三维模型的局部匹配和检索方法研究
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摘要
随着三维模型技术和互联网技术的不断发展，越来越多的三维模型制作软件和三维模型文件被共享在互联网上面，同时三维模型技术的应用领域也越来越广泛，如产品设计、制造仿真、虚拟现实、3D网络游戏等。尤其是最近几年3D打印机的出现，三维模型的应用已经开始普及至家庭用户，使得家庭用户可以应用3D打印机打印自己所需的三维模型。因此，研究和开发三维模型搜索引擎帮助企业用户、家庭用户快速、准确的检索到自己所需的三维模型，是最近几年的研究热点之一。
论文针对三维模型特征描述和检索这一问题展开研究，主要工作包括以下几个方面：
研究了基于形状统计方法的特征提取算法，针对传统的D2形状描述算法的不足，提出了一种基于面积算子的三维模型检索算法，该算法首先将对三角网格模型进行模型简化处理，使得表达三维网格模型的点和面的集合达到最小化，然后对三维网格模型上的顶点进行统计分析，对每个顶点所关联的三角形的面积进行计算，并对点相关的面积进行归一化处理，然后对点关联的面积序列进行通傅里叶变换，得到特征向量，做出面积分布图，通过计算模型间特征向量的差异，得到模型间的差异，进而检索出相似的三维模型。实验表明，和类似的基于形状统计的模型检索算法相比较，该方法可以获得更好的检索结果。
针对三维模型检索中的局部特征描述和匹配问题，提出了一种基于顶点邻域属性的三维模型检索算法，该算法首先统计三维网格模型的相关属性和顶点的邻域顶点相关属性，包括邻域的质心、顶点到邻域质心的矢量、顶点到邻域质心的距离、顶点的法向矢量、顶点的曲率以及顶点的法向矢量和顶点邻域质心矢量之间的夹角等，接着对邻域顶点的属性中的2个角度进行16等分，形成一个16×16规模的特征矩阵，然后采用一组特定的矩阵相似度计算方法计算特征矩阵间的相似度，最后计算模型整体的相似度，以此来代替二个三维模型的相似度。通过和其他检索算法的比较实验表明，该方法对具有较丰富局部特征的模型可以获得更好的检索结果。
提出了一种基于法向夹角直方图的三维模型检索算法。算法首先对三维模型进行预处理，接着定义了三维模型上的三角网格各个顶点的法向与三角网格之间的夹角计算方法，然后根据三角网格三个顶点的法向与三角网格之间的夹角，对三角网格进行分类，根据夹角是锐角还是钝角，将三角网格分成四种类型，对每种类型的三角网格集合构造形状分布曲线，通过对模型的四条形状分布曲线的比较，得出两个模型的相似度，从而实现模型的相似性检索。实验表明，该算法的检索准确率和检索效率方面要由于其他类似的直方图算法。
在三维模型的局部匹配和检索方面，引入了三维分割技术，首先采用基于Laplace-Beltrami算子特征函数的模型特征描述方法，采用有限元算子方法离散化和求解Laplace-Beltrami算子特征值问题，将算子特征函数值作为三维模型的特征描述符；然后采用K均值聚类方法，对特征描述符进行聚类分析，聚类后的结果将三维模型分割成多个局部区域；最后采用指派问题中的匈牙利算法计算三维网格模型之间的局部区域与整体模型之间的匹配度，从而得到模型间的匹配结果。
为了验证前面提到的算法，设计了一个三维模型检索系统的原型系统，系统中提供了多种检索算法，包括面积分布算子算法、顶点邻域属性算法和基于LB算子特征函数的算法以及课题组其它成员设计的算法。
With the technology of3D model and Internet technology continues to evolve,more and more3D software and3D model files are shared on internet, and3Dmodel technology applications are increasingly being used just like product design,3D online game, simulation assembly and virtual reality. Especially in recent years,3D printers making3D model has begun to spread to home users and enable userscan print3D models with3D printers. So the research and development of3D modelsearch engines to help business users, home users to quickly and accurately retrievethe desired3D model of their own, is one of the focus in recent years.
The main contents of the dissertation are presented as follows:
Based on statistical feature extraction algorithm, proposes a area distributionsbased method outlying with3D system. According to the method, first summary thetotal area and average area of the vertex of the3D model, then normalized the list ofthe area distributions list and Fourier transform the list; last get the final areadistributions list model, and map the search of the model to the compare of the areadistributions list. Experiments were conducted to the comparison of evaluate theproposed algorithm utilizing the Engineering Shape Benchmark (ESB) database.The experiential results show that the proposed technique effectively reflected thesimilarity among engineering models, and the match result of the model whichextremely similar was accurate and the retrieval performance was significantlyimproved compared to traditional shape distribution method.
Propose a new3D CAD model retrieval method. Properties associated with thevertex will be extracted from3D model to be calculated into description operators.First, calculate the Gaussian curvature of vertices and translate it into the angle α, atthe same time, calculate angle β between the vector from vertex to center of massand normal vector of vertex. We use angel α and angel β to build a3D plane matrixgrid by splitting α and β with pi/16, define grid function O at each cell and its valueis the sum of distances from all vertices to center of masses, then a characteristicmatrix of model16×16is generated. Finally compute the similarity between twomodels by specific rules. Use matrix similarity to measure the similarity of the twomodels, so as to achieve similarity retrieval. Use the ESB library of PurdueUniversity and model library of Princeton University to carry out retrievalexperiment and the results show that the algorithm in the paper has higher retrievalaccuracy.
Propose a new3D model retrieval method based on normal-angle histogram.The method firstly makes the pretreatment for3D model, and defines the calculation method of the normal at every vertex of the triangular mesh in3D model and theincluded angle among the triangular meshes. Then it classifies the triangular mesh inaccordance with the normal at three vertexes of the triangular mesh and the includedangle among the triangular meshes, and divides the triangular mesh into four typesas per the included angle whether acute angle or obtuse angle, constructs the shapedistribution curve for every type of triangular mesh collection, obtains the similarityof two shapes by comparison of four shape distribution curves of3D model, andaccordingly realizes the similarity retrieval of3D model. The test indicates that theretrieval accuracy rate and the retrieval efficiency of the algorithm are superior toother similar histogram algorithm.
Propose a new3D model retrieval method based on normal-angle histogram.The method firstly makes the pretreatment for3D model, and defines the calculationmethod of the normal at every vertex of the triangular mesh in3D model and theincluded angle among the triangular meshes. Then it classifies the triangular mesh inaccordance with the normal at three vertexes of the triangular mesh and the includedangle among the triangular meshes, and divides the triangular mesh into four typesas per the included angle whether acute angle or obtuse angle, constructs the shapedistribution curve for every type of triangular mesh collection, obtains the similarityof two shapes by comparison of four shape distribution curves of3D model, andaccordingly realizes the similarity retrieval of3D model. The test indicates that theretrieval accuracy rate and the retrieval efficiency of the algorithm are superior toother similar histogram algorithm.
In partial matching and retrieval, we have introduced a3D segmentationtechnique. The partial description based on the eigenfunction of theLaplace-Beltrami operator is an important way. A large number of eigenfunctionvalues of any point on the surface of the model form a eigenvector; based on thisvector, K-means clustering method will be used to query the model which is dividedinto several regions; for each region, based on the Hungarian method which is usedin the solving of optimal assignment problem, search a corresponding region in thecompared model, so that achieving the partial matching between the two models.
To validate the algorithm mentioned previously, we design and implement a3Dmodel retrieval system. The model library of this system is Engineering ShapeBenchmark which provided by Purdue University. Serival retrieval method wereimplement include area distribution algorithm, method based on property of vertex,method based on Laplace-Beltrami operator and other methods. We use this systemto validate our algorithm, analysis retrieval results and improve our algorithm.
论文针对三维模型特征描述和检索这一问题展开研究，主要工作包括以下几个方面：
研究了基于形状统计方法的特征提取算法，针对传统的D2形状描述算法的不足，提出了一种基于面积算子的三维模型检索算法，该算法首先将对三角网格模型进行模型简化处理，使得表达三维网格模型的点和面的集合达到最小化，然后对三维网格模型上的顶点进行统计分析，对每个顶点所关联的三角形的面积进行计算，并对点相关的面积进行归一化处理，然后对点关联的面积序列进行通傅里叶变换，得到特征向量，做出面积分布图，通过计算模型间特征向量的差异，得到模型间的差异，进而检索出相似的三维模型。实验表明，和类似的基于形状统计的模型检索算法相比较，该方法可以获得更好的检索结果。
针对三维模型检索中的局部特征描述和匹配问题，提出了一种基于顶点邻域属性的三维模型检索算法，该算法首先统计三维网格模型的相关属性和顶点的邻域顶点相关属性，包括邻域的质心、顶点到邻域质心的矢量、顶点到邻域质心的距离、顶点的法向矢量、顶点的曲率以及顶点的法向矢量和顶点邻域质心矢量之间的夹角等，接着对邻域顶点的属性中的2个角度进行16等分，形成一个16×16规模的特征矩阵，然后采用一组特定的矩阵相似度计算方法计算特征矩阵间的相似度，最后计算模型整体的相似度，以此来代替二个三维模型的相似度。通过和其他检索算法的比较实验表明，该方法对具有较丰富局部特征的模型可以获得更好的检索结果。
提出了一种基于法向夹角直方图的三维模型检索算法。算法首先对三维模型进行预处理，接着定义了三维模型上的三角网格各个顶点的法向与三角网格之间的夹角计算方法，然后根据三角网格三个顶点的法向与三角网格之间的夹角，对三角网格进行分类，根据夹角是锐角还是钝角，将三角网格分成四种类型，对每种类型的三角网格集合构造形状分布曲线，通过对模型的四条形状分布曲线的比较，得出两个模型的相似度，从而实现模型的相似性检索。实验表明，该算法的检索准确率和检索效率方面要由于其他类似的直方图算法。
在三维模型的局部匹配和检索方面，引入了三维分割技术，首先采用基于Laplace-Beltrami算子特征函数的模型特征描述方法，采用有限元算子方法离散化和求解Laplace-Beltrami算子特征值问题，将算子特征函数值作为三维模型的特征描述符；然后采用K均值聚类方法，对特征描述符进行聚类分析，聚类后的结果将三维模型分割成多个局部区域；最后采用指派问题中的匈牙利算法计算三维网格模型之间的局部区域与整体模型之间的匹配度，从而得到模型间的匹配结果。
为了验证前面提到的算法，设计了一个三维模型检索系统的原型系统，系统中提供了多种检索算法，包括面积分布算子算法、顶点邻域属性算法和基于LB算子特征函数的算法以及课题组其它成员设计的算法。
With the technology of3D model and Internet technology continues to evolve,more and more3D software and3D model files are shared on internet, and3Dmodel technology applications are increasingly being used just like product design,3D online game, simulation assembly and virtual reality. Especially in recent years,3D printers making3D model has begun to spread to home users and enable userscan print3D models with3D printers. So the research and development of3D modelsearch engines to help business users, home users to quickly and accurately retrievethe desired3D model of their own, is one of the focus in recent years.
The main contents of the dissertation are presented as follows:
Based on statistical feature extraction algorithm, proposes a area distributionsbased method outlying with3D system. According to the method, first summary thetotal area and average area of the vertex of the3D model, then normalized the list ofthe area distributions list and Fourier transform the list; last get the final areadistributions list model, and map the search of the model to the compare of the areadistributions list. Experiments were conducted to the comparison of evaluate theproposed algorithm utilizing the Engineering Shape Benchmark (ESB) database.The experiential results show that the proposed technique effectively reflected thesimilarity among engineering models, and the match result of the model whichextremely similar was accurate and the retrieval performance was significantlyimproved compared to traditional shape distribution method.
Propose a new3D CAD model retrieval method. Properties associated with thevertex will be extracted from3D model to be calculated into description operators.First, calculate the Gaussian curvature of vertices and translate it into the angle α, atthe same time, calculate angle β between the vector from vertex to center of massand normal vector of vertex. We use angel α and angel β to build a3D plane matrixgrid by splitting α and β with pi/16, define grid function O at each cell and its valueis the sum of distances from all vertices to center of masses, then a characteristicmatrix of model16×16is generated. Finally compute the similarity between twomodels by specific rules. Use matrix similarity to measure the similarity of the twomodels, so as to achieve similarity retrieval. Use the ESB library of PurdueUniversity and model library of Princeton University to carry out retrievalexperiment and the results show that the algorithm in the paper has higher retrievalaccuracy.
Propose a new3D model retrieval method based on normal-angle histogram.The method firstly makes the pretreatment for3D model, and defines the calculation method of the normal at every vertex of the triangular mesh in3D model and theincluded angle among the triangular meshes. Then it classifies the triangular mesh inaccordance with the normal at three vertexes of the triangular mesh and the includedangle among the triangular meshes, and divides the triangular mesh into four typesas per the included angle whether acute angle or obtuse angle, constructs the shapedistribution curve for every type of triangular mesh collection, obtains the similarityof two shapes by comparison of four shape distribution curves of3D model, andaccordingly realizes the similarity retrieval of3D model. The test indicates that theretrieval accuracy rate and the retrieval efficiency of the algorithm are superior toother similar histogram algorithm.
Propose a new3D model retrieval method based on normal-angle histogram.The method firstly makes the pretreatment for3D model, and defines the calculationmethod of the normal at every vertex of the triangular mesh in3D model and theincluded angle among the triangular meshes. Then it classifies the triangular mesh inaccordance with the normal at three vertexes of the triangular mesh and the includedangle among the triangular meshes, and divides the triangular mesh into four typesas per the included angle whether acute angle or obtuse angle, constructs the shapedistribution curve for every type of triangular mesh collection, obtains the similarityof two shapes by comparison of four shape distribution curves of3D model, andaccordingly realizes the similarity retrieval of3D model. The test indicates that theretrieval accuracy rate and the retrieval efficiency of the algorithm are superior toother similar histogram algorithm.
In partial matching and retrieval, we have introduced a3D segmentationtechnique. The partial description based on the eigenfunction of theLaplace-Beltrami operator is an important way. A large number of eigenfunctionvalues of any point on the surface of the model form a eigenvector; based on thisvector, K-means clustering method will be used to query the model which is dividedinto several regions; for each region, based on the Hungarian method which is usedin the solving of optimal assignment problem, search a corresponding region in thecompared model, so that achieving the partial matching between the two models.
To validate the algorithm mentioned previously, we design and implement a3Dmodel retrieval system. The model library of this system is Engineering ShapeBenchmark which provided by Purdue University. Serival retrieval method wereimplement include area distribution algorithm, method based on property of vertex,method based on Laplace-Beltrami operator and other methods. We use this systemto validate our algorithm, analysis retrieval results and improve our algorithm.
引文
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