﻿ 基于学习的网格特征边界边识别 Learning-Based Identification for Feature Boundary Edges of Meshes

Computer Science and Application
Vol.08 No.04(2018), Article ID:24529,9 pages
10.12677/CSA.2018.84054

Learning-Based Identification for Feature Boundary Edges of Meshes

Baiyun Zhang, Yingzhong Zhang, Xiaofang Luo

School of Mechanical Engineering, Dalian University of Technology, Dalian Liaoning

Received: Apr. 4th, 2018; accepted: Apr. 19th, 2018; published: Apr. 26th, 2018

ABSTRACT

Feature boundary edge recognition is the basis for subsequent applications of complex triangular mesh models. It is difficult to identify feature edges that can meet actual requirements by using single threshold and decision rules. In this paper, the geometric characteristics of the feature boundary edge are analyzed. Based on the machine learning method, a learning-based method for identifying feature boundary edges of triangular mesh model is proposed and implemented. In this method, the feature boundary edge recognition is formalized as the classification problem of triangular edges. A 17-dimensional eigenvector to describe the geometric characteristics of feature boundary edges is analyzed and constructed, which consists of a dihedral angle, curvatures and a shape diameter. The eigenvector training data set is obtained by manual annotation, and is inputted into the general BP-AdaBoost classifier to train it in order to make it have the capability to identify feature boundary edges. The trained BP-AdaBoost classifier can identify the feature boundary edges correctly. It is proved by examples that the identification result is in line with the expectation.

Keywords:Triangular Mesh Model, Feature Boundary Edge, Machine Learning, Curvature, BP-AdaBoost Classifier

1. 引言

2. 特征边的几何特征分析

2.1. 特征边界线

Figure 1. Triangular mesh model and feature boundary line of gear parts

2.2. 特征边界线的几何特征

2.2.1. 主要几何特征

1) 二面角(Dihedral angle)：两个三角形面之间的夹角。在三角网格模型中，通常特征边界边处的二面角都小于平坦处的二面角，即二面角小于某一给定阈值的边可能是边界边，反之，则不是。

2) 曲率(Curvature)：曲线的曲率就是针对曲线上某个点的切线方向角对弧长的转动率，通过微分来定义，它表明了曲线偏离直线的程度，曲率是几何体不平坦程度的一种衡量。在三维欧氏空间中的曲线和曲面的曲率有平均曲率、主曲率和高斯曲率三个基本要素。

3) 形状直径：SDF [11] 定义在三维模型表面每个点上的一个实值函数，它反映了网格表面上每个面到网格对面的距离。在三角网格模型中，特征边界边处边界边顶点的形状直径较大。

2.2.2. 特征边界线识别问题

3. 基于学习的特征边界识别

3.1. 识别方法的总体方案

1) 特征边界识别学习模型

2) 特征边界识别模型

3.2. 几何特征向量

Figure 2. Learning-Based feature boundary recognition scheme

1) 二面角

2) 曲率

3) 形状直径和全局曲率

3.3. 学习训练数据

1) 读入STL或其他格式的网格模型文件；

2) 系统内构建一个基于面的网格拓扑模型，将STL网格文件读入后，系统重构网格顶点、边和三角面之间的拓扑关系，从而可以高效地查询各个网格元素。

Figure 3. Feature edge geometric feature vector selection

Figure 4. Manual marking window for training data

3) 采用OpenGL技术实现了一个对网格模型标记的交互工具，例如边鼠标选择和自动捕捉、模型缩放和旋转、模型渲染和边界绘制等。

4) 对标记选择边自动计算出上述17个特征值的特征向量，能将训练数据保存输出在一个关系表中。

1) 数据选择和网络初始化

2) 弱分类器(BP网络节点)训练

(1)

3) 计算预测弱分类器序列权重，并根据测试数据进行权重调整

(2)

4) 组合得到强分类函数

(3)

1) 网格预处理。首先将要识别的网格模型输入进行预处理，将所有两面角小于10度(10度为特征边最低阈值，可以修改)的三角边过滤，没有必要参与识别，大大减少了识别的数据量。

2) 几何特征向量计算。对参与识别三角边，按照上述方法计算该边的17维特征向量，获得一组由边标识的特征向量组。

3) 将边标识的特征向量组输入训练后的分类器，获得是否是特征边分类结果。

4) 连接相邻分类为特征边的三角边形成特征边段，最后对分类特征边段细化、连接和样条拟合，输出识别的特征边界。

4. 识别实验

Figure 6. The identification process of feature boundary based on classifier

5. 结束语

Learning-Based Identification for Feature Boundary Edges of Meshes[J]. 计算机科学与应用, 2018, 08(04): 487-495. https://doi.org/10.12677/CSA.2018.84054

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