CN102622609B - A 3D Model Automatic Classification Method Based on Support Vector Machine - Google Patents

A 3D Model Automatic Classification Method Based on Support Vector Machine Download PDF

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CN102622609B
CN102622609B CN 201210051160 CN201210051160A CN102622609B CN 102622609 B CN102622609 B CN 102622609B CN 201210051160 CN201210051160 CN 201210051160 CN 201210051160 A CN201210051160 A CN 201210051160A CN 102622609 B CN102622609 B CN 102622609B
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刘贞报
张凤
布树辉
唐小军
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Haian Juli Magnetic Material Co ltd
Northwestern Polytechnical University
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Abstract

The invention discloses a method for automatically classifying three-dimensional models based on a support vector machine. The method comprises the steps as follows: carrying out dimension reduction and characteristic decomposition on a geodesic distance matrix; creating binary classifiers for the characteristics of the three-dimensional models by using the support vector machine; and combining every two of the binary classifiers in a 'one-to-one' way by using the support vector machine to form a polynary classifier. According to the method, the three-dimensional models can be automatically classified, so that the robustness of the characteristic extraction process of the models is higher, the computing speed is higher, the characteristic extraction time is greatly shortened, and fewer three-dimension model training sample conditions can be well corresponded. The method has higher generalization performance and good expansion capability and non-linearity performance.

Description

一种基于支持向量机的三维模型自动分类方法A 3D Model Automatic Classification Method Based on Support Vector Machine

技术领域 technical field

本发明涉及一种三维模型的自动分类方法。The invention relates to an automatic classification method of three-dimensional models.

背景技术 Background technique

作为继声音、图像和视频之后的第四代多媒体数据类型,三维模型是最直观、最具表现力的多媒体信息。随着激光扫描技术、三维建模软件技术以及网络技术的快速发展,三维模型的创建和应用越来越广泛,三维模型资源越来越丰富。企业产品类型及品种的增多、产品数据规模的膨胀,使得产品设计中三维模型的分类研究具有重要的理论与工程意义。而基于形状的三维模型分类作为计算机图形学领域的一个新兴研究热点,在工业产品的模型设计、虚拟现实、模拟仿真、3D游戏、计算机视觉、分子生物学和三维地理信息等各个领域获得了广泛的应用。As the fourth-generation multimedia data type after sound, image and video, 3D model is the most intuitive and expressive multimedia information. With the rapid development of laser scanning technology, 3D modeling software technology and network technology, the creation and application of 3D models are becoming more and more extensive, and 3D model resources are becoming more and more abundant. The increase of enterprise product types and varieties and the expansion of product data scale make the classification research of 3D models in product design have important theoretical and engineering significance. As an emerging research hotspot in the field of computer graphics, shape-based 3D model classification has gained extensive attention in various fields such as model design of industrial products, virtual reality, simulation, 3D games, computer vision, molecular biology, and 3D geographic information. Applications.

在目前国内外公开的文献中,在Z.Barutcuoglu and C.Decoro,“Hierarchical shapeclassification using Bayesian aggregation”,IEEE International Conference on ShapeModeling and Applications,2006.中提出了基于Bayesian aggregation的分类方法,对语义层次结构中的三维模型进行分类。在层次结构模型中,使用相对独立的分类器对每一类模型进行分类时,产生的分类结果将会与层次结构中“父-子”关系发生分歧。为了保持一致,一个样本图形必须不能被只分为一类,除非这个图形已经在层次结构中被分为“父”类。在给定的用于一个任意形状描述符的一些独立的分类器的情况下,把它们每一个很可能不一致的分类结果结合起来,然后在贝叶斯的框架下获得一组最一致的分类结果。最终利用分层结构来提高整个分类结果的精度。在Z.Liu,J.Mitani,Y.Fukui and S.Nishihara,“A 3D shape classifier with neural network supervision”,International Journal of Computer Applications in Technology,Vol.38,No.1-3,2010.中提出了基于监督型神经网络的三维模型分类方法,该方法该提供了一种基于监督点空间的密度分布的三维图形分类器。首先通过特征化点空间的密度分布提取出低阶的特征样本,然后训练一个前馈控制的神经网络来学习这些特征,从而获得一个有效的分类器。此分类器分为两个阶段,分别为用于训练数据的训练阶段和评估分类效果的测试阶段。而需要注意的是分类器的精度不仅和每个样本的权重相关,而且和神经网络中的隐藏阶层的隐藏单元个数息息相关。隐藏单元个数不同,分类精度也会有很大差别。因此在训练分类器时,选择最恰当的隐藏单元个数是非常有必要的。In the current public literature at home and abroad, in Z.Barutcuoglu and C.Decoro, "Hierarchical shapeclassification using Bayesian aggregation", IEEE International Conference on ShapeModeling and Applications, 2006. A classification method based on Bayesian aggregation is proposed, and the semantic hierarchy Classify the 3D models in . In a hierarchical structure model, when a relatively independent classifier is used to classify each type of model, the resulting classification results will diverge from the "parent-child" relationship in the hierarchical structure. For consistency, a sample graph must not be classified into only one class unless the graph has been classified into a "parent" class in the hierarchy. Given a number of independent classifiers for an arbitrary shape descriptor, combine the classification results of each of them that are likely to be inconsistent, and then obtain the most consistent set of classification results under the framework of Bayesian . Finally, the hierarchical structure is utilized to improve the accuracy of the overall classification results. Proposed in Z.Liu, J.Mitani, Y.Fukui and S.Nishihara, "A 3D shape classifier with neural network supervision", International Journal of Computer Applications in Technology, Vol.38, No.1-3, 2010. A 3D model classification method based on supervised neural network is proposed, which provides a 3D graph classifier based on the density distribution of supervised point space. Firstly, low-order feature samples are extracted by characterizing the density distribution of the point space, and then a feed-forward controlled neural network is trained to learn these features to obtain an effective classifier. This classifier is divided into two phases, a training phase for training data and a testing phase for evaluating classification performance. It should be noted that the accuracy of the classifier is not only related to the weight of each sample, but also closely related to the number of hidden units in the hidden layer of the neural network. The number of hidden units is different, and the classification accuracy will also vary greatly. Therefore, it is very necessary to choose the most appropriate number of hidden units when training the classifier.

但上述两种三维模型分类方法有几点不足:However, the above two 3D model classification methods have several shortcomings:

(1)基于Bayesian aggregation的三维模型分类方法主要是针对属于层次结构中的三维模型进行分类,具有一定的局限性,适用范围较小;(1) The 3D model classification method based on Bayesian aggregation is mainly aimed at classifying 3D models belonging to the hierarchical structure, which has certain limitations and a small scope of application;

(2)基于神经网络的三维模型分类方法不能对应非刚性变形,另外,分类精度较低。(2) The 3D model classification method based on the neural network cannot correspond to non-rigid deformation, and in addition, the classification accuracy is low.

发明内容 Contents of the invention

为了克服现有分类方法分类范围局限、无法应对非刚性变形以及精度较低的问题,本发明提供一种三维模型自动分类方法,该分类方法针对通用物体的三维模型或CAD模型进行自动分类。首先,为了获取三维模型的非刚性变换的特征,本发明计算三维模型任意两个顶点的测地线距离,通过获取测地线分布作为全局特征。本发明对测地线距离矩阵进行降维和特征分解,然后利用支持向量机构建三维模型特征的二元分类器,并采用支持向量机二元分类器的“一对一”两两组合构成多元分类器。本发明可以对三维模型进行自动分类。In order to overcome the problems of limited classification scope, inability to deal with non-rigid deformation, and low precision of existing classification methods, the present invention provides an automatic classification method for 3D models, which automatically classifies 3D models or CAD models of general objects. First, in order to obtain the characteristics of the non-rigid transformation of the 3D model, the present invention calculates the geodesic distance between any two vertices of the 3D model, and obtains the geodesic distribution as a global feature. The invention performs dimensionality reduction and feature decomposition on the geodesic distance matrix, and then uses the support vector machine to construct the binary classifier of the three-dimensional model features, and adopts the "one-to-one" pairwise combination of the support vector machine binary classifier to form a multiple classification device. The invention can automatically classify three-dimensional models.

本发明解决其技术问题所采用的技术方案包括以下步骤:The technical solution adopted by the present invention to solve its technical problems comprises the following steps:

(1)计算三维模型任意两个顶点的测地线距离。本发明通过特征化顶点的距离获取每个三维模型网格的全局特征,利用全局特征训练分类器对新输入的距离特征进行分类。本发明采用三维网格顶点的测地线距离获取三维形状的全局特征,测地线距离不会随着一个三维形状的部分发生弯曲等非刚性变化而改变,也不会随着刚性变换而变化。本发明将三维网格上任意两个顶点的测地线距离的计算转换成带约束的动态规划问题,实际上是从起点出发动态规划一条到达终点的最短路径,获取该路径的长度,从而得到任意两顶点测地线距离。(1) Calculate the geodesic distance between any two vertices of the 3D model. The present invention obtains the global feature of each three-dimensional model grid by characterizing the distance of vertices, and uses the global feature to train a classifier to classify the newly input distance feature. The present invention uses the geodesic distance of the vertices of the three-dimensional grid to obtain the global features of the three-dimensional shape, and the geodesic distance will not change with non-rigid changes such as bending of a part of a three-dimensional shape, nor will it change with rigid transformations . The present invention converts the calculation of the geodesic distance between any two vertices on the three-dimensional grid into a dynamic programming problem with constraints. In fact, it starts from the starting point and dynamically plans a shortest path to the end point, and obtains the length of the path, thereby obtaining The geodesic distance between any two vertices.

(2)测地线距离矩阵的降维和特征分解。因为三维网格任意两顶点可以构成测地线距离矩阵,该矩阵的特征值代表了该三维网格的全局特征,本发明考虑对该测地线距离矩阵进行特征分解。然而,大规模三维网格形状具有N=1M以上的顶点数量,将会构成N*N=1M*1M的高维矩阵,对该矩阵进行特征分解需要O(N3)的计算复杂度,在一个合理的时间内根本无法实现。因此,本发明研究了一种降维方法,该方法目的在于从三维形状的大规模顶点中采样极少的代表性顶点,这些顶点测地线距离构成的低维矩阵与所有顶点构成的高维矩阵的特征分解近似相等,从而避免对高维矩阵进行特征分解的计算压力。然后进一步对测地线距离进行高斯化,其目的在于降低较长的测地线距离对特征分解的影响,增强本分类方法的鲁棒性,最后采用Jacobi方法对低维矩阵进行特征分解。(2) Dimensionality reduction and eigendecomposition of geodesic distance matrix. Because any two vertices of a three-dimensional grid can constitute a geodesic distance matrix, and the eigenvalues of the matrix represent the global characteristics of the three-dimensional grid, the present invention considers the eigendecomposition of the geodesic distance matrix. However, the large-scale 3D grid shape has more than N=1M vertices, which will constitute a high-dimensional matrix of N*N=1M*1M, and the eigendecomposition of this matrix requires a computational complexity of O(N 3 ). It simply cannot be achieved in a reasonable amount of time. Therefore, the present invention has studied a kind of dimensionality reduction method, and this method purpose is to sample very few representative vertices from the large-scale vertices of three-dimensional shape, and the low-dimensional matrix that these vertices geodesic distances form is combined with the high-dimensional matrix that all vertices form The eigendecomposition of matrices is approximately equal, thereby avoiding the computational pressure of performing eigendecomposition on high-dimensional matrices. Then the geodesic distance is further Gaussianized, the purpose of which is to reduce the influence of longer geodesic distance on the eigendecomposition and enhance the robustness of the classification method. Finally, the Jacobi method is used to decompose the low-dimensional matrix.

(3)利用支持向量机构建三维模型特征的二元分类器。本发明将多分类问题化解为多个二元分类器的投票表决问题,采用二元分类器两两组合的方式构成多元分类器。根据提取的样本的特征向量,通过二元分类器进行分类,实现二元分类器的两个类标的输出。本发明通过支持向量机方法构建一个二元分类器,通过利用Lagrange函数求解约束优化问题确定支持向量机的参数,同时引入高斯径向基核函数将样本空间映射到高维,达到线性可分。(3) Using support vector machine to construct binary classifier of 3D model features. The invention resolves the multi-category problem into the voting problem of multiple binary classifiers, and forms the multi-classifier by combining two binary classifiers. According to the feature vector of the extracted sample, it is classified by the binary classifier, and the output of the two class labels of the binary classifier is realized. The invention constructs a binary classifier through the support vector machine method, and determines the parameters of the support vector machine by using the Lagrange function to solve the constraint optimization problem, and simultaneously introduces a Gaussian radial basis kernel function to map the sample space to a high dimension, thereby achieving linear separability.

(4)利用二元分类器组合成多元分类器。本发明采用步骤(3)得到的支持向量机二元分类器的“一对一”两两组合构成多元分类器。因此,对于K分类问题,将K类训练样本两两组合,可构建L=K(K-1)/2个训练集,分别使用支持向量机二元分类器对每对训练集进行学习,产生L个二元分类器。在对测试样本的分类中采用“投票法”来决定分类结果。(4) Combine binary classifiers into multi-class classifiers. The present invention uses the "one-to-one" pairwise combination of the support vector machine binary classifiers obtained in step (3) to form a multi-element classifier. Therefore, for the K classification problem, the K class training samples can be combined in pairs to construct L=K(K-1)/2 training sets, and the support vector machine binary classifier is used to learn each pair of training sets, resulting in L binary classifiers. In the classification of test samples, the "voting method" is used to determine the classification results.

本发明的有益效果是:The beneficial effects of the present invention are:

本发明实现了一种三维模型的自动分类方法,该方法可以提取三维模型的测地线特征,采用支持向量机方法建立二元分类器,根据“投票法”原则由两两组合的多个二元分类器组成一个多元分类器,从而实现三维模型的自动分类。首先,本发明提取的测地线距离可以适应三维模型的刚性变换和非刚性变换,模型的特征提取过程的鲁棒性更强,而且,在测地线距离计算时采用了动态规划方法,提升了计算速度;其次,本发明提出一个降维方法高效计算测地线距离矩阵的特征分解,大大缩短了特征提取的时间;第三,本发明采用支持向量机方法作为二元分类器,优点在于1)可以很好的对应较少的三维模型训练样本状况;2)具有较强泛化性能,提高分类鲁棒性;3)具有很多的核方法支持,使得该分类器具有良好的扩充能力以及非线性性能。实验证明,本发明构成的三维模型自动分类器,具有分类精度高,适用三维模型范围广的特点。The invention realizes an automatic classification method of a three-dimensional model, which can extract the geodesic features of the three-dimensional model, adopt the support vector machine method to establish a binary classifier, and combine multiple binary The meta-classifiers form a multi-class classifier, which enables the automatic classification of 3D models. First of all, the geodesic distance extracted by the present invention can adapt to the rigid transformation and non-rigid transformation of the 3D model, and the feature extraction process of the model is more robust. Moreover, the dynamic programming method is used in the calculation of the geodesic distance, which improves the Secondly, the present invention proposes a dimensionality reduction method to efficiently calculate the eigendecomposition of the geodesic distance matrix, which greatly shortens the time of feature extraction; thirdly, the present invention uses the support vector machine method as a binary classifier, which has the advantage of 1) It can well correspond to the situation of fewer 3D model training samples; 2) It has strong generalization performance and improves the classification robustness; 3) It has a lot of kernel method support, which makes the classifier have good expansion ability and non-linear performance. Experiments have proved that the three-dimensional model automatic classifier constituted by the present invention has the characteristics of high classification accuracy and a wide range of applicable three-dimensional models.

下面结合附图和实施实例对本发明进一步说明。The present invention will be further described below in conjunction with the accompanying drawings and implementation examples.

附图说明 Description of drawings

图1为该发明实现的总流程图;Fig. 1 is the general flowchart that this invention realizes;

图2为本发明提出的测地线距离矩阵的降维方法;Fig. 2 is the dimension reduction method of the geodesic distance matrix proposed by the present invention;

图3为基于支持向量机的分类流程;Fig. 3 is the classification process based on support vector machine;

图4为支持向量机中最优分类面的简单表达形式。Figure 4 is a simple expression of the optimal classification surface in the support vector machine.

具体实施方式 Detailed ways

结合附图,具体实施步骤以下做详细说明。In conjunction with the accompanying drawings, the specific implementation steps are described in detail below.

如附图1所示,本发明实现三维模型自动分类的总流程,该总流程图包含了实现最终分类所需的各个主要步骤。首先,给定一个三维网格模型,计算三维模型任意两个顶点的测地线距离,然后对测地线距离矩阵进行降维和特征分解,得到三维网格模型全局特征,该特征利用支持向量机构建二元分类器对其分类,并采用支持向量机二元分类器的“一对一”两两组合构成多元分类器,利用该多元分类器可以获得分类结果。在测试阶段,可以通过获取的三维网格模型全局特征,输入到支持向量机二元分类器以及多元分类器进行测试。因此,本发明可以实现对三维模型进行自动分类。As shown in Figure 1 , the present invention realizes the general flow of three-dimensional model automatic classification, and the general flow chart includes each main step required to realize the final classification. First, given a 3D grid model, calculate the geodesic distance between any two vertices of the 3D model, then perform dimensionality reduction and eigendecomposition on the geodesic distance matrix to obtain the global features of the 3D grid model, which use the support vector mechanism Build a binary classifier to classify it, and use the "one-to-one" pairwise combination of the support vector machine binary classifier to form a multi-class classifier, and use this multi-class classifier to obtain classification results. In the testing stage, the acquired global features of the 3D grid model can be input to the support vector machine binary classifier and multi-class classifier for testing. Therefore, the present invention can automatically classify three-dimensional models.

结合附图,具体实施步骤以下做详细说明。In conjunction with the accompanying drawings, the specific implementation steps are described in detail below.

一、计算三维模型任意两个顶点的测地线距离。1. Calculate the geodesic distance between any two vertices of the 3D model.

本发明假设待分类的三维模型由多边形网格进行表现,每个网格由顶点、边、多边形根据拓扑关系构成。本发明通过特征化顶点的距离获取每个网格的全局特征,利用全局特征训练分类器对新输入的距离特征进行分类。但是,本发明并没有直接使用顶点的欧式距离进行特征化,原因在于欧式距离无法应对三维网格的非刚性变形,然而,很多三维模型都存在一定的弯曲等柔性变换,因此欧式距离将对非刚性变换鲁棒性较差,直接影响了最终的分类结果,使得本分类器分类精度变差。因此,本发明采用顶点的测地线距离获取三维形状的全局特征,测地线距离不会随着一个三维形状的部分发生弯曲而变化,该距离对于非刚性变换是不变的。The present invention assumes that the three-dimensional model to be classified is represented by polygonal grids, and each grid is composed of vertices, edges, and polygons according to topological relationships. The present invention obtains the global feature of each grid by characterizing the distance of vertices, and uses the global feature to train a classifier to classify the newly input distance feature. However, the present invention does not directly use the Euclidean distance of the vertices for characterization, because the Euclidean distance cannot cope with the non-rigid deformation of the 3D grid. Rigid transformation has poor robustness, which directly affects the final classification result and makes the classification accuracy of this classifier worse. Therefore, the present invention uses the geodesic distance of the vertices to obtain the global features of the three-dimensional shape. The geodesic distance will not change with the bending of a part of the three-dimensional shape, and the distance is invariant to the non-rigid transformation.

三维网格上任意两个顶点的测地线距离实际上是从起点出发动态规划一条到达终点的最短路径。设起点和终点的路径上存在任意两个相邻顶点,分别为vi和vj,起点和终点的最短路径可以用公式表达成一个优化问题:The geodesic distance between any two vertices on the three-dimensional grid is actually the shortest path to the destination dynamically planned from the starting point. Assuming that there are any two adjacent vertices on the path between the start point and the end point, vi and vj respectively, the shortest path between the start point and the end point can be expressed as an optimization problem by formula:

minmin ΣΣ ii ,, jj || vv ii -- vv jj ||

本发明通过求解上述优化问题,从而计算三维网格任意两点的测地线距离。方法如下:The present invention calculates the geodesic distance between any two points of the three-dimensional grid by solving the above optimization problem. Methods as below:

设起始顶点为v0,终止顶点为vn。起点至终点之间的路径上每个顶点vi记录着到起点的测地线距离di,其中di∈R是从起始顶点v0到任意顶点vi的最短路径的长度。vi-1为vi连接的近邻三维网格顶点,其距离用欧式距离衡量。优化问题的表达式如下:Let the start vertex be v 0 and the end vertex be v n . Each vertex v i on the path between the start point and the end point records the geodesic distance d i to the start point, where d i ∈ R is the length of the shortest path from the start vertex v 0 to any vertex v i . v i-1 is the adjacent three-dimensional mesh vertices connected by v i , and its distance is measured by Euclidean distance. The expression of the optimization problem is as follows:

d0=0d 0 =0

di=min(di-1+||vi-1-vi||)d i = min(d i-1 +||v i-1 -v i ||)

本发明采用动态规划方法,利用迭代式规划方式,保证每一步路径最短,动态性的规划出最终结果,该方法可以产生全局最短的路径。该动态规划过程利用宽度搜索来实现,即每次搜索对三维网格顶点的k-近邻进行遍历。本发明采用顶点、边和多边形的近邻存储列表来实现三维网格拓扑结构,在三维网格读入过程创建顶点的近邻列表、边的近邻列表、多边形的近邻列表,而且,顶点的近邻列表包含了近邻顶点、近邻边、近邻多边形,边的近邻列表包含了近邻顶点、近邻边、近邻多边形,多边形的近邻列表包含了近邻多边形。因此k-近邻的遍历仅仅需要O(1)的时间复杂度,可以保证遍历速度足够快,从而增加了动态规划速度。另外,为了进一步加快规划速度,以应对大规模的三维网格,本发明在动态规划的过程中增加了两个约束条件,即满足该约束条件的三维网格顶点优先遍历。The present invention adopts a dynamic programming method and an iterative planning method to ensure the shortest path at each step and dynamically plan the final result, and the method can generate the global shortest path. The dynamic programming process is realized by width search, that is, each search traverses the k-nearest neighbors of the vertices of the three-dimensional grid. The present invention adopts the neighbor storage lists of vertices, edges and polygons to realize the three-dimensional grid topology structure, and creates the neighbor list of vertices, the neighbor list of edges, and the neighbor list of polygons in the three-dimensional grid reading process, and the neighbor list of vertices includes Neighbor vertices, neighbor edges, and neighbor polygons are included. The neighbor list of edges includes neighbor vertices, neighbor edges, and neighbor polygons. The polygon neighbor list includes neighbor polygons. Therefore, the traversal of k-nearest neighbors only needs O(1) time complexity, which can ensure that the traversal speed is fast enough, thereby increasing the dynamic programming speed. In addition, in order to further speed up the planning speed to cope with large-scale three-dimensional grids, the present invention adds two constraint conditions in the process of dynamic programming, that is, the vertices of the three-dimensional grid satisfying the constraint conditions are traversed preferentially.

第一条约束条件为The first constraint is

(vi-vs)·(vt-vs)>0(v i -v s )·(v t -v s )>0

该约束条件实质上约定每次动态规划的规划方向(vi-vs)与起点到终点方向(vt-vs)一致。该方向为优先规划的方向,一旦到达终点即可停止规划,增加该约束条件将大大增加动态规划的速度,使得任意两点测地线距离的计算速度加快。The constraints essentially stipulate that the planning direction (v i -v s ) of each dynamic programming is consistent with the direction (v t -v s ) from the start point to the end point. This direction is the direction of priority planning. Once the end point is reached, the planning can be stopped. Increasing this constraint will greatly increase the speed of dynamic programming, making the calculation of the geodesic distance between any two points faster.

第二条约束条件为The second constraint is

d(vi,vs)≥||vt-vs||2 d(v i ,v s )≥||v t -v s || 2

该约束条件保证,在遍历过程中,两个顶点的测地线距离d(vi,vs)必须大于起终点的欧式距离||vt-vs||2。由于两点欧式距离是空间的最短距离,一定小于等于两点的测地线距离,因此在规划过程中,在还没有达到欧式距离时,无需判定是否已经到达了终点,可以节约时间。This constraint guarantees that during the traversal process, the geodesic distance d(v i , v s ) of two vertices must be greater than the Euclidean distance ||v t -v s || 2 between the start and end points. Since the Euclidean distance between two points is the shortest distance in space, it must be less than or equal to the geodesic distance between two points. Therefore, in the planning process, when the Euclidean distance has not been reached, there is no need to determine whether the end point has been reached, which can save time.

本发明的上述步骤可以快速计算任意两点的测地线距离。The above steps of the present invention can quickly calculate the geodesic distance between any two points.

二、测地线距离矩阵的降维和特征分解。2. Dimensionality reduction and eigendecomposition of geodesic distance matrix.

通过步骤1)计算三维网格任意两顶点的测地线距离,从而构成一个高维矩阵D,其中行和列的索引对应着三维网格顶点的索引,每个矩阵元素代表着任意两个三维网格顶点的测地线距离。因为测地线距离矩阵的特征值代表了该三维网格的全局特征,本发明考虑对该测地线距离矩阵进行特征分解。然而,大规模三维网格形状具有N=1M以上的顶点数量,将会构成N*N=1M*1M的高维矩阵,对该矩阵进行特征分解需要O(N3)的计算复杂度,在一个合理的时间内根本无法实现。因此,本发明研究了一种高维测地线距离的降维方法,该方法目的在于从三维形状的大规模顶点中采样极少的代表性顶点,这些顶点测地线距离构成的低维矩阵与所有顶点构成的高维矩阵的特征分解近似相等,从而避免对高维矩阵进行特征分解的计算压力,大大加快了本发明的训练速度和运行分类速度。如附图2所示,该降维方法步骤如下:Calculate the geodesic distance between any two vertices of the three-dimensional grid through step 1), thereby forming a high-dimensional matrix D, where the index of the row and column corresponds to the index of the vertices of the three-dimensional grid, and each matrix element represents any two three-dimensional The geodesic distance of the mesh vertices. Because the eigenvalues of the geodesic distance matrix represent the global characteristics of the three-dimensional grid, the present invention considers the eigendecomposition of the geodesic distance matrix. However, the large-scale 3D grid shape has more than N=1M vertices, which will constitute a high-dimensional matrix of N*N=1M*1M, and the eigendecomposition of this matrix requires a computational complexity of O(N 3 ). It simply cannot be achieved in a reasonable amount of time. Therefore, the present invention studies a dimensionality reduction method of high-dimensional geodesic distances, the purpose of which is to sample very few representative vertices from large-scale vertices of three-dimensional shapes, and the low-dimensional matrix formed by the geodesic distances of these vertices It is approximately equal to the eigendecomposition of the high-dimensional matrix formed by all vertices, thereby avoiding the calculation pressure of performing eigendecomposition on the high-dimensional matrix, and greatly accelerating the training speed and running classification speed of the present invention. As shown in Figure 2, the steps of the dimensionality reduction method are as follows:

1)计算所有测地线距离的数学期望值,这里d(i,j)是两个顶点索引i和j的测地线距离。1) Calculate the mathematical expectation of all geodesic distances, where d(i, j) is the geodesic distance of two vertex indices i and j.

dm=E[d(i,j)]d m =E[d(i,j)]

2)设降维矩阵为L,初始为空。首先选择测地线距离最大的一对顶点索引(x1,x2),添加到空的降维矩阵L,该降维矩阵变化为:2) Let the dimensionality reduction matrix be L, which is initially empty. First select a pair of vertex indices (x 1 , x 2 ) with the largest geodesic distance and add them to the empty dimensionality reduction matrix L. The dimensionality reduction matrix changes as:

LL == 00 dd (( xx 11 ,, xx 22 )) dd (( xx 22 ,, xx 11 )) 00

3)按照原矩阵索引顺序,遍历网格顶点列表,将满足以下两个条件的顶点索引x与降维矩阵中已选顶点的相应距离追加到矩阵L中。3) Traverse the grid vertex list according to the index order of the original matrix, and add the corresponding distance between the vertex index x and the selected vertex in the dimensionality reduction matrix to the matrix L that meets the following two conditions.

a)该顶点x到矩阵L的所有顶点索引xj的测地线距离大于数学期望值dma) The geodesic distance from the vertex x to all vertex indices x j of the matrix L is greater than the mathematical expectation d m :

dd (( xx ,, xx jj )) >> dd mm ,, ∀∀ jj

b)该顶点x到矩阵L的所有顶点xj的测地线距离之和最大:b) The sum of the geodesic distances from the vertex x to all vertices x j of the matrix L is the largest:

xx == argarg maxmax ΣΣ jj dd (( xx ,, xx jj ))

4)重复步骤3),直到满足以下任意一个停止条件:4) Repeat step 3) until any of the following stop conditions are met:

a)矩阵的顶点个数超过了设定值k。在本专利里设定k=64;a) The number of vertices of the matrix exceeds the set value k. Set k=64 in this patent;

b)已经没有三维网格顶点满足3)步骤所设定的条件。b) There is no 3D grid vertex meeting the conditions set in step 3).

通过上述的降维步骤之后,原始矩阵D的维数降低到k值,很容易在短时间内进行特征分解。然而,在进行了矩阵降维之后,我们进一步对测地线距离进行高斯化,其目的在于降低较长的测地线距离对特征分解的影响,增强本分类方法的鲁棒性。方法如下:After the above-mentioned dimension reduction steps, the dimension of the original matrix D is reduced to k value, and it is easy to perform eigendecomposition in a short time. However, after performing matrix dimensionality reduction, we further Gaussianize the geodesic distance, the purpose of which is to reduce the influence of longer geodesic distance on eigendecomposition and enhance the robustness of this classification method. Methods as below:

dd ijij ′′ == expexp (( -- dd ijij 22 // 22 σσ 22 ))

其中,是dij两点的测地线距离,σ是高斯宽度,d′ij为高斯化的测地线距离。在本专利中,我们定义高斯宽度σ为Among them, is the geodesic distance between two points in d ij , σ is the Gaussian width, and d′ ij is the Gaussianized geodesic distance. In this patent, we define the Gaussian width σ as

σ=max(i,j){dij}σ=max(i,j){d ij }

即所有顶点之间的测地线距离的最大值。将σ定义为这种数据相关的形式可以使最后的特征分解结果做到对均匀缩放不变,本发明定义该值目的在于将测地线距离进行标准化。本发明通过对大量的实验结果的观察可以得知,只要σ足够大,最后的特征分解关于σ是相对稳定的。That is, the maximum value of the geodesic distance between all vertices. Defining σ as this data-dependent form can make the final eigendecomposition result invariant to uniform scaling, and the purpose of defining this value in the present invention is to standardize the geodesic distance. The present invention can be known through the observation of a large number of experimental results, as long as σ is large enough, the final eigendecomposition is relatively stable with respect to σ.

在对测地线距离矩阵进行降维和高斯化之后,本发明对矩阵D进行特征分解,计算其特征值。特征分解式子如下:After performing dimension reduction and Gaussization on the geodesic distance matrix, the present invention performs eigendecomposition on the matrix D and calculates its eigenvalues. The characteristic decomposition formula is as follows:

Dv=λvDv=λv

其中,本专利采用通用的Jacobi方法进行特征分解,将特征值从大到小排序。Among them, this patent adopts the general Jacobi method for eigendecomposition, and sorts the eigenvalues from large to small.

Figure BDA0000139946740000072
Figure BDA0000139946740000072

本发明将特征值构成的向量

Figure BDA0000139946740000073
通过截断(cutoff)方式再次降维,将从设定的c处较小的特征值截断舍弃。在本专利中经过试验观察,设定c=16。降维后的向量
Figure BDA0000139946740000074
将作为本发明分类器的输入特征,通过计算每个样本的输入特征对分类器进行训练,同样,实际运行中,先提取该输入特征,然后输入到已训练完成的分类器对其分类。The present invention forms the vector of eigenvalues
Figure BDA0000139946740000073
The dimension is reduced again by cutoff, and the smaller eigenvalues from the set c are cut off and discarded. Through experimental observation in this patent, c=16 is set. Reduced vector
Figure BDA0000139946740000074
As the input feature of the classifier of the present invention, the classifier is trained by calculating the input feature of each sample. Similarly, in actual operation, the input feature is extracted first, and then input to the trained classifier to classify it.

三、利用支持向量机构建三维模型特征的二元分类器。3. Construct a binary classifier of 3D model features by using support vector machine.

本发明将多分类问题化解为多个二元分类器组合问题。多分类问题和二元分类问题之间存在一定的对应关系。如果一个问题为多类可分,则这多类中任意两类之间一定可分;反之,在一个多分类问题中,如果已知其任意两两可分,则通过一定的组合法则,可由两两可分来最终实现多类可分。不同的组合法则就形成了不同的分类算法,组合法则将在步骤4)详细阐述。本发明提出采用支持向量机方法对步骤2)提取的三维模型特征进行二元分类。基于支持向量机的分类流程如附图3所示,通过步骤2)提取一组三维网格模型的特征作为分类样本,划分为训练集合和测试集合,对本发明的支持向量机进行训练,选择核函数,并通过优化方式选择分类面的法向系数,以及通过支持向量集合确定分类面的偏移参数,以确定分类面,形成二元分类器,然后通过二元分类器组合为多元分类器,对于训练集合和测试集合可以输出分类结果。基于0      支持向量机的二元分类器实现方法如下。The invention resolves the multi-classification problem into a combination problem of multiple binary classifiers. There is a certain correspondence between multi-classification problems and binary classification problems. If a problem is multi-class separable, then any two classes in the multi-class must be separable; on the contrary, in a multi-class problem, if any two of them are known to be separable, then through certain combination rules, it can be obtained by Two-by-two can be separated to finally realize multi-category separability. Different combination rules form different classification algorithms, and the combination rules will be elaborated in step 4). The present invention proposes to use a support vector machine method to perform binary classification on the three-dimensional model features extracted in step 2). As shown in accompanying drawing 3, the classification process based on support vector machine is as shown in accompanying drawing 3, by step 2) the feature of extracting a group of three-dimensional grid model is as classification sample, is divided into training set and test set, support vector machine of the present invention is trained, select kernel function, select the normal coefficient of the classification surface by optimization, and determine the offset parameters of the classification surface through the set of support vectors to determine the classification surface, form a binary classifier, and then combine the binary classifier into a multi-class classifier, Classification results can be output for the training set and test set. The implementation method of binary classifier based on 0 support vector machine is as follows.

假设对于由三维网格模型构成的特征样本集(xi,yi),其中,i∈[1,n],特征xi∈RM,位于M维的特征空间。yi∈{+1,-1}为类别标签。由此特征样本集可得到分类面方程为:Assume that for a feature sample set ( xi , y i ) composed of a three-dimensional mesh model, where i∈[1,n], the feature x i ∈RM is located in an M-dimensional feature space. y i ∈ {+1, -1} is the category label. From this feature sample set, the classification surface equation can be obtained as:

H(x)=ωTx+b=0H(x)=ω T x+b=0

其中ω是M维特征空间的向量,为分类面的法向系数,b是标量,为分类面的偏移参数。利用ω和b可以确定分类面的位置。所构造的分类面需要将两类样本明显的分开,即满足当yi=1时,H(xi)=1,同样,当yi=-1时,H(xi)=-1。Where ω is a vector of M-dimensional feature space, which is the normal coefficient of the classification surface, and b is a scalar, which is the offset parameter of the classification surface. Using ω and b can determine the location of the classification surface. The constructed classification surface needs to clearly separate the two types of samples, that is, when y i =1, H( xi )=1, and similarly, when y i =-1, H(xi ) =-1.

如附图4所示,基于结构风险最小化原则,在将两类样本正确分开的条件下,使分类间隔最大。分类面就位于两条边界线的中间,通过支持向量来确定边界线的点。当支持向量获得后,就不再需要其他的样本,可以缩减样本处理时间。根据几何学的知识,两条边界线的距离为2/||ω||2,本方面采用的方法即利用优化方法获得最大的距离,即最小化本发明考虑到干扰因素,引入松弛变量ξ和惩罚系数C,确定分类面的问题可转化为以下最优问题的求解,引入两个约束条件:As shown in Figure 4, based on the principle of structural risk minimization, the classification interval is maximized under the condition that the two types of samples are correctly separated. The classification surface is located in the middle of the two boundary lines, and the point of the boundary line is determined by the support vector. When the support vector is obtained, no other samples are needed, which can reduce the sample processing time. According to the knowledge of geometry, the distance between two boundary lines is 2/||ω|| 2 , the method adopted in this aspect is to use the optimization method to obtain the maximum distance, that is, to minimize The present invention considers the interference factor, introduces the slack variable ξ and the penalty coefficient C, and the problem of determining the classification surface can be transformed into the solution of the following optimal problem, and introduces two constraints:

yiTxi+b)≥1-ξi y iT x i +b)≥1-ξ i

ξi≥0ξ i ≥ 0

在上述约束下,求函数Under the above constraints, find the function

11 22 || || ωω || || 22 ++ CC ΣΣ ii == 11 NN ξξ ii

的最小值。这个约束优化问题可以通过构造Lagrange函数求解,构造Lagrange函数如下:minimum value. This constrained optimization problem can be solved by constructing a Lagrange function, which is constructed as follows:

QQ (( ωω ,, bb ,, ξξ ,, αα ,, ββ )) == 11 22 || || ωω || || 22 ++ CC ΣΣ ii == 11 NN ξξ ii -- ΣΣ ii == 11 NN αα ii (( ythe y ii (( ωω TT xx ii ++ bb )) -- 11 ++ ξξ ii )) -- ΣΣ ii == 11 NN ββ ii ξξ ii

求解Lagrange函数的最小值,对上述函数关于ω和b求其最小值,这个最小值必在鞍点处求得。因此,该鞍点满足如下条件:Find the minimum value of the Lagrange function, and find the minimum value of the above function with respect to ω and b, and this minimum value must be obtained at the saddle point. Therefore, the saddle point satisfies the following conditions:

∂∂ QQ ∂∂ ωω == 00 ,, ∂∂ QQ ∂∂ bb == 00 ,, ∂∂ QQ ∂∂ ξξ == 00

αi(yiTxi+b)-1+ξi)=0α i (y iT x i +b)-1+ξ i )=0

βiξi=0β i ξ i =0

αi≥0,βi≥0,ξi≥0α i ≥ 0, β i ≥ 0, ξ i ≥ 0

求解得到:Solve to get:

ω = Σ i = 1 N α i y i x i , Σ i = 1 N α i y i = 0 , αii=C ω = Σ i = 1 N α i the y i x i , Σ i = 1 N α i the y i = 0 , α ii =C

代入到Lagrange函数中,得到:Substituting into the Lagrange function, we get:

QQ (( αα )) == ΣΣ ii == 11 NN αα ii -- 11 22 ΣΣ ii == 11 ,, jj == 11 NN αα ii αα jj ythe y ii ythe y jj xx ii TT xx jj

其中系数αi满足where the coefficient α i satisfies

Σ i = 1 N α i y i = 0 , αi≥0 Σ i = 1 N α i the y i = 0 , α i ≥ 0

因此,利用上述最优的分类面参数建立如下的分类判别函数:Therefore, the following classification discriminant function is established by using the above optimal classification surface parameters:

Hh (( xx )) == signsign (( ΣΣ ii ,, jj == 11 NN αα ii ythe y ii (( xx ii TT xx jj )) ++ bb ))

其中,in,

bb == 11 || Uu || ΣΣ ii ∈∈ Uu (( ythe y ii -- ωω TT xx ii ))

这里U表示支持向量集合的元素个数。Here U represents the number of elements in the support vector set.

本发明根据式中H(x)的值的符号,判断样本x所属二元分类的类别。According to the sign of the value of H(x) in the formula, the present invention judges the category of the binary classification to which the sample x belongs.

本发明采用了非线性方法来尝试对三维网格特征进行二元分类,利用非线性向量将三维网格特征映射到高维特征空间,使其线性可分。定义非线性向量The present invention uses a nonlinear method to try to perform binary classification on the three-dimensional grid features, and uses nonlinear vectors to map the three-dimensional grid features to a high-dimensional feature space to make them linearly separable. define nonlinear vector

该向量将m维输入特征x映射到k维特征空间,使其该分类数据在高维特征空间可以线性可分。相应的分类判别函数为:This vector maps the m-dimensional input feature x to the k-dimensional feature space, so that the classification data can be linearly separable in the high-dimensional feature space. The corresponding classification discriminant function is:

Hh (( xx )) == signsign (( ΣΣ ii ,, jj == 11 NN αα ii ythe y ii (( ΦΦ TT (( xx ii )) ·· ΦΦ (( xx jj )) )) ++ bb ))

我们考虑引入核函数K(xi·x)解决上式中高维计算引发计算复杂和过学习问题。只要在输入空间找到一个满足Mercer条件的适当的核函数,就可以用该核函数来代替高维特征空间的内积运算,所构造的最优分类面的判别函数为:We consider introducing the kernel function K( xi x) to solve the computational complexity and over-learning problems caused by high-dimensional calculation in the above formula. As long as an appropriate kernel function that satisfies the Mercer condition is found in the input space, the kernel function can be used to replace the inner product operation of the high-dimensional feature space. The discriminant function of the constructed optimal classification surface is:

Hh KK (( xx )) == signsign (( ΣΣ ii ,, jj == 11 NN αα ii ythe y ii KK (( xx ii ·· xx )) ++ bb ))

本发明尝试了三种常用的核函数,包括线性核函数、高斯径向基核函数以及Sigmoid核函数。其中线性核函数表达式如下The present invention tries three common kernel functions, including linear kernel function, Gaussian radial basis kernel function and Sigmoid kernel function. The expression of the linear kernel function is as follows

K(xi·xj)=xi·xj K(x i ·x j )=x i ·x j

高斯径向基函数表达式如下:The Gaussian radial basis function expression is as follows:

KK (( xx ii ·&Center Dot; xx jj )) == expexp {{ -- || || xx ii -- xx jj || || 22 22 σσ 22 }}

其中σ是样本的方差。where σ is the variance of the sample.

Sigmoid核函数的表达式如下:The expression of the Sigmoid kernel function is as follows:

K(xi·xj)=tanh{gxi·xj-h}K(x i ·x j )=tanh{gx i ·x j -h}

它构成多层感知器神经网络,其中参数g为比例因子,h为偏移因子。It constitutes a multi-layer perceptron neural network, where the parameter g is the scaling factor and h is the offset factor.

通过试验发现,高斯径向基的核函数给出了较好的分类性能,因此,本发明采用高斯径向基函数作为支持向量机的核函数。It is found through experiments that the kernel function of the Gaussian radial basis provides better classification performance, so the present invention adopts the Gaussian radial basis function as the kernel function of the support vector machine.

四、利用二元分类器组合成多元分类器4. Combining binary classifiers into multivariate classifiers

由于三维形状分类问题主要集中在多分类,本发明采用步骤3)构建的二元分类器组合成一个多元分类器。通常,多分类方法主要有:一对一,一对多和有向无环图。其中一对一分类法是较好的多分类法,适用于实际应用,并且计算效率较高,两类样本趋于平衡,使分类判别更趋合理化。本发明使用的是一对一分类法。对于K分类问题,将K类训练样本两两组合,可构建L=K(K-1)/2个训练集,分别使用支持向量机二元分类器对每对训练集进行学习,产生L个二元分类器。在对测试样本的分类中采用“投票法”:将测试样本输入由K类样本构造的L个二元分类器,如果样本x输出结果判定为该类,给该类加一票。所有L个二元分类器对测试样本分类后,K类中哪一类得票最多,就判定测试样本属于哪一类。从而,本发明实现了一个三维模型的自动分类方法。Since the three-dimensional shape classification problem mainly focuses on multi-classification, the present invention combines the binary classifiers constructed in step 3) into a multi-class classifier. Usually, multi-classification methods mainly include: one-to-one, one-to-many and directed acyclic graph. Among them, the one-to-one classification method is a better multi-classification method, which is suitable for practical applications and has high calculation efficiency. The two types of samples tend to be balanced, which makes the classification and discrimination more reasonable. The present invention uses a one-to-one classification method. For the K classification problem, the K-class training samples are combined in pairs to construct L=K(K-1)/2 training sets, and each pair of training sets is learned using the support vector machine binary classifier to generate L Binary classifier. The "voting method" is adopted in the classification of test samples: input the test samples into L binary classifiers constructed from K class samples, if the output result of sample x is judged to be of this class, add one vote to this class. After all L binary classifiers classify the test samples, which one of the K classes gets the most votes will determine which class the test samples belong to. Thus, the present invention implements an automatic classification method for three-dimensional models.

本发明效果可以通过以下实验进一步说明。实验数据集来自加拿大McGillUniversity Shape Benchmark,该三维模型数据集共包含10类通用形状,包括动物、人、机械等,具体类别见表1。本发明将该数据集分为训练集和测试集。训练集合包含10类形状,每类10个模型,共100个模型。测试集合包含10类形状,每类10个模型,共100个模型。在训练集上训练得到多元分类器,在测试集上评估多元分类器的分类结果。训练时,把训练集的10类形状分别分配各自的类标,取其中任意两类的样本值进行训练学习,这样就可以得到一个由45个二元分类器组成的多元分类器。测试时将10类样本值依次输入该多元分类器就可以得到所有的分类结果。对分类结果进行统计,统计结果如表1所示,其中误差率和正确率分别是指分类错误和分类正确的三维模型的数目占分类模型总数目的百分比。The effect of the present invention can be further illustrated by the following experiments. The experimental data set comes from McGillUniversity Shape Benchmark, Canada. The 3D model data set contains 10 types of general shapes, including animals, humans, machinery, etc. The specific categories are shown in Table 1. The present invention divides the data set into a training set and a test set. The training set contains 10 categories of shapes, 10 models in each category, and a total of 100 models. The test set contains 10 categories of shapes, 10 models in each category, and a total of 100 models. A multi-classifier is trained on the training set, and the classification results of the multi-classifier are evaluated on the test set. During training, the 10 types of shapes in the training set are assigned their respective class labels, and the sample values of any two types are taken for training and learning, so that a multi-classifier composed of 45 binary classifiers can be obtained. During the test, all the classification results can be obtained by inputting the sample values of 10 categories into the multivariate classifier in sequence. The classification results are counted, and the statistical results are shown in Table 1, where the error rate and the correct rate refer to the percentages of the number of 3D models that are classified incorrectly and correctly classified to the total number of classified models.

表1本发明在三维模型测试集上的分类精度Table 1 The classification accuracy of the present invention on the three-dimensional model test set

从分类结果中可以看出,本发明提出的三维模型自动分类方法的分类精度达到86%,这在现有的三维模型分类方法中具有一定的优越性,具有良好的分类的性能,同时,应对复杂通用模型和非刚性变换具有较强的鲁棒性。以上整体所述是本发明的优选实施方式,本领域技术人员在不脱离本发明原理的前提下,可以做出若干改进,包括改变支持向量机的核函数等,本发明的范围由所附权利要求书及其等同限定。As can be seen from the classification results, the classification accuracy of the three-dimensional model automatic classification method proposed by the present invention reaches 86%, which has certain advantages in the existing three-dimensional model classification method, and has good classification performance. It is robust to complex general models and non-rigid transformations. The above overall description is a preferred embodiment of the present invention. Those skilled in the art can make some improvements without departing from the principle of the present invention, including changing the kernel function of the support vector machine, etc. The scope of the present invention is defined by the appended rights Requirements and their equivalents.

Claims (1)

1. A three-dimensional model automatic classification method based on a support vector machine is characterized by comprising the following steps:
(1) obtaining the global characteristics of each three-dimensional model mesh through the distance of the characteristic peak, and classifying the newly input distance characteristics by using a global characteristic training classifier;
(2) sampling few representative vertexes from large-scale vertexes of the three-dimensional shape, wherein the characteristic decomposition of a low-dimensional matrix formed by the vertex geodesic distances is approximately equal to that of a high-dimensional matrix formed by all the vertexes, further Gaussian processing is carried out on the geodesic distances, and finally, a Jacobi method is adopted to carry out characteristic decomposition on the low-dimensional matrix;
(3) the method comprises the steps of establishing a binary classifier of three-dimensional model features by using a support vector mechanism, establishing a binary classifier by using a support vector machine method, determining parameters of the support vector machine by solving a constraint optimization problem by using a Lagrange function, and simultaneously introducing a Gaussian radial basis kernel function to map a sample space to a high dimension to achieve linear divisibility; classifying through a binary classifier according to the extracted feature vector of the sample to realize the output of two class labels of the binary classifier; forming a multi-element classifier by combining two binary classifiers in pairs;
(4) combining every two of the support vector machine binary classifiers obtained in the step (3) one to form a multivariate classifier, combining every two of K training samples to solve the K classification problem, constructing L (K-1)2 training sets, and learning each pair of training sets by using the support vector machine binary classifiers respectively to generate L binary classifiers; voting is used in classifying the test samples to determine the classification result.
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