基于等距特征映射算法在人脸识别问题中的数学建模

Mathematical Modeling of Face Recognition Based on Isometric Feature Mapping Algorithm

该文梳理了人脸识别技术的相关研究文献,并以FG-NET人脸数据库为样本库,对随机选取的实验分析对象进行预处理后,建立合理的数学模型.通过等距特征映射(ISOMAP)算法进行非线性降维,将高维空间的数据信息映射到低维空间,再通过特征提取的方法来判别图像的相似度.该算法以多维尺度变换(MDS)为基础,将欧氏距离替换为数据点间的测地线距离,使数据信息在降维后损失最小,实现高维空间的数据信息在低维空间的有效表达,在较大减小计算量的基础上,提高图像识别率.同时,运用MATLAB软件进行编程验证,结果表明,同一个人在不同年龄段的人脸识别率达到了88.89%,不同人在不同年龄段的人脸识别率达到了91.67%.

This paper combs the relevant research literature of face recognition technology,and based on the FG-NET face database,we establish a reasonable mathematical model after pre-processing the randomly selected experimental analysis image.The equidistant feature mapping(ISOMAP)algorithm is used to reduce the dimension of nonlinearity,and the data information in the high-dimensional space is mapped to the low-dimensional space.Then the similarity of the image is discriminated by the method of feature extraction.The algorithm is based on the multidimensional scale transformation(MDS),replacing the Euclidean distance with the geodesic distance between data points,minimizing the loss of data information after dimension reduction,and effectively expressing the data in high dimensional space in low dimensional space.Information,to achieve greater reduction in the amount of calculation on the basis of improving image recognition rate.At the same time,using MATLAB software to verify the program,the results show that face recognition rate of the same person in different ages reaches 88.89%,face recognition rate of different people in different ages is 91.67%.