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基于张量投票的去噪特征提取

Denoised Feature Extraction Based on the Tensor Voting Theory

作者: 专业:计算数学 导师:李崇君 年度:2010 学位:硕士  院校: 大连理工大学

Keywords

Tensor Voting Theory, Feature Point, Principal Curvature, Principal Direction, Robust Detection, Contextual Feature

        曲面上的特征线具有很好的几何背景。特征线,即曲面上曲率变化剧烈的曲线,是曲面特征的重要标志。由于特征线及其子集在诸如图像分析,人脸识别,曲面分割,网格光顺以及网格补洞等众多领域都有很广泛的应用,因此鲁棒的提取出特征线通常是一件很重要的事情。近期出现了很多在密集三角网格上提取特征线的算法,而精确的估算三角网格上的离散主曲率是提取特征线的关键所在。估算主曲率的方法有很多,如全局拟合估算主曲率和运用差分估算主曲率。在一般情况下,为估算主曲率首先要建立一个局部坐标系,而后续的计算都是在该局部坐标系下进行的。由于是局部坐标,一般的算法很难在具有噪声的网格上准确的提取出特征来。本文讨论了一个基于张量投票的提取特征的鲁棒性算法。张量投票的特征提取算法可以将特征点区分为角点,尖锐的边点以及面点。在用张量投票提取特征时,我们加入了对关联特征的应用,即计算中用到网格点周围的信息。由于加入了网格点周围点的信息,在估算主曲率时,算法不再具有局部性,从而就能提取出网格中对应于重要特征的特征线,并且这样的算法具有抗噪特性。数值实验表明此算法是有效的,并且能达到较好的效果。
    Crest lines have a nice mathematical background. Crest lines, as curves on a surface along which the surface bends sharply, are powerful shape descriptors. Because crest lines and their subsets have numerous applications in image analysis, face recognition, smoothing, surface segmentation and hole-filling, robust extraction of crest lines is a very important issue.Recently, some algorithms for the detection of crest lines on dense triangle meshes have been presented. Reliable computations of discrete principal curvature measures on meshes are key to the detection of crest lines. In general, in order to estimate the principal curvature of a point, we need a local coordinate system, which are followed by all subsequent calculations. Owing to over-locality, it is inadequate to detect significant crest lines from a noise model. In this paper, a method is discussed for robust detection of crest lines. The method is based on the tensor voting theory. It classifies a feature into a corner, a sharp edge and a face. We have made improvements by incorporating the method with contextual information, the attributes of neighboring points. So it provides a basis for robustly detecting salient crest lines corresponding to potentially important features. Consequently, the algorithm is immune to noisy mesh. Comparative results indicate that our algorithm yields favorable detection results and is effective.
        

基于张量投票的去噪特征提取

摘要4-5
Abstract5
引言8-11
1 基础知识11-20
    1.1 曲面曲率的基本知识11-15
        1.1.1 光滑曲线曲面的曲率11-13
        1.1.2 离散曲率估计相关的定理定义13-15
        1.1.3 Weingarten矩阵15
    1.2 曲率表示的特征15-16
    1.3 三角网格基本知识16-20
2 特征提取方法总结20-30
    2.1 基于张量投票的特征提取20-22
        2.1.1 法向张量投票矩阵20-21
        2.1.2 法向张量投票矩阵的特征值分析21-22
    2.2 需要估算曲率的特征提取方法22-26
        2.2.1 全局拟合的特征提取方法22-24
        2.2.2 局部拟合的特征提取方法24-26
    2.3 基于有限差分曲率估算的特征提取26-29
        2.3.1 计算每个面的第二基本形式27-28
        2.3.2 坐标转换并加权平均28
        2.3.3 估算主曲率沿主方向的方向导数28-29
    本章小结29-30
3 关联特征的去噪特征提取30-33
    3.1 局部特征和关联特征30
    3.2 关联特征过滤30-31
    3.2 连接特征线31-33
4 数值实验33-37
结论37-38
参考文献38-41
攻读硕士学位期间发表学术论文情况41-42
致谢42-44
        
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