Abstract Feathers are the main raw material of shuttlecock. The quality of feather is a key factor in shuttlecock production and detection of feather defects is a challenging problem. In this paper, an automatic detection for feather defects was proposed that relies on fuzzy, Lie Group and machine learning theory. First, the feather images were enhanced using fuzzy set. Then, a covariance matrix was constructed as features of the defect region and Riemannian metric was assigned on a Riemannian manifold with a Lie group structure. The mean covariance matrix with nonsymmetric structure was proved to have a Lie group structure. To establish the automatic detection of feather defects, this study introduced Riemann mean and membership degree into the machine learning method of Fisher linear discriminant to implement feature recognition. Experiments were performed to demonstrate the feasibility of features of defect region as a differential manifold.

中文翻译：

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基于李群和模糊Fisher判据的羽毛球生产羽毛缺陷自动检测

摘要 羽毛是羽毛球的主要原料。羽毛质量是羽毛球生产的关键因素，检测羽毛缺陷是一个具有挑战性的问题。本文提出了一种基于模糊、李群和机器学习理论的羽毛缺陷自动检测方法。首先，使用模糊集增强羽毛图像。然后，构建协方差矩阵作为缺陷区域的特征，并在具有李群结构的黎曼流形上分配黎曼度量。证明非对称结构的平均协方差矩阵具有李群结构。为了建立羽毛缺陷的自动检测，本研究将黎曼均值和隶属度引入到Fisher线性判别的机器学习方法中来实现特征识别。