中文摘要：

探讨抛物线、双曲线、椭圆3种非线性Radon变换及其性质，分析它们之间的关系，并将所述3种非线性Radon变换应用于人脸识别．通过对这3种非线性Radon变换及其性质研究得出，当抛物线、双曲线及椭圆的形状参数趋于无穷大时，图像抛物线Radon变换与线性Radon变换相等，双曲线Radon变换与椭圆Radon变换相等；同时，非线性Radon变换具有降噪功能和表达图像纹理特征的特点．文中将受噪声污染的人脸图像分别表示为3种非线性Radon变换下的特征矩阵，并结合PCA算法应用于人脸识别．实验结果表明非线性Radon变换在人脸识别中的有效性．

英文摘要：

Three nonlinear Radon transforms, including parabola, hyperbola, and ellipse Radon transform, are studied respectively, and the relationships among them are analyzed. Then, the three nonlinear Radon transforms are applied to face recognition. When shape parameters of parabola, hyperbola, and ellipse are approximately infinite, linear Radon transform of image is equal to parabola Radon transform and hyperbola Radon transform is equal to ellipse Radon transform. Nonlinear Radon transform possesses the characters of reducing noise and can be used to represent texture features of image. Moreover, polluted face images are represented by feature matrix via three nonlinear Radon transforms, and then combined with principal component analysis in face recognition. Experimental results demonstrate the validity of nonlinear Radon transform in face recognition.