Isomap对人脸图像的降维处理  

Isomap dimensionality reduction processing of face images

作　　者：刘瑞银[1] 张汇洋 LIU Ruiyin;ZHANG Huiyang(College of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《沈阳师范大学学报（自然科学版）》2024年第4期346-349,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11401393)。

摘　　要：人脸图像数据常常由几千或几万个像素点组成,每个像素点都代表一个特征。在进行人脸识别、图像分类等任务时,若使用全部像素点,会导致特征维度非常高,进而造成分析处理数据效率低下、储存成本过高等问题,此时对数据进行降维就极为重要。等距特征映射(isometric feature mapping,Isomap)是流形学习中一个非线性降维方法。对于人脸这样的高维流形结构,Isomap可以找到最优的低维表示,并保持原始数据之间的拓扑关系,从而更好地捕捉数据的局部结构和流形特征,例如人脸的表情、姿态、光照等因素。利用Isomap方法对jaffe人脸数据集中的部分人脸灰度图像进行降维处理,对高维数据进行可视化,得到该组数据的各个表情的位置分布,以此来展示Isomap对人脸图像数据的降维效果。Face image data is often made up of thousands or tens of thousands of pixels,each of which represents a feature.When performing tasks such as face recognition and image classification,if all pixels are used,the feature dimension will be very high,which will lead to problems such as low efficiency and high storage cost of data analysis and processing,so it is extremely important to reduce the dimensionality of data.Isometric feature mapping(Isomap)is a nonlinear dimensionality reduction method in manifold learning.For high-dimensional manifold structures such as human faces,Isomap can find the optimal low-dimensional representations and maintain the topological relationship between the original data,so as to better capture the local structure and manifold features of the data,such as facial expressions,postures,lighting,and other factors.In this paper,the Isomap method was used to reduce the dimensionality of some face grayscale images in the jaffe face dataset,and the high-dimensional data were visualized to obtain the position distribution of each expression in this group of data,so as to demonstrate the dimensionality reduction effect of Isomap on the face image data.

关 键 词：人脸图像 降维 等距特征映射 可视化 

分 类 号：O212[理学—概率论与数理统计]