折痕识别中的李群核研究

Research on Lie Group Kernel in Feather Quill Crease Recognition

针对毛杆折痕难以检测问题,提出了一种基于均值协方差描述子和李群核的折痕识别方法。均值协方差描述子是目标图像的特征模型,可以将各种类型特征自然地融入统一的特征模型中,实现了基于多特征的折痕识别。由于构建的均值协方差矩阵不具有对称结构,首先证明其具有李群结构,并赋予具有双不变度量性质的Log-Euclidean黎曼度量。推导了黎曼流形中内积空间的度量形式,给出李群核函数表达式,并以此设计了基于李群核的识别算法。实验结果表明均值协方差矩阵比协方差矩阵更适合构建折痕特征;而且该算法具有更好的线性可分性。

Aiming at the detection difficult problem of feather quill crease, an algorithm for feather quill crease recognition was proposed based on mean covariance descriptor and manifold kernel. Mean region covariance descriptor was employed to represent the object which enables efficient fusion of different types of features and modalities into a unified feature model, used as multi-cue integration for crease recognition. Due to that mean covariance matrix is not symmetric, we first proved that mean covariance matrix forms a Lie group. Based on Lie group theory, geodesic distance can be computed between two group elements in the Log-Euclidean framework with double invariance properties. Then this article designed recognition algorithm based on Lie group kernel with metrics of inner product space and manifold kernel function expres- sion which were deduced. The experiment section gave classification comparison through the algorithm in separate methods using mean eovariance matrix and covariance matrix. The results show that mean eovari- ante matrix is more suitable for constructing feather quill crease features and the proposed algorithm has better linear distribution.