Adam optimizer (initial learning rate 1e-3, batch size=1) is used during training, and Early Stopping is used to prevent overfitting. At the same time, automatic mixed precision (AMP) is enabled to accelerate training and reduce memory consumption.

[0155] To further analyze the sensitivity of the model to the training configuration, different data set split ratios were tried. Finally, an 80% training / 20% validation split was chosen to strike a balance between training stability and evaluation reliability.

[0156] The experimental procedure of this embodiment is as follows:

[0157] The FASP framework proposed in this embodiment includes three main stages:

[0158] Significance-driven point sampling: The local mean curvature and normal perturbation are calculated for each vertex and normalized to obtain a significance score. Key vertices in structure-sensitive regions are selected by enhanced farthest point sampling. The sampling process is fully differentiable by introducing the Gumbel-Softmax strategy.

[0159] Connection modeling based on graph attention: An initial k-nearest neighbor graph is constructed on the sampled key points, and a multi-head graph attention network (GAT) is used to predict the connection probability between vertex pairs. GAT contains three layers, each with 8 attention heads, and the hidden dimension is 128. All weight parameters are initialized using Xavier uniform initialization. During training, the loss function consists of the geometric reconstruction error (Chamfer distance) and the significance preservation constraint:

[0160]

[0161] where .

[0162] Adaptive triangle classification and simplification: Candidate triangle patches are generated according to the predicted connection probability (threshold 0.5). A lightweight multi-layer perceptron (MLP, containing two layers, hidden units 64) evaluates the retention probability of each triangle patch based on geometric features (area, normal variance, internal angle variance) and significance features. Triangle patches with a probability greater than 0.6 are retained. The final simplification process integrates these retained triangle patches into an improved QEM process, adjusting the edge contraction cost by distance from key vertices.

[0163] Comparison of sampling methods:

[0164] To further verify the performance of the FASP method proposed in this embodiment on the point sampling task, multiple typical Zigong lamp models are selected, including the Cauldron model, the Nian model, the Rabbit model and the Snake model, which are respectively compared with the traditional random sampling (RAN), uniform sampling (UNI) and farthest point sampling (FPS) strategies. The experiment aims to compare the comprehensive performance of different methods under different sampling rates (0.1, 0.2, 0.3). Four commonly used geometric evaluation indexes, including chamfer distance (CD), normal consistency (NC), curvature error (CE) and roughness error (RE), are selected to quantitatively analyze the experimental results.

[0165] Tables 1 to 4 show the quantitative evaluation results of the above models under different sampling rates. Overall, the FASP method proposed in this embodiment performs better or close to other methods in most experimental settings, especially in local feature preservation, curvature sensitive areas and geometric detail preservation.

[0166] Specifically, from the Cauldron model in Table 1, under the lowest sampling rate of 0.1, the chamfer distance (CD=1.598) of the FASP method is better than the traditional FPS (CD=1.625) and UNI (CD=1.696) methods, and significantly better than the random sampling (CD=1.706); in terms of normal consistency (NC), FASP also performs optimally (NC=0.242). At the same time, in terms of curvature error (CE=0.018) and roughness error (RE=0.147), FASP also has obvious advantages. When the sampling rate increases to 0.2 and 0.3, the geometric performance advantage of the FASP method is still maintained, especially in the performance of normal consistency and roughness error, which shows that it can stably preserve geometric details and curvature features under high sampling rate.

[0167] Analyzing the Nian model in Table 2, when the sampling rate is 0.1, the chamfer distance (CD=2.397) of the FASP method is significantly better than other methods (FPS=2.412, UNI=2.423); the normal consistency (NC=0.126) is also higher than the random (0.104) and uniform (0.105) methods. In addition, the FASP method performs significantly better in terms of curvature error and roughness error, especially at higher sampling rates (0.2 and 0.3), FASP is significantly better than other methods in RE index, highlighting the effectiveness of preserving model surface roughness and details.

[0168] The Rabbit model in Table 3 shows similar trends. At the 0.1 sampling level, the FASP method again achieved the lowest chamfer distance (CD = 0.610) and curvature error (CE = 0.033), indicating the best preservation of geometric features. In addition, in the normal consistency (NC = 0.218) and roughness error (RE = 0.025) indicators, the FASP method was also superior to other methods, reflecting its effective preservation ability for local recessed areas and hollow details of the model. As the sampling rate increased to 0.3, the FASP method's indicators remained leading or sub-optimal, confirming its consistent performance in different complexity models and multiple sampling levels.

[0169] Finally, for the Snake model shown in Table 4, at the 0.1 sampling level, the chamfer distance (CD = 0.888) and curvature error (CE = 0.038) of the FASP method were significantly better than other methods. In addition, in the normal consistency (NC = 0.142) and roughness error (RE = 0.043) indicators, FASP also showed effective preservation of surface structure and geometric details. Especially when the sampling rate increased to 0.2 and 0.3, the CD, CE, and RE indicators of the FASP method were still significantly better than traditional methods, showing stable and significant geometric detail preservation advantages.

[0170] Table 1: Quantitative evaluation of point sampling for the Cauldron model

[0171]

[0172] Table 2: Quantitative evaluation of point sampling for the Nian model

[0173]

[0174] Table 3: Quantitative evaluation of point sampling for the Rabbit model

[0175]

[0176] Table 4: Quantitative evaluation of point sampling for the Snake model

[0177]

[0178] In summary of the above experimental results, it can be clearly observed that the FASP method proposed in this embodiment exhibits significant advantages under different models and multiple sampling rates, especially in local geometric detail preservation, surface curvature sensitivity, and model roughness preservation. The experimental data fully demonstrate the effectiveness and generalization ability of the FASP method in actual cultural heritage three-dimensional modeling tasks, which can effectively preserve the visual and geometric features of the original model while significantly reducing the model complexity.

[0179] Comparison of mesh simplification methods:

[0180] In this embodiment, multiple 3D mesh models from Zigong color lamp real scene scanning dataset are selected as test objects and compared with the classic QEM algorithm. The goal of the study is to systematically evaluate the performance of the FASP method proposed in this embodiment in different simplification tasks. The simplification results of the three most representative models, Nian model, Rabbit model and Snake model, are shown in Figure 2 Figure 4 , which intuitively shows the effects and advantages of different methods at different simplification levels.

[0181] Specifically, as shown in Figure 2 , at a simplification rate of 0.05, the traditional QEM algorithm can maintain the overall basic shape of the ingot model, but the details of the local concave area are obviously lost, for example, the concave structure at the bottom and edge appears serious degradation and fuzzification. In contrast, the FASP method can more completely retain the concave elements and edge details of the ingot model under the same conditions, making the local geometry more clear and complete. In addition, when the simplification rate is further reduced to 0.01, the QEM algorithm will merge the claws and toes of the feet into one, resulting in significant blurring of the structural features, while the FASP method can better distinguish the structural relationship between the toes and the claws, significantly improving the fidelity of the local geometry.

[0182] Figure 3 The simplification results of the SNAKE model under different simplification rates are shown. It is found that when the simplification rate is 0.2, the FASP method is significantly better than the traditional QEM algorithm, especially in the detail retention of the sharp edge area of the model, which can effectively maintain the clarity and continuity of the edge features. When the simplification rate is reduced to 0.05, the QEM algorithm causes significant degradation of the details of the SNAKE hand, with the local contour appearing fuzzy; while the FASP method can still clearly and completely show the key structural features of the hand, demonstrating stronger local structure retention capability.

[0183] On the rabbit model of Figure 4 , when the simplification rate is set to 0.1, the FASP method shows a more fine detail retention capability in the concave area of the rabbit's head, effectively maintaining the integrity of the local geometric contour, significantly improving the visual consistency of the structure compared with the QEM method. In addition, at a simplification rate of 0.05, for the hollow details of the guitar part of the rabbit model, the FASP method can more completely retain the hollow geometric contour and edge features, while the QEM method produces obvious detail loss and structural degradation in the structure simplification of the hollow area.

[0184] ​In summary, under different typical models and various levels of simplification conditions, the FASP method proposed in this embodiment has significant advantages in preserving the overall structural integrity and local decorative details. In particular, in high-curvature areas, complex ornamentation, and hollow structures, the geometric fidelity and visual consistency are significantly better than the traditional QEM method.

[0185] As Figure 5 shown, the Chamfer distance comparison chart of each sampling method under different simplification rates of this embodiment; wherein, Figure 5 (a) of the (a) is the Chamfer distance comparison of each sampling method under different simplification rates of Nian model, Figure 5 (b) of the (b) is the Chamfer distance comparison of each sampling method under different simplification rates of Cauldron model, Figure 5 (c) of the (c) is the Chamfer distance comparison of each sampling method under different simplification rates of Rabbit model, Figure 5 (d) of the (d) is the Chamfer distance comparison of each sampling method under different simplification rates of Snake model.

[0186] To further verify the effectiveness of the FASP method proposed in this embodiment in the task of mesh simplification, this embodiment conducts a number of experiments on the four typical models (Nian, Cauldron, Rabbit and Snake) of Zigong colored lamp dataset and TOSCA test set. Under the conditions of four simplification rates of 0.5, 0.3, 0.1 and 0.05, the performance of FASP and traditional QEM algorithm is systematically quantitatively evaluated.

[0187] The maximum error (MAX), mean error (Mean) and root mean square error (RMS) are calculated in the experiment to comprehensively measure the geometric fidelity of the model in multiple dimensions such as overall consistency, local volatility and worst case. The results are shown in Tables 5 to 8. FASP method shows significant advantages in all simplification rates and different models. At high simplification rates (0.5 and 0.3), FASP can effectively reduce the overall error and maintain the structural continuity; at low simplification rates (0.1 and 0.05), especially in high-curvature and complex decorative areas, FASP still significantly improves the detail retention capability, with an average reduction of more than 30% in maximum error and root mean square error.

[0188] Table 5: Quantitative evaluation of Nian model mesh simplification

[0189]

[0190] Table 6: Quantitative evaluation of Cauldron model mesh simplification

[0191]

[0192] Table 7: Quantitative evaluation of mesh simplification for Rabbit model

[0193]

[0194] Table 8: Quantitative evaluation of mesh simplification for Snake model

[0195]

[0196] It can be seen through further analysis that in the Hausdorff distance evaluation of the general model, the FASP method reduces the error by an average of about 42.73%, and achieves an average reduction of 28.99% in Hausdorff distance on the Nian model. In the Rabbit and Snake models, FASP reduces the maximum error by about 27.15% and 34.22% respectively, fully verifying its geometric consistency and detail preservation advantage in diversified morphology. Although FASP is similar to QEM in a few individual indicators, the overall trend shows that FASP has a significantly better fidelity in local features, curvature regions and visually sensitive areas than traditional methods, reflecting stronger generalization ability and robustness.

[0197] In summary, the method of the present embodiment exhibits good adaptability and significant performance improvement at different simplification levels, and can effectively maintain the global outline and local geometric features of the model under high compression ratio conditions, providing a more practical and efficient solution for high-fidelity three-dimensional model simplification.

[0198] The present embodiment aims to improve the geometric fidelity and detail preservation ability of mesh simplification methods based on quadratic error metric (QEM) in complex three-dimensional models by introducing perceptual feature guided keypoint sampling and graph neural network modeling. The present embodiment proposes an efficient feature-aware point sampling strategy that uses local curvature and normal perturbation to comprehensively evaluate vertex saliency, and constructs structural correlation information between vertices combined with multi-head graph attention mechanism. On this basis, the generated saliency sampling points are used to guide the QEM simplification process, and by adjusting the edge collapse priority and error weight, fine-grained control of local sensitive regions is achieved, thereby enhancing the visual consistency and local geometric accuracy of the simplified model.

[0199] The above-described embodiments are only descriptions of the preferred modes of the present application and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art shall fall within the scope of protection determined by the claims of the present application.

Claims

1. A method for recognizing the geometric features of colored lights based on graph neural networks, characterized in that, include: The key vertex set is obtained by performing perception-driven filtering on the colored lights. Based on the set of key vertices, multi-head attention-guided connection probability modeling is performed, and the connection probability between vertex pairs is predicted. Based on the connection probability between the vertex pairs, adaptive perception classification of triangular facets is performed to obtain the final set of triangular facets that retains the geometric features of the colored lights. The key vertex selection for perception-driven operation of colored lights, and the acquisition of the key vertex set, include: For each colored light, calculate the local mean curvature and the rate of change of the vertex normal direction, and normalize them to obtain the significance score of the fixed point; Based on the saliency score, key vertices in the structurally sensitive region are selected by enhanced farthest point sampling to obtain the set of key vertices; Key vertices in structure-sensitive regions are selected using enhanced farthest-point sampling, including: Step 1. From the input vertex set Randomly select a vertex from the sampled data as the initial sampling vertex. Step 2. In each iteration, select the vertex that is furthest from the currently sampled vertex set and has a significance score greater than a preset score threshold from the unsampled vertex set and add it to the sampling set. ; Step 3. Repeat step 2 until the set of sampled vertices is reached. The number of vertices has reached the preset target number. ; Based on the aforementioned set of key vertices, multi-head attention-guided connection probability modeling is performed, and the connection probability between vertex pairs is predicted, including: Based on the set of key vertices, an initial sparse adjacency graph is constructed using the k-nearest neighbor strategy; For each key vertex, construct a rich feature representation that integrates geometric and perceptual attributes; A multi-head graph attention mechanism is introduced based on the initial sparse adjacency graph, and combined with the rich feature representation, the probability of connection between vertex pairs is dynamically predicted.

2. The method for recognizing geometric features of colored lights based on graph neural networks according to claim 1, characterized in that, Dynamically predicting the probability of connections between vertex pairs includes: Calculate the connection weight of the h-th attention head for any pair of connected vertices; Through the The connection weights generated by each attention point are averaged and aggregated to obtain the final connection weights. Based on the final connection weights, the connection probabilities between vertices are obtained using the Sigmoid function.

3. The method for recognizing geometric features of colored lights based on graph neural networks according to claim 1, characterized in that, The rich features are represented as follows: in, To enrich feature representation, As vertices The three-dimensional coordinate position, It is the normal vector. These are the normalized vertex mean curvature and the rate of change of the normal, respectively.

4. The method for recognizing geometric features of colored lights based on graph neural networks according to claim 2, characterized in that, The connection weight of the h-th attention head is: in, Let h be the connection weight of the h-th attention head. and They are the first The feature transformation matrix and attention weight parameters of each attention head, denoted as follows: This indicates a feature concatenation operation. It is a non-linear activation function. As vertices In the initial graph, the neighbor set is k, which is the number of nearest neighbors used to construct the initial adjacency graph. The index of the current center vertex. It is a neighboring vertex of a vertex.

5. The method for recognizing geometric features of colored lights based on graph neural networks according to claim 1, characterized in that, Based on the connection probabilities between the vertex pairs, adaptive perceptual classification of triangular faces is performed to obtain the final set of triangular faces that retain the geometric features of the colored lights, including: Based on the connection probability between the vertex pairs, an initial set of candidate triangle faces is generated; For the initial set of candidate triangles, construct the feature representation of each candidate triangle; where the feature representation of the candidate triangle includes: the geometric shape of the triangle, vertex saliency and local topological features; The feature representation of the candidate triangle is input into a preset triangle classifier to obtain the retention probability of the candidate triangle. Candidate triangles with a retention probability greater than a preset retention probability threshold are retained as the final set of triangles.

6. The method for recognizing geometric features of colored lights based on graph neural networks according to claim 5, characterized in that, Based on the connection probabilities between the vertex pairs, an initial set of candidate triangle faces is generated, including: For any three vertices in the vertex set, if the connection probability between any two pairs of the corresponding three vertices exceeds a preset connection threshold, then an initial candidate triangle is formed.

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