局部k最近邻加权线性回归的光谱反射率重建  

Research on Spectral Reflectance Estimation Using Locally Weighted Linear Regression within k-Nearest Neighbors

作　　者：卢德俊 爨凯旋 张伟峰[1] LU De-jun;CUAN Kai-xuan;ZHANG Wei-feng(School of Mathematics&Informatics,South China Agricultural University,Guan gzhou 510642,China)

机构地区：[1]华南农业大学数学与信息学院,广东广州510642

出　　处：《光谱学与光谱分析》2018年第12期3708-3712,共5页Spectroscopy and Spectral Analysis

基　　金：国家自然科学基金项目(61375006;91746102);广东省优秀青年教师培养计划(Yq2013032)资助

摘　　要：现实中很多场景都需要精确的颜色表示,如纺织、印刷、艺术品扫描存档、在线商品展示等。光谱反射率是决定物体颜色的本质属性,如果知道了光谱反射率,就可以重现物体在任何光照和观测条件下的颜色。采用专业仪器测量光谱反射率有成本高、分辨率低、测量时间慢等问题。随着数码成像设备的普及,基于相机RGB响应值的光谱反射率重建算法具有重要现实意义。光谱反射率重建的目的是建立低维RGB响应值到高维光谱反射率向量的映射关系,回归方法在这一领域已取得广泛应用。由于光谱反射率向量所处的空间是嵌在高维欧氏空间中的一个低维子流形,在训练样本有限的条件下,传统的全局回归方法不能有效地学习该流形结构,往往导致过拟合,使得学习出来的模型泛化能力较差。局部线性回归方法虽然可以改善全局回归过拟合的问题,但是局部学习方法易受例外点的影响,导致拟合不足。针对这一问题,提出一种基于局部加权线性回归的光谱反射率重建方法,这种方法在一个k最近邻范围约束内,给每个局部训练样本赋予不同的权重,从而有所侧重地利用局部训练样本来估计光谱反射率。实验结果表明,基于局部k最近邻加权线性回归的方法能更有效地利用局部信息,缓解过拟合和拟合不足,更准确地重建光谱反射率。Many real applications require accurate color re production,such as textile,printing,art painting archiving and online product exhibition.The most accurate and informative way to represent a natural object’s color is to use its spectral reflectance.However,the very professional meas uring instrument of spectrophotometer has the drawbacks of being expensive and h aving low measuring resolution and slow measuring speed.As digital cameras have become the most widely used devices for color acquisition,developing accurate reflectance estimation methods from RGB responses has received increasing attent ion.The aim of spectral reflectance estimation is to build estimation function between RGB tristimulus values and the spectral reflectance vector from training samples.Regression methods have been widely used for this problem.Recent stud ies have shown that natural objects’reflectance resides on a lower dimensional submanifold which is embedded in the high-dimensional ambient Euclidean space.Due to the limitation of high dimensional and low training sample size,previous global regression approaches could not exploit the local manifold structure wel l and are prone to be over-fitting.Local linear regression method can improve the problem of overfitting,but the local learning method is susceptible to the influence of outliers,which will lead to under-fitting.Aiming at this problem,this paper proposes a spectral reflectance estimation method based on locally weighted linear regression,which gives different weights to each local training sample within a k-nearest neighbor constraint.The experimental results sh ow that the method based on locally weighted linear regression can make more eff ective use of local information,alleviate the over-fitting and under-fitting and reconstruct the spectral reflectance more accurately.

关 键 词：光谱反射率重建 局部加权线性回归 k最近邻 权值函数 

分 类 号：TH744[机械工程—光学工程]