Nonlinear Unmixing Method Of Mixed Pigment On Improved N-FINDR And Polynomial Post-nonlinear Model

Painted artifacts are an important part of cultural heritage.Artists use different pigments to paint the surface to form vivid colors and patterns.The pigments are an important material that constitute rich information on the surface of painted artifacts.In the field of protection and restoration,it is necessary to accurately know the types of pigments,so that workers can formulate reasonable and scientific restoration plans based on the results of pigment identification.This is because in the process of painting,artists often use painting skills to mix different pigments.Therefore,there is a phenomenon of pigment mixing on the surface of cultural relics,which brings challenges to the pigment identification and color restoration.Using hyperspectral technology to identification pigment has hence been a research hotpot.In order to determine the types of pigments,the method of hyperspectral unmixing is usually used.Due to the simplicity of the linear spectral model and the clear physical meaning,the pigment unmixing is mostly based on the linear spectral model.But the complexity of pigment mixing brings difficulties to the unmixing of pigments,and the precision is not high.Based on this,this paper aims to achieve nonlinear unmixing of mixed pigments from the perspective of both spectral mixing models and nonlinear dimensionality reduction of data to obtain higher accuracy of pigment abundance.To determine the type of unknown pigments,we selected commonly used painting pigments and constructed a pigment spectral library as the basis for pigment identification.Pigment unmixing can obtain the spectra and proportions of pigment endmembers in the mixed pigment spectrum.First,five endmember extraction methods based on geometric simplex were studied,and a better method was obtained.Secondly,we started by studying the spectral characteristics of different types of mixed pigments,and then compared the unmixing accuracy of the linear spectral model and the nonlinear spectral models.Finally,the locally linear embedding(LLE)non-linear dimensionality reduction method is introduced,and a non-linear unmixing method based on an improved N-FINDR and polynomial posterior model is proposed.It is also applied to hyperspectral images of Chinese paintings and frescoes to determine the types and proportions of pigments on the painting surfaces.The main research results are as follows:(1)Construction a pigment spectral library.Commonly used pigments are selected,and three different types of pigment samples are obtained according the substrates,including powder or lump samples,paper samples,and fresco samples.Then,ASD Field Spec 4 spectroradiometer was used to obtain the reflectance spectra of pigment samples,covering the wavelength range of visible light-short-wave infrared(350-2500nm).Based on this,a pigment spectral library was established.In addition,the chemical composition of mineral pigments was detected by a portable fluorometer Thermo Fisher XL3T900.Finally,all pigment samples data were integrated into the pigment spectral library system for management.(2)Study on the method of endmember extraction of mixed pigments.The reflectance spectra of five mineral pigments were obtained,and hyperspectral images were simulated according to different conditions.Then,five endmember extraction methods were used to obtain the endmembers spectra,which were compared with the real pigment spectra.Finally,the result showed that the endmember extraction based on simplex identification via split augmented lagrangian(SISAL)and minimum volume constrained non-negative matrix factorization(MVC-NMF)can obtain higher precision.(3)Study on the nonlinear spectral mixing model.Mixed pigments sample used five mineral pigments were made in the laboratory,and the reflectance spectra were measured.The abundance of pure pigments in mixed pigments were calculated using linear spectral model and nonlinear spectral models.The results showed that the spectral mixing of different types of pigments are more in line with nonlinear,and the unmixing accuracy of the nonlinear spectral model are higher,especially the polynomial post-nonlinear model(PPNM).Finally,a Chinese painting was used for verification,and the types and proportions of pigments in the mixed area on the surface of the Chinese painting were obtained.(4)A nonlinear unmixing method combining N-FINDR and PPNM models based on local linear embedding is proposed.A non-linear mixed pigment unmixing method is proposed based on the complex mixing of pigments on the surface of artefacts and the existence of non-linear effects in the mixed pigments spectra.Firstly,by introducing the LLE method,a non-linear endmember extraction method is obtained by improving on the original N-FINDR.The method is also used to obtain the endmembers spectra of pigments in mixed pigments.Then,the constructed pigment spectral library is used to determine the type of pigment by the spectral identification method.Finally,PPNM was used to perform non-linear unmixing to obtain abundance maps of the different pigments.The application was demonstrated with hyperspectral images of Chinese paintings and murals,and the results showed that the unmixing method is able to obtain higher accuracy endmembers spectra and pigment abundance maps.