A Novel Spectral Matching Approach for Pigment: Spectral Subsection Identiﬁcation Considering Ion Absorption Characteristics

remote sensing

Article A Novel Spectral Matching Approach for Pigment: Spectral Subsection Identiﬁcation Considering Ion Absorption Characteristics

Yiyi Liu 1,2, Shuqiang Lyu 1,2,*, Miaole Hou 1,2 , Zhenhua Gao 1,2, Wanfu Wang 3,4 and Xiao Zhou 5

1 School of Geomatics and Urban Spatial Informatics, Beijing University of Civil Engineering and Architecture, No.15 Yongyuan Road, Daxing District, Beijing 102616, China; [email protected] (Y.L.); [email protected] (M.H.); [email protected] (Z.G.) 2 Beijing Key Laboratory for Architectural Heritage Fine Reconstruction & Health Monitoring, No.15 Yongyuan Road, Daxing District, Beijing 102616, China 3 The Conservation Institute of Dunhuang Academy, Dunhuang, Gansu 736200, China; [email protected] 4 National Research Center for Conservation of Ancient Wall Paintings and Earthen Sites, Dunhuang Academy, Dunhuang, Gansu 736200, China 5 Chinese Academy of Cultural Heritage, Beijing 100029, China; [email protected] * Correspondence: [email protected]; Tel.: +86-13671298885

Received: 16 September 2020; Accepted: 15 October 2020; Published: 18 October 2020

Abstract: Background: Hyperspectral technology has made it possible to perform completely non-invasive investigations on pigment analysis, in particular, on pigment identification. The most commonly used method of pigment identification is to compare the spectral similarity between ones of unknown target and ones in spectral library, which requires a comprehensive and complete spectral library and is based on overall shape of the spectrum. To a certain extent, it may ignore some of the key absorption characteristics of the spectrum. Methods: A novel spectral matching method was proposed based on the spectrum divided into subsections for identification according to the main ion absorption characteristics. Main works: (1) establishing a spectral library suitable for typical pigment identification of painting; (2) discussing the main components, as well as the absorption positions of the ions and functional groups contained in pigments frequently used by artists; (3) presenting a novel spectral matching algorithm carried on spectral subsections for pigment identification; (4) verifying the feasibility and applicability of proposed method by a Chinese painting and a fresco. Conclusions: The proposed method can correctly identify the main pigments or components contained in the mixed area, which is better than the traditional method and more convenient than the unmixing method, except for some limitations in detecting white and black pigments.

Keywords: hyperspectral technology; pigment identiﬁcation; spectral subsection; ion absorption characteristic; fresco conservation

1. Introduction As more attention is drawn on the conservation of cultural relics, the use of modern technology to preserve information on the surface of cultural relics to achieve the protection and inheritance of that has become an important development trend in this ﬁeld. Painted artifacts refer to a kind of cultural relics that adhere pigments to the substrate material through the binding media, including frescoes, paintings, painted potteries, painted clay sculptures, ancient architectural oil paintings, etc. The color on the surface of the precious painted artifacts with a long history such as Chinese paintings and frescoes will appear to be lost or faded in some degree. On the other hand, pigments with vivid

Remote Sens. 2020, 12, 3415; doi:10.3390/rs12203415 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, 3415 2 of 22 colors are important elements reflecting the artistic, historical, and research values of painted artifacts. Therefore, pigment identification plays an important role in scientific preservation and restoration of painted artifacts. Many modern techniques can provide essential information about materials used in painted artifacts, for example, their pigments composition [1,2]. A set of different instruments and various techniques, including X-Ray diffraction (XRD), scanning electron microscopy coupled to energy dispersive spectroscopy (SEM-EDS), and several spectroscopies, were used to identify the complex composition structure of different green earths [3]. Five portable spectroscopic techniques, namely X-ray fluorescence (XRF), mid-infrared reflectance spectroscopy, near infrared reflectance spectroscopy, and UV-Vis spectroscopy in absorption and emission, were used to study the materials in a painting by Pierre-Auguste Renoir, “A woman at her toilette,” which has been examined using conventional micro-sampling techniques. The potential and limitations of the in-situ and non-invasive approaches were evaluated in pigments identification of painting [4]. Fiber optic Fourier transform-infrared (FT-IR) reflectance spectroscopy was used to acquire the reflectance spectra of two pigments, which were processed by principal components analysis and Mahalanobis distance [5]. In [6], a practical approach was developed to identify dyes in works of art from samples as small as 25 µm in diameter with the surface-enhanced Raman scattering (SERS). Two organic compounds were used to demonstrate the sensitivity of SERS at the single-molecule level. The practical application of SERS to cultural heritage studies were examined, including the selection of appropriate substrates, the development of analytical protocols, and the building of SERS spectral databases. Some of them require collecting sample from the cultural relics for testing, which is generally not allowed. Another important technique for identifying pigments is the diffuse reflectance spectroscopy, which was firstly introduced to identifying pigments on surface of relics in 1995 [7]. This technique, which can also be categorized as hyperspectral technology due to its high spectral resolution in the remote sensing field, can rapidly acquire punctual reflectance spectra. It has increasingly become a kind of non-invasive and efficient way for detecting materials [8]. Wang et al. [9] developed a fiber optics reflectance spectrophotometer to identify pigments in a nondestructive way considering the special demands of protecting relics. The shape, characteristic reflectance peak, as well as the peak in the first derivative of the reflectance spectrum were employed to identify the pigments on colored pottery figurines and frescoes of Tang dynasty tombs in Xian, China. The results were reliable and verified by XRF analysis. The potential of non-invasive in situ analytical techniques such as portable Raman, portable X-ray fluorescence, portable optical microscope, and fiber optics reflectance spectroscopy has been used for studying painted layers of Renaissance terracotta polychrome sculptures belonging to the statuary of Santo Sepolcro Church in Milan. The results obtained pointing out the contribution of these techniques to the compositional diagnostic, providing complete information, in some cases better than micro-destructive techniques, on the kind of pigments used on the external painted layers. Moreover, a comparison with the results obtained before the last conservation work (2009) with micro-destructive techniques allowed ascertaining the removal of the external painted layers during the conservation operations [10]. In [11], a fiber spectroradiometer, with the aid of calibrated luminescence imaging spectroscopy, was used for identifying cadmium pigments and distinguishing among cadmium sulfide, cadmium zinc sulfide, and cadmium sulfoselenide. Cadmium pigments are semiconductors that show band edge luminescence in the visible range so as to realize pigments identification. It is necessary to further the work for finding features of other pigments for identification as well. The Fiber Optics Diffuse Reflectance Spectroscopy (FORS) technique was employed to explore the pigments on Byzantine wall painting. Its potential and reliability were assessed by several analytical techniques, such as environmental SEM-EDX, Attenuated Total Reflectance FTIR (ATR-FTIR), and micro-Raman Spectroscopy. The results confirmed the effectiveness of FORS technique for wall painting pigments’ identification, offering key advantages such as instrument mobility and rapid data collection, which are of utmost significance in the field archaeological research [12]. In [13], UV-Vis-NIR FORS combined other approaches were used to investigate the modern and contemporary mural paintings. Its results Remote Sens. 2020, 12, 3415 3 of 22 confirmed that the materials used by Keith Haring for the mural Tuttomondo (1989) have the same composition of the new Caparol acrylic paints, except for the case of yellow pigment. However, the previous studies focused on the feasibility and reliability of reflectance spectroscopy in pigments identification of colored relics. The identification methods mainly rely on the manual search for spectral characteristics. The accuracy and efficiency of the method are limited by comparing the shape, reflection peak, and absorption valley with the standard pigment spectra. Moreover, the wavelength range of above instruments is in visible and infrared (<1000 nm), which cannot distinguish the pigments with the same color very well, because some reflectance characteristics located in the wavelength are greater than 1000 nm [14]. In order to improve the accuracy and efficiency of this kind of reflectance spectrum to identify pigments, its spectral range has been extended to 2500 nm, which is often used in the spot spectrum measurement in hyperspectral remote sensing. Moreover, some automatic methods based on the curve matching of reflectance spectrum have also been proposed, and they all need standard spectral library as the reference. For materials on the earth, there are several generally approved spectral libraries available [15], such as the United States Geological Survey-MIN (USGS-MIN) [16], Jet Propulsion Laboratory (JPL) [17], John Hopkins University (JHU) [18], International Geological Correlation Program-264 (IGCP-264) [19], and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) [20]. As for pigments, there are also some spectral libraries established as the reference for pigment recognition. Cosentino [21] developed a FORS database of 54 historical pigments commonly used in artwork, which was built by collecting the reflectance spectra of pigments in pure powder and applied with different binders. The spectra cover the 360–1000 nm spectral range. Now, the database is available on-line and can be download freely. Balas et al. [22] employed a hyperspectral imaging device and proposed an approach to identify and map pigments in paintings by El Greco and his workshop with the aid of a properly selected spectral classifier. They also built a spectral library by collecting the spectra of a series of pigment material replicas developed by using original methods covering almost the entire palette of Renaissance painters. The spectra cover the 370–1100 nm spectral range. Bayarri et al. [23] applied several hyperspectral techniques for the study, conservation, and management of rock art. Many methods in hyperspectral remote sensing, such as calibration, transformation, and mapping, were discussed and combined to study the panels in the Cave of El Castillo in Puente Viesgo, Cantabria, Spain. A spectral library was also built to identify the pigments used in the artworks. Wu et al. [24] utilized a shortwave infrared hyperspectral imaging device covered 1000–2500 nm to examine cultural relics. A painting created in Qing Dynasty (1636–1912) was selected as the sample. They extracted several kinds of information from this painting, such as color, pigment composition, and damage characteristics. In total, 12 kinds of typical Chinese painting pigments were also measure by a portable ground object spectrometer as the reference of pigment identification. The automatic methods of spectral matching can be divided into two categories: the matching method based on the overall curve similarity and the matching method based on the feature similarity extracted from the spectral curve. The first kind of method commonly used for spectral identification is to calculate the similarity between unknown spectrum and standard spectra in spectral library based on certain similarity indexes, such as mean distance, Spectral Angle Mapping (SAM), and correlation coefficient. In [25], the FORS was used to identify pigments in pictorial layers of works of art thanks to a spectra database of dry powdered mineral pigments. The mean distance between the spectral curve of the pigment to be identified and that of the standard pigment was used to calculate the similarity. And the best fit was given by the smallest mean distance computed for all the spectra in the database. Shi et al. [26] identified azurite pigment on the surface of a painting “80th birthday of Chongqing’s Empress Dowager” kept in the Forbidden City, Beijing, China, which was painted by Yao Wenhan, a famous painter in the 18th century in China. The SAM between the spectral curve on the painting and that of the standard pigment stored in USGS spectral library was used to identify the pigments. In [27], a method of spectral information divergence based on statistical manifold space was proposed, which improved Remote Sens. 2020, 12, 3415 4 of 22 the measurement standard of information divergence into Riemannian metric. The difference in component probability of the spectral vector was regarded as the probability variation. The pigment was identified by spectral information divergence, which effectively improved the matching accuracy. Another commonly used method for spectral identification is to calculate the similarity of features extracted or enhanced from unknown spectra and reference spectra. It differs from the above-mentioned method in that it not only relies on the spectral curve in the standard spectral library, but also the spectral features enhanced for the similarity calculation. Typically, constraining the spectral shape is more important than the spectral magnitude because the former has a direct relationship with the composition of the target [28]. Therefore, it is necessary to enhance the spectral absorption characteristics of unknown spectra and reference spectra before spectral identification to obtain more accurate results. The methods for spectral absorption characteristics enhancement include the first derivative calculation and continuum removal of the spectrum. The derivative analysis of spectra has been widely applied in hyperspectral remote sensing and chemical analysis [29,30]. Fonseca et al. [31] used FORS to non-invasively identify madder- and cochineal based pigments on works of art. The features extracted in the first derivative transformation of the FORS spectra instead of the absorption features were used for pigment identification. This study provided a more robust means of primary identification and could be used to create a decision tree for the identification of madder and cochineal pigments based solely on FORS. Continuum removal is another widely used method for processing and analyzing spectra. It can not only highlight the absorption characteristics of spectral curves, but also normalize them to a unified spectral background, which is beneficial for the comparison between spectra measured in different environments. Furthermore, the original curve after removed continuum can be used for calculating the spectral characteristic parameters in the absorption bands. Wu et al. [32] performed continuum removal both on unknown spectra and reference spectra before spectral matching, and then used the least squares method for spectral features fitting to realize spectral identification. Cen et al. [33] highlighted the absorption and reflection characteristics on the spectral curve after continuum removal of mineral pigment collected, and extracted the band characteristics by using various spectral analysis methods. The identification and analysis of the main pigments of Thangka were realized by quantifying the spectral characteristics such as wavelength position, depth, symmetry, etc. It is of great significance to the identification, restoration, digital archiving, and reproduction of Thangka. However, due to the similar spectral reflectance characteristics of different pigments with the same color, the above methods are prone to false matching in spectral matching of different materials with the same color [34]. Moreover, the colors on surfaces observed by our naked eyes or instruments are usually caused by a mixture of several kinds of pigments due to painting skills. The recognition ability of the above methods for mixed pigments is also very limited. Since the absorption positions of main ions and functional groups in pigments will appear in certain intervals [35], we developed a pigment identification method based on the special ion absorption characteristics on subsection of pigment’s reflectance spectra. It could extract the certain intervals for spectral subsection identification, which can locate key features of unknown spectra accurately. This method is also effective for the identification of mixed pigments. In Section1, the paper starts from an overall introduction of context of the study and a brief review of related works. Section2 introduces the spectral identification methods proposed in the study in detail, followed by describing the typical pigment spectral library established by our team, the typical ion absorption positions of pigments, Spectral Absorption Index (SAI) and SAM used in our novel method. The description of experiment and the presentation of results presented in Section3. Furthermore, the results are explained and discussed in Section4. In Section5, the conclusion is briefly summarized and future work is outlined as well. Remote Sens. 2020, 12, 3415 5 of 22

2. Materials and Methods The overall process of this study is given in Figure1. A spectral library suitable for typical pigment identification on surface of paintings is established. Furthermore, a novel spectral subsection Remote Sens. 2020, 12, x FOR PEER REVIEW 5 of 25 identification (SSI) method considering ion absorption characteristics is proposed to identify the types oftypes pigments of pigments on the on surface the surface of painted of painted artifacts. artifact It iss. carriedIt is carried out on out a on Chinese a Chinese painting painting created created in a laboratory,in a laboratory, and an and outdoor an outdoor fresco infresco Qutan in Temple,Qutan Temple, Qinghai Qinghai Province, Province, China, created China, in created 1392. Moreover, in 1392. theMoreover, traditional the identificationtraditional identification method using method the entire using spectrum the entire is spectrum also applied is also to the applied two samples to the two for comparison.samples for Finally,comparison. either theFinally, known either truth valuethe kn orown X-ray truth fluorescence value or (XRF) X-ray spectrometer fluorescence is used(XRF) to verifyspectrometer the identification is used to verify effect andthe identifica applicabilitytion of effect the method.and applicability of the method.

Figure 1.1. TheThe overall overall process process of the study (SSI, spectralspectral subsection identiﬁcationidentification (SSI) methodmethod considering ionion absorptionabsorption characteristics;characteristics; XRF,XRF, X-rayX-ray ﬂuorescence).fluorescence).

2.1. SSI Method The SSI method adopts the SAI or SAM method basedbased on the absorption feature of the unknown spectrum in eacheach characteristicscharacteristics subsection to calculate the similarities with standard spectra in corresponding subsection.subsection. TheThe ﬁnal final results results represent represen thet the presence presence of eachof each pigment pigment in mixturein mixture using using the index,the index, which which are calculated are calculated based based on the on weights the weig assignedhts assigned to the top to three the top results three of eachresults subsection. of each Assubsection. shown in As Figure shown2, thein Figure process 2, can the beproc carriedess can out be in carried the next out steps. in the next steps.

Remote Sens. 2020, 12, 3415 6 of 22 Remote Sens. 2020, 12, x FOR PEER REVIEW 6 of 25

FigureFigure 2. The 2. spectral The spectral subsection subsection identiﬁcation identification method method (SAI, (SAI, Spectral Spectr Absorptional Absorption Index; Index; SAM, SAM, Spectral AngleSpectral Mapping). Angle Mapping).

(1) Perform(1) Perform the continuum the continuum removal removal on on the the unknownunknown spectrum spectrum and and the thestanda standardrd spectra spectra in pigment in pigment spectralspectral library. library. (2) Determine(2) Determine the numberthe number of of subsections subsections forfor thethe unknown spectrum spectrum as sub_int as sub_int. The. five The detection five detection rangesranges should should be checked be checked one byone one by to one select to select the characteristic the characteristic subsection(s), subsection(s), where where the unknownthe unknown spectrum has significant absorption characteristics as sub_int = (sub_int1, sub_int2, ... spectrum has significant absorption characteristics as sub_int = (sub_int1, sub_int2, ... sub_intm) sub_intm) (m is the number of subsections, 0 < m ≤ 5), for subsequent spectral subsection (m is the number of subsections, 0 < m 5), for subsequent spectral subsection identification. identification. ≤ (3) If(3) the If unknown the unknown spectrum spectrum does does not not have have any any characteristic characteristic subsection, the the whole whole spectrum spectrum will will be used forbe used traditional for traditional identification. identification. Then, Then, go go to to step step (9). (9). (4) Judge(4) Judge whether whether there there is is a a single single absorption feature feature in each in each subsection. subsection. If it is false, If it then is false, go to thenstep go to (6). step (6). (5) If there is a single absorption feature in the subsection, the similarities between spectra will be (5) If therecalculated is a single by using absorption SAI. Firstly, feature the inSAI the is subsection,calculated within the similarities the subsection between of the unknown spectra will be calculatedspectrum by and using all standard SAI. Firstly, spectra the in SAIthe pigment is calculated spectral within library as the SAI_u subsection and SAI_s of = the(SAI_s unknown1, spectrumSAI_s and2, ...SAI_s all standardn). Secondly, spectra the difference in the pigment is calculated spectral between library each as elementSAI_u inand SAI_sSAI_si and =the(SAI_s 1, SAI_sSAI_u2, ... .SAI_s Finally,n). the Secondly, smaller the the absolute difference value is result calculated of (SAI_s betweeni-SAI_u), each the higher element is the in similaritySAI_si and the between the corresponding standard spectrum and the unknown spectrum in this subsection. SAI_u. Finally, the smaller the absolute value result of (SAI_si-SAI_u), the higher is the similarity The top three results with the highest similarity in each subsection will be selected. Then, go to between the corresponding standard spectrum and the unknown spectrum in this subsection. step (7). The(6) top If there three is resultsno single with absorption the highest feature similarity in the subsection, in each the subsection similarities will between be selected. spectra will Then, be go to step (7).calculated by SAM. Firstly, the standard spectra within the subsection are extracted from (6) If therepigment is no spectral single absorptionlibrary (after featurecontinuum in removal) the subsection,. Then, we the calculate similarities the cosine between of the spectral spectra will be calculatedangles between by SAM. them Firstly,and the theunknown standard spectrum spectra in corresponding within the subsection subsection. The are larger extracted the from pigmentcosine spectral value libraryof the spectral (after continuum angle, the removal).higher is the Then, similarity we calculate between the the cosine corresponding of the spectral standard spectrum and the unknown spectrum in this subsection. The top three results with the angles between them and the unknown spectrum in corresponding subsection. The larger the highest similarity in each subsection will be selected. cosine(7) Assign value the of theweights. spectral The angle,top three the pigments higher is obta theined similarity in each between subsection the by corresponding step (5) or (6) are standard spectrumassigned and weights the unknown of 3/3m, spectrum 2/3m, and in1/3 thism in subsection. order of ranking, The top respectively, three results where with m is the the highest similaritynumber in eachof subsections subsection of the will entire be selected.spectrum, and 0 < m ≤ 5. It should be noted that the higher (7) Assign the weights. The top three pigments obtained in each subsection by step (5) or (6) are assigned weights of 3/3m, 2/3m, and 1/3m in order of ranking, respectively, where m is the number of subsections of the entire spectrum, and 0 < m 5. It should be noted that the higher ranking ≤ indicates that the pigment has a higher similarity with the unknown spectrum in this subsection. Therefore, the larger fraction will be assigned to the pigment. However, the pigment with the Remote Sens. 2020, 12, 3415 7 of 22

largest fraction in one subsection cannot be directly considered to exist in the mixed area, because the final identification result needs to be obtained by accumulating the weight scores of all the subsections. (8) Calculate the corresponding weighted index of each result according to the weights. According to the resulting weights of each characteristic subsection, the weighted index of each result is calculated. In that way, the existence of each pigment in mixture can be represented by the percentage. Moreover, the weighted index of pigment indicates the possibility of existence of the pigment, although it is not a strictly statistical probability. (9) To obtain the final identification result.

2.2. Spectral Library Establishment

2.2.1. Samples of Spectral Library

Pigment Selection The suitable pigments for establishing spectral library is crucial for spectral identification, because it usually affects the quality of identification results [36]. After careful investigation and comparison, 32 kinds of pigments of Jiang Sixutang, a famous brand established 300 years ago, were selected for sample making, including 24 kinds of mineral pigments and eight kinds of botanical and chemical pigments [37] (see Table1). As shown in Table1, the number following the pigment name means that it was painted in the corresponding times.

Table 1. Pigments selected for samples making.

Type Tone Pigment Name Cinnabar Zinnober Red Vermilion Ocher Orpiment1 Yellow Realgar Orpiment2 Malachite Green Malachite2 Malachite3 Azurite Mineral pigments Azurite1 Azurite2 Blue Azurite3 Lapis Hackmanite Chalk Calcite Muscovite Clam meal White Lead white Titanium white Silver Alum Black Biotite Red lead Crimson Red Madder Eosin Botanical and chemical pigments Yellow Gamboge Blue Cyanine White Lead white Black Ink Remote Sens. 2020, 12, 3415 8 of 22

Glue Preparation Since the mineral pigments cannot be directly drawn on the paper, it was necessary to configure a certain concentrationRemote Sens. 2020, 12 of, x FOR the PEER glue REVIEW before making experimental samples. There are8 ofmany 25 types of glue for painting, and the choice of them varies dependingBlack on the region.Ink The glue produced by Jiang Sixutang was selected for the study and used as the following steps. Firstly, the desired amount of Glue Preparation glue was soaked four times with cold water, and then, hot water at about 80 ◦C was added six times after it had expanded.Since the mineral pigments cannot be directly drawn on the paper, it was necessary to configure a certain concentration of the glue before making experimental samples. There are many types of glue for painting, and the choice of them varies depending on the region. The glue produced by Jiang Sample DesignSixutang was selected for the study and used as the following steps. Firstly, the desired amount of glue was soaked four times with cold water, and then, hot water at about 80 °C was added six times In this study, the sample block of pigment was designed to be a size of 4 cm 4 cm to ensure after it had expanded. × a sufficient spaceSample Design for spectral data collection. The Raw Xuan type of paper from Rongbaozhai, with no aluminum on the surface, was selected as a base material to reduce the influence on spectrum. In this study, the sample block of pigment was designed to be a size of 4 cm × 4 cm to ensure a Most samplessufficient were paintedspace for spectral in one data time, collection. twotimes, The Raw and Xuan three type of times paper withfrom Rongbaozhai, a brush to with get no three different thickness of pigmentsaluminum on to the ensure surface, that was selected the absorption as a base material characteristics to reduce the of influence pigment on spectrum. components Most can also be observed assamples the thickness were painted of the in one samples time, two changed. times, and Partthree times of the with sample a brushblocks to get three of glueddifferent pigments are thickness of pigments to ensure that the absorption characteristics of pigment components can also shown in Figurebe observed3. as the thickness of the samples changed. Part of the sample blocks of glued pigments are shown in Figure 3.

FigureFigure 3. The 3. The sample sample blocksblocks of ofglued glued pigments. pigments. 2.2.2. The Instruments2.2.2. The Instruments for Data for CollectionData Collection The instrument used to acquire the spectral data was Analytical Spectral Devices (ASD) The instrumentFieldSpec4 used portable to acquirespectroradiometer, the spectral whose data specif wasic parameters Analytical were Spectralshown in Table Devices 2. The (ASD) data FieldSpec4 portable spectroradiometer,collection was carried whose out in specifica dark room parameters to avoid the were interference shown from in all Table external2. The light data sources. collection was carried out inTwo a dark halogen room lamps, to which avoid can the provide interference a source of fromlight that all is external closest to sunlight, light sources. were chosen Two as halogenan lamps, artificial light source for spectral data collection. In the study, if the region of interest (ROI) was large which can provideenough, athe source spectra would of light be collected that is closestby using the to well-sealed sunlight, probe were and chosen the internal as an halogen artificial light light source for spectral datasource collection. provided by the In probe thestudy, would be if used the for region illumination. of interest Otherwise, (ROI) the fibers was would large be enough, directly the spectra would be collectedtaken outby for usingdata collection the well-sealed and two halogen probe lamps and would the be internalused for illumination, halogen lightsuch as source the data provided by collection in field. It is necessary to measure each sample multiple times and the data are averaged the probe wouldas a standard be used spectral for illumination.curve in order to prevent Otherwise, external the light fibers sources would and reduce be operational directly takenerrors. out for data collection and two halogen lamps would be used for illumination, such as the data collection in field. It is necessary toTable measure 2. Parameters each of sample the Analytical multiple Spectral times Device (ASD) and FieldSpec4 the data portable are averaged spectroradiometer. as a standard spectral Name Parameters curve in order to prevent externalSpectral Range light (Continuous sources Coverage) and reduce operational 350-2500 errors.nm Spectral Bands 2151 Table 2. Parameters of the AnalyticalSpectral Spectral Width Device (ASD) FieldSpec4 2.5 nm portable spectroradiometer. 350–1000 nm @ 3 nm; Spectral Resolution 1001–2500 nm @ 8 nm NameSize Parameters 12.7 × 35.6 × 29.2 cm Weight 5.44 kg Spectral Range (Continuous Coverage) 350–2500 nm Spectral Bands 2151 The instrument used for auxiliary verification about the reliability of spectral identification Spectral Width 2.5 nm results was a portable XRF of XL3T900 with CCD camera, which can be performed for more than 40 350–1000 nm @ 3 nm; Spectral Resolution 1001–2500 nm @ 8 nm Size 12.7 35.6 29.2 cm × × Weight 5.44 kg

The instrument used for auxiliary veriﬁcation about the reliability of spectral identiﬁcation results was a portable XRF of XL3T900 with CCD camera, which can be performed for more than 40 kinds of elements analyses. In this study, the portable XRF was used to test the same region of interest collected by ASD, using the soil model, and the acquisition time of each point is 60 s. Remote Sens. 2020, 12, x FOR PEER REVIEW 9 of 25 Remote Sens. 2020, 12, 3415 9 of 22 kinds of elements analyses. In this study, the portable XRF was used to test the same region of interest collected by ASD, using the soil model, and the acquisition time of each point is 60 s. 2.2.3. The Typical Pigment Spectral Library 2.2.3. The Typical Pigment Spectral Library In the study, a typical pigment spectral library was built by the spectral data collected on the In the study, a typical pigment spectral library was built by the spectral data collected on the laboratorylaboratory pigment pigment samples, samples, which which was was the the basisbasis fo forr identifying identifying pigment pigment types types on painting on painting surfaces. surfaces. It containedIt contained 32 kinds 32 kinds of pigments, of pigments, 95 95 spectra spectra in in total, total, some some of of which which areare shownshown in Figure Figure 4.4. Most Most of of the pigmentsthe pigments had a thickness had a thickness of one of layer, one twolayer, layers, two la andyers, threeand three layers, layers, while while the the Alum Alum and and Azurite Azurite (piece) were(piece) only painted were only with painted one layer.with one layer.

FigureFigure 4. 4.Some Some spectra spectra inin the typical pigment pigment spectral spectral library. library.

2.3. Typical2.3. Typical Ion AbsorptionIon Absorption Positions Positions of of Pigments Pigments As perAs theper investigationthe investigation of theof the absorption absorption position position ofof mainmain ions and and function function groups groups contained contained in commonlyin commonly used pigment used pigment [35,38 [35,38],], a complete a complete summary summary is is shown shown in in Table Table3 3..

TableTable 3. Components 3. Components and and typical typical ion ion absorptionabsorption position position of of commonly commonly used used pigments. pigments. Absorption Position of Absorption Position of Tone Pigment Name Main Component Absorption Position of Absorption Position of Tone Pigment Name Main Component Metal Cation (μm) Function Group (μm) Metal Cation (µm) Function Group (µm) Cinnabar HgS CinnabarZinnober HgS HgS Hg+: 0.6 Red + VermilionZinnober HgS HgS Hg : 0.6 Red Vermilion HgS Ocher Fe2O3 Fe3+: 0.9 3+ Orpiment1Ocher As Fe22SO33 Fe : 0.9 Yellow Realgar As4S4 0.55 Orpiment1 As2S3 Orpiment2 As2S3 Yellow Realgar As4S4 0.55 2+ Orpiment2 As2S3 Cu : 0.8, Strong decline Green Malachite CuCO3·Cu(OH)2 CO32−: 2.29,2.52 2+before 0.52 Cu : 0.8, Strong decline 2 Green Malachite CuCO3 Cu(OH)2 Cu2+: 0.8, Strong decline CO3CO2−: 1.90,2.05,2.28;3 −: 2.29,2.52 Azurite Cu3[CO·3]2(OH)2 before 0.52 before 0.52 OH−: 1.45,1.95,2.35,2.50 2+ 2 Cu : 0.8, Strong decline CO3 −:− 1.90,2.05,2.28; Azurite Cu3(Na,Ca)[CO3]24~8(OH) 2 OH : 1.40; Mixing ofbefore Na and 0.52 other OH−: 1.45,1.95,2.35,2.50 Blue Lapis (Al6Si6O24) H2O: 1.90; impurities: 0.6 (Na,Ca)(SO4,S)1~2 EnvelopeOH water:: 1.40; 2.50 4~8 Mixing of Na and other − Blue Lapis (Al6Si6O24) Mixing of Na and other H2O: 1.90; Hackmanite Na4(Al3Si3O12)Cl impurities: 0.6 H2O: 1.90 (SO4,S)1~2 impurities: 0.6 Envelope water: 2.50 Chalk CaCO3 Mixing of Na and other Hackmanite Na4(Al3Si3O12)Cl H2O: 1.90 impurities: 0.6 CO32−: 1.88,2.00,2.16, Calcite CaCO3 (2.30)2.35,(2.50)2.55 Chalk CaCO3 K2Al4(Si6Al2O20) OH−:1.40; 2+ 2 White Muscovite Fe : 0.44,0.9 CO3 −: 1.88,2.00,2.16, Calcite(OH,F) CaCO4 Al-O-H: 2.20,2.35,2.45 3 (2.30)2.35,(2.50)2.55 Clam meal CaO K Al (Si Al O ) OH :1.40; TitaniumMuscovite white 2 4 TiO62 2 20 Fe2+ : 0.44,0.9 − (OH,F)4 Al-O-H: 2.20,2.35,2.45 White Silver Al Clam meal CaO Titanium white TiO2 Silver Al OH−: Alum KAl3(SO4)2(OH)6 1.01,1.35,1.45,1.78,2.00, 2.17,2.33,2.50

Black Biotite K(Mg,Fe)3AlSi3O10(F,OH)2 OH−:1.40 Remote Sens. 2020, 12, 3415 10 of 22

According to the absorption positions summarized in Table3, it can be found that the main cations include Cu2+, Fe2+, Fe3+, and Hg+, whose absorption positions generally appear before the wavelength 2 of 1000 nm. The main functional groups are CO3 − and OH−, whose absorption positions generally appearRemote Sens. after 2020 the, 12 wavelength, x FOR PEER REVIEW of 1000 nm. It is further subdivided and defined as the detection 10 range of 25 for the spectral subsection identification method. The first range is for cations detection, including 350–550 nm, 600–900 nm, and 700–1120 nm. Another one is for functional group detection,OH−: including Alum KAl3(SO4)2(OH)6 1.01,1.35,1.45,1.78,2.00,2.17, 1400–1600 nm and 2300–2400 nm. 2.33,2.50 K(Mg,Fe)3AlSi3O10(F, Black Biotite OH−:1.40 2.4. SAI and SAM OH)2 SAI is a comprehensive spectral absorption characteristic parameter. It was first proposed by WangAccording et al. and appliedto the absorption in extracting positions mineral summarized composition fromin Table hyperspectral 3, it can be image found [39 ].that The the specific main 2+ 2+ 3+ + descriptioncations include is shown Cu , in Fe Figure, Fe 5, andand Equations Hg , whose (1)–(3). absorption positions generally appear before the wavelength of 1000 nm. The main functional groups are CO32− and OH-, whose absorption positions generally appear after the wavelength of W1000= λnm2 .λ It1, is further subdivided and defined as the (1) detection range for the spectral subsection identification− method. The first range is for cations λ λm detection, including 350–550 nm, 600–900 nm,d = and2 −700–1120, nm. Another one is for functional group (2) detection, including 1400–1600 nm and 2300–2400 Wnm. dr + (1 d)r2 SAI = 1 − , (3) 2.4. SAI and SAM rm whereSAIλ1 ,isλ 2a, andcomprehensiveλm are the wavelength spectral absorption of the point characteristicS1, S2, and parameter.M, W is the It width was first of the proposed absorption by feature,Wang etd al.is and the symmetryapplied in ofextracting the absorption mineral feature, compositionr1, r2, and fromrm hyperspectralare the reflectance image of [39]. the pointThe specificS1, S2, anddescriptionM, and SAIis shownreflects in theFigure relative 5 and depth Equations characteristics (1)–(3). of the spectrum.

Figure 5. Parameters of Spectral Absorption Index. Figure 5. Parameters of Spectral Absorption Index. In the SAM method, the spectral curve of n bands is considered as a n-dimensional vector. Generally, the cosine of the angle between two spectral vectors is calculated to evaluate the similarity W=λ -λ , (1) between these spectra, whose range will be 0 to 1. The2 1 larger the cosine value, the more similar the spectra are. λ -λ d= 2 m , (2) W 3. Experiments and Results

dr1+1-dr2 3.1. Experiment of a Chinese Painting SAI= , (3) rm A Chinese painting was drawn on rice paper by using several commonly used mineral and where λ1, λ2, and λm are the wavelength of the point S1, S2, and M, W is the width of the absorption botanical pigments. During the drawing process, the pigments used were recorded as the reference feature, d is the symmetry of the absorption feature, r1, r2, and rm are the reflectance of the point S1, data to verify the experimental results recognized in this study. S2, and M, and SAI reflects the relative depth characteristics of the spectrum. In the SAM method, the spectral curve of n bands is considered as a n-dimensional vector. Generally, the cosine of the angle between two spectral vectors is calculated to evaluate the similarity between these spectra, whose range will be 0 to 1. The larger the cosine value, the more similar the spectra are.

3. Experiments and Results

3.1. Experiment of a Chinese Painting

Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 25 Remote Sens. 2020, 12, x FOR PEER REVIEW 11 of 12

A Chinese painting was drawn on rice paper by using several commonly used mineral and RemoteA Chinese Sens. 2020 painting, 12, x FOR was PEER drawn REVIEW o n rice paper by using several commonly used mineral and 11 of 25 botanical pigments. During the drawing process, the pigments used were recorded as the reference Remotebotanical Sens. 2020pigments., 12, 3415 During the drawing process, the pigments used were recorded as the reference 11 of 22 data to verifyA Chinese the experimental painting was results drawn recognized on rice paper in this by study. using several commonly used mineral and data to verify the experimental results recognized in this study. botanical pigments. During the drawing process, the pigments used were recorded as the reference 3.1.1.data Data to Collectionverify the experimentalof the Chinese results Painting recognized in this study. 3.1.1.3.1.1. Data Data CollectionCollection of of the the Chinese Chinese Painting Painting Several typical areas were selected on the surface of the Chinese painting, and their spectra were 3.1.1.Several Data typical Collection areas ofwere the selected Chinese on Painting the surface of the Chinese painting, and their spectra were collectedSeveral by typicalusing ASD. areas In wereorder selectedto make the on thesample surface points of distributed the Chinese as painting,evenly as andpossible their on spectra the were collected by using ASD. In order to make the sample points distributed as evenly as possible on the collectedentire paintingSeveral by using surfacetypical ASD. areasand In reducewere order selected the to makeimpacts on the the ofsurfacesample subjective of the points selection,Chinese distributed painting, a grid was asand evenly drawntheir spectra ason possiblethe were on entire painting surface and reduce the impacts of subjective selection, a grid was drawn on the theorthophoto entirecollected painting of by the using painting surface ASD. firstly, In and order reduceso that to make the the sample the impacts sample points of points subjectivecan be distributed selected selection, at aseach evenly corner a grid as point. possible was drawnThen, on the on the orthophoto of the painting firstly, so that the sample points can be selected at each corner point. Then, theseentire sample painting points surfacecan be classified and reduce according the impacts to different of subjective groups andselection, analyzed a grid respectively. was drawn Due on to the orthophotothese sample of points the painting can be classified firstly, so according that the to sample different points groups can and be analyzed selected respectively. at each corner Due point. to Then, the orthophotorandomness of of the the painting grid generation, firstly, so thatin the the line- sampleby-line points spectral can be acquisition selected at process, each corner if there point. was Then, thesethe randomness sample points of the can grid be generation, classified according in the line- toby di-linefferent spectral groups acquisition and analyzed process, respectively.if there was Due to less thesepigment sample at the points intersection can be classified or the mixing according was tooto different complicated, groups some and points analyzed could respectively. be ignored Due or to theless randomness pigment at the of intersection the grid generation, or the mixing in was the line-by-linetoo complicated, spectral some acquisitionpoints could process,be ignored if or there was replacedthe randomness by others that of thewere grid more generation, suitable and in the closer line- toby-line them. spectral acquisition process, if there was lessreplaced pigment by others at the that intersection were more or suitable the mixing and closer was to too them. complicated, some points could be ignored or lessThe pigment specific atsample the intersection points are shownor the mixing in Figure was 6. tooAccording complicated, to the somedifferent points colors, could these be ignoredpoints or replacedThe by specific others sample that werepoints more are shown suitable in Figure and closer 6. According to them. to the different colors, these points are replaceddivided intoby others five groups, that were named more C1, suitable C2, C3, and C4, closer and to C5, them. listed in Table 4. The data collection are divided into five groups, named C1, C2, C3, C4, and C5, listed in Table 4. The data collection environmentThe specificThe specific of the sample Chinese sample points painting points are are is shown consistentshown inin Figure Figurewith the 66.. conditionAccording According of to spectral to the the different di libraryfferent colors, establishment, colors, these these points points environment of the Chinese painting is consistent with the condition of spectral library establishment, arewhich dividedare has divided been into describedinto five five groups, groups, in Section named named 2.2.2. C1, C1, C2,C2, C3,C3, C4, and and C5, C5, listed listed in inTable Table 4. 4The. The data data collection collection which has been described in Section 2.2.2. environmentenvironment of the of the Chinese Chinese painting painting is is consistent consistent wi withth the the condition condition of spectral of spectral library library establishment, establishment, whichwhich has beenhas been described described in in Section Section 2.2.2 2.2.2..

Figure 6. The grid and sample points on surface of the Chinese painting. Figure 6. The grid and sample points on surface of the Chinese painting. Figure 6. The grid and sample points on surface of the Chinese painting. Figure 6.Table The 4. The five regions of the onChinese surface painting. of the Chinese painting. Tablegrid 4. The and five sample regions points of the Chinese painting. Table 4. The ﬁve regions of the Chinese painting. Regions Typical Color Name of Points Number of Data Regions TypicalTable 4. Color The five regionsName of of the Po intsChinese painting.Number of Data Regions Typical Color Name of Points Number of Data Regions Typical Color Name of Points Number of Data C1 1–15 15 C1C1 1–151–15 15 15

Remote Sens. 2020, 12, x FOR PEERC1 REVIEW 15 12 of 25 Remote Sens. 2020, 12, x FOR PEER REVIEW 1–15 12 of 25 Remote Sens. 2020, 12, x FOR PEER REVIEW 12 of 25 C2C2 16–16–3030 15 15 C2 16–30 15

C3 31–45 15 C3 C2 31–4516 –30 15 15 C3 31 45 15 C3 –31–45 15

C4 46–54 9 C4C4 46–46–5454 9 9 C4 46 54 9 –

C5C5 55–55–6363 9 9 C5 55–63 9 C5 55 63 9 –

Remote Sens. 2020, 12, 3415 12 of 22

3.1.2. Pigment Identification of the Chinese Painting Using Two Methods Take the red region C1 as an example, where 15 spectra were collected. According to the method mentioned above, three characteristic subsections were determined for the SSI method. Moreover, weights were assigned in order of ranking. The results and weights of each subsection are listed in Table5. In order to simplify the table, only the numerator of the weight was written after each pigment name (Underlined and bolded), and the denominator, which was 9 (m = 3) in this set of data, was omitted. For example, the top three identification results of the first characteristic subsection of the point 1 are eosin, crimson, and cyan, with the weights given as 3/9, 2/9, and 1/9, respectively. It should be noted that the large fraction here means that the spectrum of the corresponding pigment is more similar to the unknown spectrum in this subsection. The weighted index in the last line is calculated by accumulating the scores in each subsection for all the 15 spectra, followed by averaging (divided by the number of spectra, which is 15 here).

Table 5. The identiﬁcation results and weights of each subsection in region C1.

Name of Results and Weights of Each Subsections (The Denominator is 9) Points Subsection I Subsection II Subsection III 1 Eosin3 Ocher2 Vermilion1 Crimson3 Eosin2 Cyan1 Madder3 Clam meal2 Eosin1 2 Eosin3 Vermilion2 Madder1 Crimson3 Cyan2 Eosin1 Eosin3 Clam meal2 Madder1 3 Eosin3 Ocher2 Vermilion1 Crimson3 Eosin2 Cyan1 Eosin3 Cyan2 Crimson1 4 Eosin3 Vermilion2 Madder1 Crimson3 Cyan2 Eosin1 Madder3 Cyan2 Eosin1 5 Eosin3 Vermilion2 Ocher1 Crimson3 Cyan2 Eosin1 Eosin3 Crimson2 Cyan1 6 Eosin3 Ocher2 Vermilion1 Crimson3 Eosin2 Cyan1 Eosin3 Cyan2 Madder1 7 Eosin3 Ocher2 Lapis1 Crimson3 Eosin2 Cyan1 Clam meal3 Eosin2 Madder1 8 Eosin3 Vermilion2 Madder1 Crimson3 Eosin2 Cyan1 Eosin3 Cyan2 Madder1 9 Eosin3 Vermilion2 Madder1 Crimson3 Eosin2 Cyan1 Madder3 Eosin2 Clam meal1 10 Eosin3 Ocher2 Vermilion1 Crimson3 Cyan2 Eosin1 Eosin3 Cyan2 Madder1 11 Eosin3 Ocher2 Lapis1 Crimson3 Cyan2 Eosin1 Eosin3 Cyan2 Madder1 12 Eosin3 Vermilion2 Madder1 Crimson3 Cyan2 Eosin1 Eosin3 Madder2 Cyan1 13 Eosin3 Vermilion2 Ocher1 Crimson3 Eosin2 Cyan1 Calcite3 Eosin2 Cyan1 14 Eosin3 Vermilion2 Madder1 Crimson3 Cyan2 Eosin1 Eosin3 Calcite2 Cyan1 15 Eosin3 Vermilion2 Ocher1 Crimson3 Cyan2 Eosin1 Eosin3 Cyan2 Madder1 Weighted Eosin: 0.778; Crimson: 0.356; Cyan: 0.304 Index

It should be noted that the weighted index of a pigment describes the possibility of the existence of the pigment at the test point of the painting. At the same time, it also indicates the content of the pigment to some extent. Therefore, except for the first pigment, the second, and even the third pigment might be picked out as the identification results, depending on the values of their index. The pigment would be regarded as one of the identification results if its index is greater than a given threshold. In identification of the Chinese painting, thresholds depend on the mean value of the weighted index of each region as in Equations (4) and (5): P Wi Wmean,i = (4) Ki

PN = Wmean,i W = i 1 (5) mean N where Wmean,i is the weight index mean for the ith point for a region in the Chinese painting, Wi is the sum of weights of pigment for the ith point in this region, Ki is the kind number of pigments for the ith point in the region, N is the total number of points in this region, and Wmean is the mean value of Wmean,i for N points in the region. In the pigment identiﬁcation experiment for the Chinese painting, the Wmean of each region is selected as the threshold. According to Equations (4) and (5), the thresholds of the ﬁve regions of the Chinese painting were calculated and given in Table6. Remote Sens. 2020, 12, 3415 13 of 22

Table 6. The thresholds of the Chinese painting.

Regions Thresholds C1 0.35 C2 0.26 C3 0.32 C4 0.27 C5 0.37

The identification results of C1 around the threshold are sorted in descending order of weight index as eosin (0.778), crimson (0.356), and cyan (0.304). Combined with the colors presented in this area and the threshold, the mixed pigments in this area are the most likely to contain eosin pigment, followed by crimson. In order to make the results more intuitive and clearer, the results in each subsection of all spectra are not listed. The final identification results of the five regions and the weighted indices are directly listed in Table7.

Table 7. Comparison of pigment identiﬁcation in the ﬁve regions of the Chinese painting.

Results and Weighted Results of Traditional Regions Truth Value Indices of SSI Method Eosin 0.778 Eosin Eosin C1 Crimson 0.356 Crimson Crimson Cyan 0.304 Madder Madder Crimson 0.326 Eosin Crimson C2 Ocher 0.259 Crimson Clam meal Cyan 0.237 Red lead Malachite 0.778 Malachite Malachite C3 Chalk 0.322 Ink Ink Ocher 0.289 Azurite Ocher 0.728 Malachite Ocher C4 Malachite 0.568 Ink Malachite Clam meal 0.259 Vermilion Malachite 0.728 Malachite Malachite C5 Ocher 0.619 Ink Ocher Ink 0.247 Vermilion

The pigments used in the same ﬁve regions of the Chinese painting were also identiﬁed by the traditional method of SAM, spectral features match, and binary encoding match in software ENVI. The whole spectral curves were matched with the spectral library built in this study. The weights for each algorithm were set to be 1 and the top three pigments were selected as the results in Table7.

3.1.3. Comparison of the Identification between the Two Methods in the Chinese Painting The identification results using two methods in the five regions of Chinese painting are listed in Table7. The results that meet the threshold of SSI method in each area are bolded in the second column, the top three results of traditional matching methods are listed in the third column, and the truth value recording when the Chinese painting is drawn are listed in the last column. The results identified by the SSI method and traditional method can be described as follows:

O1 C1 was painted with pigments of eosin, crimson, and madder according to the record. The eosin and crimson were identified correctly both by SSI and traditional one, while the pigment madder was missed by the approach proposed. O2 C2 was painted with pigments of crimson and clam meal. Both SSI and the traditional method correctly identified the crimson, but neither identified the clam white. Remote Sens. 2020, 12, x FOR PEER REVIEW 15 of 25

② C2 was painted with pigments of crimson and clam meal. Both SSI and the traditional method Remotecorrectly Sens. 2020 ,identified12, 3415 the crimson, but neither identified the clam white. 14 of 22 ③ C3 was painted with pigments of malachite and ink, which were correctly identified by using

O3 traditionalC3 was painted method, with while pigments the ink of was malachite missed andby using ink, whichSSI method. were correctly identified by using ④ C4traditional was painted method, with while pigments the ink of wasocher missed and mala by usingchite. SSI The method. pigments contained in the region were correctly identified by using the SSI method, but the ocher was missed by the traditional O4 C4 was painted with pigments of ocher and malachite. The pigments contained in the region were one.correctly identified by using the SSI method, but the ocher was missed by the traditional one. ⑤ C5 was painted with pigments of malachite and ocher, which are correctly identified by using O5 C5 was painted with pigments of malachite and ocher, which are correctly identified by using SSI SSI method, while the ocher was missed by using the traditional method. method, while the ocher was missed by using the traditional method.

3.2. Experiment Experiment of of a a Fresco Fresco The Qutan Qutan Temple, Temple, which is located located in in Ledu Ledu county, county, Qinghai Qinghai province, province, China, China, was was built built in in 1392. 1392. The hugehuge colorfulcolorful frescoes, frescoes, most most of themof them painted painted by the by royal the paintersroyal painters in the Ming in the and Ming Qing and Dynasties, Qing Dynasties,are the precious are the treasure precious of treasure Qutan Temple. of Qutan In thisTemple. study, In thethis spectral study, the data spectral of a small data test of areaa small located test areain the located west corridorin the west of the corridor Qutan of Temple the Qutan was Temp usedle to was study used the to applicability study the applicability of the SSI method of the SSI for methodpigment for determination. pigment determination. The tradition identificationThe tradition method identification was also method used for was comparison. also used Then, for comparison.the reliability Then, of identification the reliability results of identification was verified results by XRF. was verified by XRF.

3.2.1. Data Data Collection Collection of of the the Fresco Fresco Due to the large size of the fresco, it is difficul difficultt to perform spectra collection of all points on the frescofresco usingusing anan ASD ASD spectroradiometer. spectroradiometer. Instead, Instead, several several typical typical pigment pigment areas areas were were selected selected for study. for study.A grid A was grid drawn was drawn on the orthophotoon the orthophoto of the fresco of thebefore fresco databefore collection, data collection, and five and regions five regions of interest of interestwere selected were selected as F1-5, as where F1-5, awhere total a of total 30 spectral of 30 spectral data were data collected.were collected. Their Their specific specific location location and anddetailed detailed information information are shownare shown in Figure in Figure7 (black 7 (black points) points) and and Table Table8. As 8. the As fresco the fresco is located is located in the in thecorridor corridor on theon westthe west side side of the of temple,the temple, which which is basically is basically in a dark in a environment,dark environment, it is necessary it is necessary to use totwo use halogen two halogen lamps forlamps illumination, for illumination, and to takeand outto take the opticalout the fibers optical and fibers connect and them connect with them the pistolwith thehandle pistol for handle measurement. for measurement.

Figure 7. The grid and sample points on surface of the fresco. Figure 7. The grid and sample points on surface of the fresco.

Due to the long history of the fresco, it is impossible to obtain recordings or test results of the actual pigments used. Therefore, Therefore, th thee portable portable XRF XRF was was used used to to detect detect the the energy energy level level of of elements elements in in each region. A total of 19 test points was collected for five regions, of which the specific location and detailed information are shown in Figure7 (red points) and Table8. The high-energy elements detected Remote Sens. 2020, 12, x FOR PEER REVIEW 16 of 25 Remote Sens. 2020, 12, x FOR PEER REVIEW 16 of 25 Remote Sens. 2020, 12, x FOR PEER REVIEW 16 of 25 Remote Sens. 2020, 12, x FOR PEER REVIEW 16 of 17 Remoteeach region. Sens. 2020 A, 12total, x FOR of 19PEER test REVIEW points was collected for five regions, of which the specific location 16 ofand 25 each region. A total of 19 test points was collected for five regions, of which the specific location and detailedeach region. information A total of are 19 testshown points in wasFigure collected 7 (red for points) five regions, and Table of which 8. The the high-energy specific location elements and detailedeach region information. A total of are 19 testshown points in wasFigure collected 7 (red for points) five regions, and Table of which 8. The the high-energy specific location elements and eachdetecteddetailedRemote region. Sens.informationat each A2020 total ,test12 of, 3415pointare 19 testshown and points their in wasFigure corresponding collected 7 (red for points) values five regions, and are Tablelisted of which in8. TheTable the high-energy specific9. Among location them,elements andthe 15 of 22 detecteddetailed informationat each test pointare shown and their in Figure corresponding 7 (red points) values and are Tablelisted in8. TheTable high 9. Among-energy them,elements the detailedelementsdetected informationatwith each energy test point arehigher shown and than their in 10,000 Figure corresponding (kev) 7 (red are points)bolded. values and Inare order Tablelisted to 8.in distinguish TheTable high-energy 9. Among the difference them,elements the in elementsdetected atwith each energy test point higher and than their 10,000 corresponding (kev) are bolded. values Inare order listed to in distinguish Table 9. Among the difference them, the in detectedtheelements energy atwith level each energy of test each point higher element and than theirdetected, 10,000 corresponding (kev)in Table are 9, bolded. “++”values and Inare “+”order listed are to used in distinguish Table to indicate 9. Among the that difference itsthem, energy the in theelements energy with level energy of each higher element than detected, 10,000 (kev)in Table are 9, bolded. “++” and In “+”order are to used distinguish to indicate the that difference its energy in elementstheis at energy a each 100,000 with testlevel andenergy point of 10,000each andhigher element level, their than respectively. detected, corresponding 10,000 (kev)in TableThe are recognition values9, bolded. “++” and are In ability “+”order listed are analysis to inused distinguish Table to of indicate9 the. Among twothe that methodsdifference its them, energy can in the elements isthe at energy a 100,000 level and of 10,000each element level, respectively. detected, in TableThe recognition 9, “++” and ability “+” ar analysise used to of indicate the two that methods its energy can theisbe withat performedenergy a 100,000 energy level andby higherof comparing10,000each element than level, 10,000the respectively. detected, elements (kev) in aredetection TableThe bolded. recognition 9, “++” results Inand order ability with“+” are tothe analysis used distinguish chemical to of indicate the composition thetwo that dimethodsff itserence energy of canthe in the energy beis at performed a 100,000 andby comparing10,000 level the, respectively. elements detection The recognition results abilitywith the analysis chemical of the composition two methods of canthe isspectralbe levelat performed a 100,000 ofidentification each andby element comparing10,000 result. level, detected, the respectively. elements in Table detection The9,“ recognition++ results” and abilitywith “+” arethe analysis usedchemical of to the indicatecomposition two methods that of its canthe energy is at a spectralbe performed identification by comparing result. the elements detection results with the chemical composition of the bespectral performed identification by comparing result. the elements detection results with the chemical composition of the spectral100,000 identification and 10,000 result. level, respectively. The recognition ability analysis of the two methods can be spectral identificationTable result. 8. Five regions of interest and sample numbers on the fresco. performed by comparingTable 8. Five the regions elements of interest detection and sample results numbers with on the the chemical fresco. composition of the spectral Table 8. Five regions of interest and sample numbers on the fresco. identification result.Table 8. Five regions of interest and sample numbers on the fresco. Table 8. Five regions of interestASD and sample numbers on theXRF fresco. ASD XRF Regions Typical Color ASD XRF Regions TableTypical 8.ColorFive regions ofASD interest and sample numbersXRF on the fresco. Regions Typical Color Points NumberASD of Data Points NumberXRF of Data Regions Typical Color Points Number of Data Points Number of Data Regions Typical Color Points Number of Data Points Number of Data Points Number ofASD Data Points Number of Data XRF Regions Typical Color Points Number of Data Points Number of Data F1 1–9 Points9 NumberX1–X4 of Data Points4 Number of Data F1 1–9 9 X1–X4 4 F1 1–9 9 X1–X4 4 F1 1–9 9 X1–X4 4 F1 F1 1–9 1–99 X1–X4 9 X1–X44 4

F2 10–18 9 X5–X8 4 F2 10–18 9 X5–X8 4 F2 10–18 9 X5–X8 4 F2 F2 10–18 10–189 X5 9–X8 X5–X84 4 F2 10–18 9 X5–X8 4

F3 19–22 4 X9–X12 4 F3 19–22 4 X9–X12 4 F3 F3 19–22 19–224 X9–X12 4 X9–X124 4 F3 19–22 4 X9–X12 4 F3 19–22 4 X9–X12 4

F4 23–26 4 X13–X14 2 F4 F4 23–26 23–264 X13–X14 4 X13–X142 2 F4 23–26 4 X13–X14 2 F4 23–26 4 X13–X14 2 F4 23–26 4 X13–X14 2

F5 F5 27–30 27–304 X15–X19 4 X15–X195 5 F5 27–30 4 X15–X19 5 F5 27–30 4 X15–X19 5 F5 27–30 4 X15–X19 5 F5 27–30 4 X15–X19 5

Since XRF can only provide the type of element contained in pigment, it is hard to distinguish SinceSince XRF XRF can canonlyonly provide provide the type the of type element of element contained contained in pigment, in pigment,it is hard to it distinguish is hard to distinguish thoseSince different XRF canpigments only provide containing the typethe sameof element ions bycontained XRF. However, in pigment, it canit is stillhard be to useddistinguish as an thosethoseSince different di ﬀXRFerent canpigments pigments only provide containing containing the typethe the sameof element same ions ions bycontained byXRF. XRF. However, in However,pigment, it canit it is can stillhard still be to beuseddistinguish used as asan an auxiliary auxiliarythoseSince different method XRF canpigments to only provide provide containing certain the information typethe sameof element ionsreference bycontained XRF. for frescoHowever, in pigment, data withoutit canit is hardstill truth be to value. distinguishused as an auxiliarythose different method pigments to provide containing certain information the same ionsreference by XRF. for frescoHowever, data withoutit can still truth be value. used as an thoseauxiliarymethod different method to provide pigments to provide certain containing certain information information the same reference ionsreference by forXRF. for fresco frescoHowever, data data without withoutit can still truth be value. value.used as an auxiliary method to provide certain information reference for fresco data without truth value. auxiliary method to provideTable 9. certain Elements information detection results reference by using for frescoXRF on data the fresco. without truth value. Table 9. Elements detection results by using XRF on the fresco. TableTable 9. Elements 9. Elements detection detection results by results using byXRF using on the XRF fresco. on the fresco. Energy Table 9. Elements detection results by using XRF on the fresco. Energy Table 9.Pb Elements detectionCu results by Susing XRF onHg the fresco. Ca Energy(kev) Pb Cu S Hg Ca EnergyEnergy(kev) (kev) Pb PbCu Cu S SHg Ca Hg Ca Energy(kev)X1 1562.01Pb 278975.78Cu 0.00S 0.00Hg 26503.66Ca (kevX1 ) 1562.01Pb 278975.78Cu 0.00 S 0.00Hg 26503.66Ca X1(kev)X1X2 1562.011029.011562.01 278975.78178149.56278975.78 0.00 0.000.00 26503.6632592.03 0.00 26503.66 X2X1 1029.011562.01 178149.56278975.78 0.00 0.00 32592.0326503.66 X1X3X2 1562.011029.01139.28 278975.78195848.00178149.56 0.00 0.00 26503.6644637.4332592.03 X2X3X2 1029.01139.281029.01 195848.00178149.56178149.56 0.00 0.000.00 44637.4332592.03 0.00 32592.03 X2X4X3 1029.011252.71139.28 178149.56164159.42195848.00 0.00 0.00 32592.0344637.4339282.22 X3X4X3 1252.71139.28139.28 164159.42195848.00195848.00 0.00 0.000.00 39282.2244637.43 0.00 44637.43 X3X4 1252.71139.28 195848.00164159.42F1: Cu++, Ca+0.00 0.00 44637.4339282.22 X4X4 1252.711252.71 164159.42F1:164159.42 Cu++, Ca+0.00 0.000.00 39282.22 0.00 39282.22 X4X5 1252.71526.68 164159.42909.04F1: Cu++, Ca+175032.560.00 69704.160.00 39282.22 18542.46 X5 526.68 909.04F1 : Cu++F1:, Ca+175032.56 Cu ++, Ca+ 69704.16 18542.46 X6X5 2507.46526.68 909.04418.18F1: Cu++, Ca+158248.25175032.56 106331.3469704.16 13908.1618542.46 X6X5 2507.46526.68 418.18909.04 158248.25175032.56 106331.3469704.16 13908.1618542.46 X5X5X7X6 2378.842507.46526.68526.68 909.04387.09418.18 909.04175032.56169500.92158248.25 175032.56107834.58106331.3469704.16 18542.4623325.8413908.16 69704.16 18542.46 X7X6 2378.842507.46 387.09418.18 169500.92158248.25 107834.58106331.34 23325.8413908.16 X6X6X8X7 26293.652507.462378.842507.46 418.18696.39387.09 418.18158248.25169500.92134419.11 158248.25106331.34107834.5817502.05 13908.1623325.8423500.73 106331.34 13908.16 X8X7 26293.652378.84 696.39387.09 134419.11169500.92 107834.5817502.05 23500.7323325.84 X7X7X8 26293.652378.842378.84 387.09696.39F2: S++, 387.09 Hg+,169500.92134419.11 Ca+ 169500.92107834.5817502.05 23325.8423500.73 107834.58 23325.84 X8 26293.65 696.39F2: S++, Hg+,134419.11 Ca+ 17502.05 23500.73 X8X9 26293.6540606.54 35573.78696.39F2: S++, Hg+,134419.11136492.42 Ca+ 17502.0551.38 23500.7318149.19 X8X9 40606.5426293.65 35573.78F2: S++ 696.39, Hg+136492.42, Ca+ 134419.1151.38 18149.19 17502.05 23500.73 X10X9 56087.0540606.54 41295.6935573.78F2: S++, Hg+,166482.00136492.42 Ca+ 51.3860.08 18149.1918344.49 X10X9 56087.0540606.54 41295.6935573.78 F2: S166482.00136492.42++, Hg+ , Ca+60.0851.38 18344.4918149.19 X10X11X9 123496.9440606.5456087.05 35573.7841295.6950570.20 136492.42166482.00265214.56 51.3860.080.00 18149.1918344.496308.32 X9X11X10 123496.9456087.05 40606.54 50570.2041295.69 35573.78 265214.56166482.00 136492.4260.080.00 18344.496308.3251.38 18149.19 X10X11X12 123496.9456087.056971.97 41295.6993195.7150570.20 166482.00265214.5667959.97 344.8560.080.00 18344.4968024.496308.32 X12X11 123496.946971.97 93195.7150570.20 265214.5667959.97 344.850.00 68024.496308.32 X10 56087.05F3: 41295.69S+, Cu+, Pb+ 166482.00 60.08 18344.49 X11X12 123496.946971.97 50570.2093195.71 265214.5667959.97 344.850.00 68024.496308.32 F3: S+, Cu+, Pb+ X12 6971.97 93195.71 67959.97 344.85 68024.49 X11X13 48297.70 123496.94 25055.33F3: 50570.20S+, Cu+, 208326.78Pb+ 265214.5635.99 30534.810.00 6308.32 X12 6971.97 93195.71 67959.97 344.85 68024.49 X13 48297.70 25055.33F3: S+ , Cu+,208326.78 Pb+ 35.99 30534.81 X12X14X13 31617.8748297.70 6971.97 24609.8025055.33F3: 93195.71S+, Cu+, 176882.00208326.78Pb+ 67959.9735.9943.22 30534.8138761.93344.85 68024.49 X14X13 31617.8748297.70 24609.8025055.33 176882.00208326.78 43.2235.99 38761.9330534.81 F4: S++, Pb+, Ca+, Cu+ X13X14 48297.7031617.87 25055.3324609.80 208326.78176882.00 35.9943.22 30534.8138761.93 F4: S++, Pb+,F3: Ca+, S+ ,Cu+ Cu +, Pb+ X14 31617.87 24609.80 176882.00 43.22 38761.93 X15 94247.71 414.08F4: S++, Pb+, Ca+,188251.23 Cu+ 84.75 17509.94 X14 31617.87 24609.80 176882.00 43.22 38761.93 X13X15 94247.71 48297.70 414.08F4: S++ 25055.33, Pb+, Ca+188251.23, Cu+ 208326.7884.75 17509.9435.99 30534.81 X16X15 93331.7294247.71 823.98414.08F4: S++, Pb+, Ca+,188251.23244973.98 Cu+ 145.8684.75 17509.9414344.45 X14X16X15 93331.7294247.71 31617.87 823.98414.08 24609.80 244973.98188251.23 176882.00145.8684.75 14344.4517509.9443.22 38761.93 X15X16 94247.7193331.72 414.08823.98 188251.23244973.98 145.8684.75 17509.9414344.45 X16 93331.72 823.98F4: S++244973.98, Pb+, Ca +, Cu145.86+ 14344.45 X16 93331.72 823.98 244973.98 145.86 14344.45 X15 94247.71 414.08 188251.23 84.75 17509.94

X16 93331.72 823.98 244973.98 145.86 14344.45 X17 83581.70 556.53 160192.80 188.29 31010.53 X18 30920.21 153.00 167193.38 44.93 41051.42 X19 91778.10 683.97 216748.48 140.39 13162.02 F5: S++, Pb+, Ca+ Remote Sens. 2020, 12, 3415 16 of 22

3.2.2. Pigment Identiﬁcation of Fresco Using Two Methods Take the green region F1 of the fresco as an example, where nine spectra were collected for pigment identiﬁcation. According to the steps mentioned in Section 2.1, four characteristic subsections were determined to perform SSI method. Moreover, weights were assigned in order of ranking. As shown in Table 10, the numerator of the weight that was also written after each pigment name (underlined and bolded), and the denominator, which was 12 (m = 4) in this set of data, was omitted.

Table 10. The identiﬁcation results and weights of each subsection in region F1.

Pigments and Weights of Each Subsections (The Denominator is 12) Name of Points Subsection I Subsection II Subsection III Subsection IV Malachite3 Malachite3 Malachite3 Madder3 1 Chalk2 Ink2 Vermilion2 Eosin2 Clam meal1 Ocher1 Cinnabar1 Cyan1 Orpiment13 Malachite3 Malachite3 Malachite3 2 Orpiment22 Ink2 Vermilion2 Ocher2 Ink1 Ocher1 Cinnabar1 Titanium white1 Malachite3 Ocher3 Malachite3 Malachite3 3 Chalk2 Ink2 Vermilion2 Chalk2 Clam meal1 Clam meal1 Cinnabar1 Ink1 Malachite3 Malachite3 Malachite3 Malachite3 4 Chalk2 Ocher2 Vermilion2 Chalk2 Clam meal1 Ink1 Cinnabar1 Ink1 Malachite3 Ocher3 Malachite3 Chalk3 5 Chalk2 Ink2 Vermilion2 Malachite2 Clam meal1 Clam meal1 Cinnabar1 Ink1 Malachite3 Ocher3 Malachite3 Malachite3 6 Chalk2 Ink2 Vermilion2 Chalk2 Clam meal1 Clam meal1 Cinnabar1 Ink1 Malachite3 Ocher3 Malachite3 Chalk3 7 Titanium white2 Ink2 Vermilion2 Malachite2 Chalk1 Malachite1 Cinnabar1 Ink1 Malachite3 Malachite3 Vermilion3 Malachite3 8 Chalk2 Azurite2 Cinnabar2 Azurite2 Clam meal1 Ink 1 Gamboge1 Calcite1 Ocher3 Malachite3 Malachite3 Malachite3 9 Orpiment22 Ocher2 Vermilion2 Chalk2 Orpiment 11 Ink1 Cinnabar1 Ink1 Malachite: 0.769 Chalk: 0.250 Weighted Index Ocher: 0.213 Ink: 0.194

Similar to the above Chinese painting pigment identification experiment, in addition to the pigment with the highest index, the second or third ranked according to the threshold value may also be selected as the identification result. Considering that the fresco is located in a more complex environment, with older history, and the use of pigments is more diverse, the threshold of the fresco is set lower than that for Chinese painting pigment identification in a more relaxed condition. Therefore, the threshold for each region in the fresco will be calculated by Equation (6). The thresholds for five regions are listed in Table 11. TF = Wmean σ , (6) j − j Remote Sens. 2020, 12, 3415 17 of 22

where TFj is the threshold of the jth region in the fresco, Wmean is mean of Wmean,i as mentioned in Equation (4), σ is the standard deviation of Wmean,i for each region, and j is the number of regions (j = 1, 2, 3, 4, 5). The identification results of F1 around the threshold are sorted in descending order of weight index in the last line of Table9. It can be seen that the result with the highest weighted index in region F1 is malachite (0.769), followed by chalk (0.250), which are larger than the threshold. Therefore, these two are kept and the rest of are excluded from the final result. Combined with the colors presented in this area, the final identification result can be described as: the mixed pigments in region F1 are most likely to contain malachite, and may also exist a certain amount of chalk.

Table 11. The thresholds of ﬁve regions in the fresco.

Regions Thresholds F1 0.24 F2 0.25 F3 0.19 F4 0.23 F5 0.25

The final identification results of the five regions and their weighted indices are listed in Table 12. In addition, similar to the Chinese painting experiment, the pigments used in the same five regions of fresco are also identified by traditional method. The top three pigments are selected to show the results.

Table 12. Comparison of pigment identiﬁcation in the ﬁve regions of the fresco.

Results and Weighted Regions Results of Traditional Method XRF Results Indices of SSI Malachite Malachite:0.769 CuCO Cu(OH) 3· 2 CuCO Cu(OH) Lapis F1 3· 2 Cu++, Ca+ Chalk:0.250 (Na,Ca)4~8(Al6Si6O24)(SO4,S)1~2 CaCO3 Azurite Cu3[CO3]2(OH)2 Vermilion:0.346 Ocher HgS Fe2O3 Chalk:0.321 Zinnober F2 S++, Hg+, Ca+ CaCO3 HgS Ocher:0.309 Cinnabar Fe2O3 HgS Azurite Cu [CO ] (OH) Malachite:0.380 3 3 2 2 Lapis CuCO Cu(OH) F3 3· 2 (Na,Ca) S+, Cu+, Pb+ Azurite:0.310 4~8 (Al6Si6O24) Cu3[CO3]2(OH)2 (SO4,S)1~2 Cyan Cinnabar:0.400 HgS Hackmanite Zinnober:0.310HgS Na (Al Si O )Cl Clam meal:0.250 4 3 3 12 Orpiment 2 S++, Pb+, Ca+, F4 CaO As S Cu+ Lead white:0.250 2 3 Ocher 2PbCO Pb(OH) 3· 2 Fe O Vermilion:0.250 2 3 HgS Chalk Chalk:0.440 CaCO CaCO 3 F5 3 Lead white S++, Pb+, Ca+ Lead white:0.220 2PbCO Pb(OH) 2PbCO Pb(OH) 3· 2 3· 2 Clam mealCaO Remote Sens. 2020, 12, 3415 18 of 22

3.2.3. Comparison of Identification between Two Methods in the Fresco In Table 12, the results that meet the threshold of SSI method, and the topic three results of traditional method in each area are listed in the second and third column, respectively. Moreover, the elements with energies higher than 10,000 detected by using XRF are listed in the last column. The XRF results are approximated as the truth value, and the pigment composition elements, which are correctly identified by the two methods, are in bold to facilitate comparison. Note: Vermilion, cinnabar, and zinnober are all red pigments based on HgS. Vermilion is a synthetic pigment, which is not stable. Both cinnabar and zinnober are natural mineral pigments containing HgS. According to their particle size, they can be divided into cinnabar and zinnober. Their color is slightly different. The color of zinnober is red and yellow, which is lighter and more delicate than that of cinnabar. The results identified by the SSI method and traditional method can be described as follows:

O1 F1 may have the Cu and Ca element according to the XRF results. Both SSI and the traditional method correctly identified pigments containing these two elements. O2 F2 may have three elements, including the S, Hg, and Ca elements, according to XRF results. The SSI method correctly identified all of these elements, while the Ca was missed by using the tradition method. O3 F3 may have the mixed pigments containing S, Cu, and Pb. Both of the two methods correctly identified the pigments containing Cu, but missed the other two elements. O4 F4 may have four kinds of elements, including S, Pb, Ca, and Cu. The SSI method correctly identified three of them but missed the Cu in the final result. Only one kind of pigment containing the S element was identified by the traditional method. O5 F5 may be a mixture containing the S, Pb, and Ca elements according to XRF results. Both SSI and the traditional method correctly identified pigments containing the Pb and Ca. While they missed the S in the final result.

It should be noted that high-energy Ca elements were detected in some regions, including F1, F2, F4, and F5, which may be caused by the presence of white pigments containing Ca in the mixture, or the base materials of the fresco were collected during the test. Signiﬁcantly, Wang et al. [40] collected 22 painting pigment samples from the gallery and architectural painting of Qutan Temple in Qinghai Province. They were analyzed by radioisotopic XRF and XFD and more than 20 kinds of inorganic mineral pigments were recognized. The results are summarized in Table 13 according to their colors. It can be seen that the pigments are basically consistent with that detected by XRF in this study.

Table 13. Inorganic mineral pigment analysis results.

Number Color of Samples Pigments 1 Green Malachite, Atacamite, Eriochalcite 2 Red Cinnabar, Red lead 3 Light red Lead oxide 4 Blue Azurite 5 Light blue Lapis 6 Black Lead white 7 Light yellow Gypsum, Lead white 8 Brown Lead dioxide 9 White Lead white, Calcite

4. Discussion In this paper, some typical points of interest on a Chinese painting and a fresco were performed using the SSI method and the traditional method, respectively, to determine the type of pigment in Remote Sens. 2020, 12, 3415 19 of 22 these mixed regions. In addition, for the identification of pure samples, we have also performed rigorous experiments and confirmed that the two methods have the same ability to identify pure mineral pigments with the same accuracy rate of 100%. Based on the consideration that the overall research focuses on identifying the type of pigment in mixed area, the experiment of pure samples identification as well as the results are not included in this paper. Based on the final identification results of the two methods, and combined with the known truth value of pigments or the XRF results, the accuracy of the two methods were calculated in Table 14. Specifically, the accuracy of the Top 3 using the SSI method was obtained by dividing the number of pigments that be correctly identified by the number of actually used at that region, while the Top 3 using the traditional method were calculated by dividing the number of correctly identified element types by the number of elements with above 10,000 kev energy detected by XRF in the same area. The correctness of the first matching result and the correct rate of the top three matching results are used to evaluate the two methods.

Table 14. Pigment identiﬁcation accuracy of the two methods.

Method C1 C2 C3 C4 C5 (Average) Accuracy SSI method √ √ √ √ √ 100.0% Top 1 Traditional method √ √ √ √ 80.0% × SSI method 67% 50% 50% 100% 100% 73.4% Top 3 Traditional method 100% 50% 100% 50% 50% 70.0% Method F1 F2 F3 F4 F5 (Average) Accuracy SSI method √ √ √ √ √ 100.0% Top 1 Traditional method √ √ √ 60.0% × × SSI method 100% 100% 33% 75% 67% 75.0% Top 3 Traditional method 100% 67% 33% 25% 67% 58.4%

In the Chinese painting experiment, the pigments used during the drawing process were recorded as the truth value. Therefore, through comparing with the result of the SSI method, it can be summarized as follows:

(1) By using the SSI method, the correct rate of the first result in the five regions is 100.0%, and of the top three results 73.4%. Combined with the results of Chinese painting in Table7, this method has limited ability to identify white and black pigments. Nevertheless, the first result obtained by this method is reliable, and the top three results can correctly identify the main components in the mixed area on the surface of Chinese painting. (2) Through applying the traditional method, the correct rate of the first result is 80.0%, and of the top three results 70.0%, which are lower than for the SSI method. Moreover, combined with the results presented in Table7, the traditional method missed the ocher and white pigments in each mixed area.

In the fresco experiment, there were no recordings or test results about the actual pigments used due to its long history. Therefore, the XRF results of each ROI were used for qualitative analysis of mixture’s components in this paper. It should be noted that, with the limitation of the instrument, only the elements detected by XRF can be used to assist in verifying the identification ability of the proposed method. The instrument can only provide the energy ranking of the commonly used elements contained in the test regions. Therefore, it is difficult to distinguish different pigments with the same element composition, and it is hard to know the possibility of botanical pigments in the mixture. Nevertheless, it can still be used as a means of auxiliary analysis to provide a certain information reference for fresco data without truth values:

(1) By using the SSI method, the correct rate of the first result in the five regions is 100.0%, and of the top three results 75.0%. Combined with the identification results of the fresco (in Table 12) and the color of each ROI (in Table8), the first result obtained by using SSI method is reliable. Remote Sens. 2020, 12, 3415 20 of 22

(2) By using the traditional method, the correct rate of the ﬁrst result is 60.0%, and of the top three results 58.4%. It can be seen that the accuracy of the traditional method is also lower than that of the SSI method, even for the fresco.

From the above discussion, it can be concluded that the SSI method can detect the main components contained in the area where multiple pigments are mixed, and the identiﬁcation result is also consistent with the visual color presented in the area. However, there was some trouble in identifying white and black pigments according to the experiment results of Chinese painting. The possible reason is that the key of the SSI method is to identify the type of pigment in the mixture based on the absorption position of the ion contained in the mineral pigment. However, the black pigment used in the Chinese painting experiment in this paper is ink, of which main component is carbon. It is not a mineral pigment, and its spectral characteristics are not obvious. Therefore, it is diﬃcult to detect out by using the SSI method. On the other hand, according to the use records of Chinese painting pigments, the use of white pigments in the C2 region (the ROI of Chinese painting) is small, which may be the reason why white pigments are not detected by the SSI method. Moreover, it is hard to verify whether there are botanical pigments in the mixture, or to distinguish whether the Ca element in the XRF results is from white pigment or the base material due to the instrument limitations in the fresco experiment. Nevertheless, in general, based on the truth records and the qualitative analysis from the XRF detection results, it can be seen that the SSI method has better performance on identifying multiple typical components in mixed region than the traditional method.

5. Conclusions In the study, a typical pigment spectral library is established based on the pigment samples in laboratory. Then, a spectral subsection identification of pigments considering ion absorption characteristics, which divides spectrum into several characteristic subsections based on the main ion absorption position of each pigment, is proposed for determining the pigment type. Furthermore, it is applied to a Chinese painting and a fresco to test the applicability, and the traditional method is also used for comparison. It can be concluded that the first result obtained by the proposed method can correctly identify the main pigment or component contained in the mixed region, and compared with the traditional method, it can also provide a more complete and more accurate result. The accuracy of the pigment identified by SSI is higher than the traditional method both in the Chinese painting and the fresco experiment. According to a suitable threshold depending on weighted index, the SSI method can even provide a second or a third pigment identified in a simpler way than the unmixing method. It is better than the conventional identification method that can match only one pigment at a time, and its complexity lies in the traditional method of pigment recognition and spectral unmixing method, which can get more than one pigments at one time for a single point. However, the proposed method has some limitations in detecting white and black pigments, so that some of the processes may need to be further refined to show a more significant identification advantage. In addition, the proposed method is carried out on the identification of one-dimensional spectral data in this paper. How effective the method is for hyperspectral images, which cannot be ignored, will be further studied.

Author Contributions: Conceptualization, Y.L., S.L., and M.H.; methodology, Y.L. and S.L.; validation, Y.L., Z.G., W.W., and X.Z.; formal analysis, Y.L., S.L., and X.Z.; resources, W.W.; writing—original draft preparation; writing—review, all authors. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Research Fund of the National Key Research and Development Program (No. 2017YFB1402105), the Great Wall Scholars Training Program Project of Beijing Municipality Universities (No. CIT&TCD20180322), and the Independent Project of Chinese Academy of Cultural Heritage (No. 2018JBKY13). Acknowledgments: The authors would like to thank Songnian Li from Ryerson University, Canada for his constructive comments on the preparation and many rounds of revisions of the paper and guidance during the research. Remote Sens. 2020, 12, 3415 21 of 22

Conﬂicts of Interest: The authors declare no conﬂict of interest.

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