Mapping Pigments in a Painting with Low Frequency Electron Paramagnetic Resonance Spectroscopy

heritage

Article Mapping Pigments in a Painting with Low Frequency Electron Paramagnetic Resonance Spectroscopy

Shane McCarthy, Haley Wiskoski and Joseph P. Hornak *

RIT Magnetic Resonance Laboratory, Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology, Rochester, NY 14623-5604, USA; [email protected] (S.M.); [email protected] (H.W.) * Correspondence: [email protected]

Abstract: An electron paramagnetic resonance (EPR) mobile universal surface explorer (MOUSE) was recently introduced for noninvasively studying paramagnetic pigments in paintings. This study determined that the EPR MOUSE could map the spatial locations of four pigments in a simple impasto painting. Results from three spectral identiﬁcation algorithms were examined to assess their ability to identify the pigments using an unsupervised approach. Resulting pigment maps are displayed as colorized images of the spatial distribution of the pigments. All three algorithms produced reasonable representations of the painting. The algorithms achieved excellent true positive, true negative, false positive, and false negative rates of ≥0.95, ≥0.98, ≤0.02, and ≤0.05, respectively, for the identiﬁcation of the pigments. We conclude that the EPR MOUSE is suitable for accurately mapping the location of paramagnetic pigments in a painting.

Keywords: low-frequency electron paramagnetic resonance spectroscopy; LFEPR; EPR; mapping pigments; EPR mobile universal surface explorer; EPR MOUSE Citation: McCarthy, S.; Wiskoski, H.; Hornak, J.P. Mapping Pigments in a Painting with Low Frequency Electron Paramagnetic Resonance 1. Introduction Spectroscopy. Heritage 2021, 4, Electron paramagnetic resonance (EPR) spectroscopy is a spectroscopy like visible 1182–1192. https://doi.org/10.3390/ absorption, Raman, and x-ray ﬂuorescence spectroscopies. EPR spectroscopy is a form of heritage4030065 magnetic resonance similar in some respects to nuclear magnetic resonance spectroscopy

Academic Editor: Costanza Miliani and magnetic resonance imaging. EPR is based on the absorption of electromagnetic radiation at frequency ν by unpaired electrons in free radicals and transition metal complexes

Received: 11 June 2021 when experiencing an applied magnetic field B. Materials with unpaired electrons are Accepted: 7 July 2021 paramagnetic, hence the origin of the spectroscopy name. EPR spectroscopy is typically Published: 10 July 2021 performed by keeping ν fixed and varying B to find the frequency and magnetic field combination that satisfies the resonance condition Publisher’s Note: MDPI stays neutral ν β with regard to jurisdictional claims in h = g B (1) published maps and institutional affil- β iations. where h is Planck’s constant, the Bohr magneton, and g the Lande g-factor of the specific unpaired electron in the sample. Many, but not all, materials with cultural heritage significance are paramagnetic and possess an EPR signal. These include complexes of transition metals such as copper, manganese, and iron and free radicals such as ultramarine and carbon-based blacks. Conventional high-frequency EPR spectroscopy, operating at Copyright: © 2021 by the authors. ν ≈ 9 GHz, has been used in archeology and art conservation to study rock [1] and Licensee MDPI, Basel, Switzerland. wall paintings [2], ceramics [3–6], pigments [7–11], marble and limestone objects [12–14], This article is an open access article paper [15,16], and varnishes used on paintings [17,18]. Unfortunately, conventional EPR is distributed under the terms and invasive, requiring a small amount of the artwork or artifact to be removed for the analysis. conditions of the Creative Commons Attribution (CC BY) license (https:// EPR is nondestructive in that the sample can be reanalyzed by another analytical technique, creativecommons.org/licenses/by/ but the sampling process has minimally altered the original artwork or artifact. 4.0/).

Heritage 2021, 4, 1182–1192. https://doi.org/10.3390/heritage4030065 https://www.mdpi.com/journal/heritage Heritage 2021, 4 1183

Heritage 2021, 4 FOR PEER REVIEW 2 Low-frequency EPR (LFEPR) [19] and the novel EPR mobile universal surface explorer (MOUSE) [20] overcome the invasive limitation of conventional EPR, allowing the analysis of the surface of any size artwork or artifact to be performed noninvasively and Low-frequency EPR (LFEPR) [19] and the novel EPR mobile universal surface ex- nondestructively. LFEPR has been demonstrated on linseed oil paints with paramagnetic plorer (MOUSE) [20] overcome the invasive limitation of conventional EPR, allowing the pigments similar to those used in renaissance paintings. Previous studies have focused on analysis of the surface of any size artwork or artifact to be performed noninvasively and identifyingnondestructively. pigments LFEPR in has single-component been demonstrated [21 on] and linseed double-component oil paints with paramagnetic [22] paint samples, inpigments addition similar to layered to those samplesused in renaissance [22], on canvas.paintings. Another Previous study studies addressed have focused imaging on the spatialidentifying distribution pigments of in singlesingle-component paramagnetic [21] andand double-component ferromagnetic components [22] paint samples, [23]. This study addressesin addition mapping to layered thesamples spatial [22], distribution on canvas. Another of multiple study pigments addressed in imaging a painting the spa- on canvas. tial distributionThe pigment of mappingsingle paramagnetic followed anand image ferromagnetic processing components approach [23]. used This in medicalstudy imag- ingaddresses that consists mapping of the sampling, spatial distribution identification, of multiple and presentation pigments in a stepspainting [24 ].on The canvas. first step in the processThe pigment is sampling mapping or followed collecting an image the LFEPR processing spectra approach point-by-point used in medical at regular im- grid locationsaging that onconsists the painting. of sampling, The identification, resultant data and cube presentation is a spatial–spatial–spectral steps [24]. The first step represen- tationin the ofprocess the painting. is sampling Sampling or collecting is followed the LFEPR by spectra identification point-by-point of the at pigment regular atgrid each grid location.locations on Identification the painting. reduces The resultant the three-dimensional data cube is a spatial–spatial–spectral spatial–spatial–spectral representa- data into a tion of the painting. Sampling is followed by identification of the pigment at each grid two-dimensional spatial–spatial map for each pigment in the painting. This was performed location. Identification reduces the three-dimensional spatial–spatial–spectral data into a bytwo-dimensional spectral identification spatial–spatial algorithms map for described each pigment later. in Inthe the painting. final step, Thispresentation, was per- the pigmentformed by maps spectral are identification converted into algorithms a single des imagecribed with later. one In the picture final step, element presentation, (pixel) for each gridthe pigment location. maps This are approach converted is consideredinto a singleunsupervised image with one mapping, picture element as spectra (pixel) are for provided, andeach a grid segmented location. imageThis approach is produced is consi withoutdered unsupervised subjective humanmapping, input as spectra on the are segmentation pro- processvided, and [25 ].a segmented image is produced without subjective human input on the seg- mentationA simple process four-color [25]. painting with blue vitriol (BV), Han blue (HB), rhodochrosite (RC),A and simple terracotta four-color red painting (TR) pigments with blue was vitriol chosen (BV), to Han demonstrate blue (HB), therhodochrosite utilization of the EPR(RC), MOUSE and terracotta to map red the (TR) location pigments of pigments was chosen in to a painting.demonstrate These the utilization pigments wereof the selected becauseEPR MOUSE they to were map paramagneticthe location of pigments and possessed in a painting. broad, These challenging-to-interpret, pigments were selected LFEPR absorptionbecause they signals. were paramagnetic See Figure1 andfor anpossessed image ofbroad, the painting.challenging-to-interpret, LFEPR absorption signals. See Figure 1 for an image of the painting.

Figure 1. An image of the 10 × 10 cm painting Palm Tree on a Beach at Twilight composed of four × Figurepigments, 1. An(rhodochrosite, image of the terracotta 10 10 red, cm blue painting vitriol, andPalm Han Tree blue) on aused Beach to demonstrate at Twilight composedthe ability of four pigments,of the EPR (rhodochrosite,MOUSE to identify terracotta and map red, the bluelocati vitriol,on of the and pigments. Han blue) Supe usedrimposed to demonstrate on the image the ability ofis thethe EPRZX sampling MOUSE grid to identify and a few and ellipses mapthe depicting location the of size the of pigments. a sampling Superimposed location. Ellipses on theare image is × thedrawnZX tosampling indicate gridthe size and of a the few 3.5 ellipses 5 mm depicting sampling region. the size See of text a sampling for details location.. Ellipses are drawn to indicate the size of the 3.5 × 5 mm sampling region. See text for details.

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2. Background 2. BackgroundThe EPR MOUSE is a unilateral LFEPR spectrometer subsystem consisting of the ra- diofrequencyThe EPR MOUSE (RF) is coil, a unilateral B field LFEPR magnet, spectrometer and mo subsystemdulation consisting magnetic of the field coils [20] (see Fig- radiofrequencyure 2). The (RF)signal coil, is B ﬁelddetected magnet, from and modulationa volume magnetic adjacent ﬁeld to coils the [ 20RF] (see coil. The surface of the Figure2). The signal is detected from× a volume adjacent to the RF coil. The surface of the samplingsampling region region is a 3.5 is× a5 mm3.5 ellipse, 5 mm and ellipse, the sampling and depththe sampling is greatest at depth the center is ofgreatest at the center of thethe ellipse. ellipse.

FigureFigure 2. A 2. conceptual A conceptual drawing drawing of the components of the ofcomponents the MOUSE, their of the connectivity MOUSE, to the their LFEPR connectivity to the LFEPR spectrometer, and the sampled region in the painting. spectrometer, and the sampled region in the painting. Unlike other surface analysis techniques where the signal detection depth is dependent on the penetrationUnlike other depth surface of the incident analysis radiation, techniques the RF, B,wh andere modulation the signal fields detection all depth is depend- influence detection depth with the EPR MOUSE. The penetration depth for the RF used in LFEPRent on can the be onepenetration meter in some depth materials, of the but theincident detection ra depthdiation, is 0 to the 1 mm RF, because B, and of modulation fields all theinfluence geometry ofdetection the RF, B, anddepth modulation with the fields. EPR MOUSE. The penetration depth for the RF used in LFEPRThe MOUSE can isbe connected one meter to thein some LFEPR materials, spectrometer but for the sourcedetection of ν, depth signal is 0 to 1 mm because detection, and the electromagnetic current. The connection to the spectrometer is via two smallof the variable geometry length cables.of the The RF, variable B, and length modulation of these cables fields. allows the MOUSE to be positionedThe meters MOUSE from the is LFEPRconnected spectrometer, to the and LFEPR thus analyze spectrometer any size of painting.for the source of ν, signal detection,LFEPR and spectra the represent electromagnetic the absorption ofcurrent. energy at Theν as aconnection function of B. Theto the amount spectrometer is via two of B examined is referred to as the magnetic field sweep width. Spectra are presented in asmall first derivative variable mode length owing cables. to the signal The acquisitionvariable leng methodth andof these hardware cables [26]. allows The the MOUSE to be high-frequencypositioned EPRmeters spectral from absorptions the LFEPR of paramagnetic spectrometer, pigments and tend thus to be broad.analyze In an any size of painting. LFEPR spectrum,LFEPR spectra these absorption represent widths the can absorption be comparable of to energy the sweep at width ν as ofa Bfunction and of B. The amount can be cut off in the spectrum at the minimum and maximum B sweep values. Figure3 presentsof B examined examples of is three referred first derivative to as the LFEPR magnetic absorptions. field The sweep spectral width. baseline Spectra be- are presented in a comesfirst derivative more difficult mode to ascertain owing as theto the absorption signal width acquisition increases. method The lack ofand a clear hardware [26]. The high- spectralfrequency baseline EPR creates spectral a challenge absorptions for algorithms usedof paramagn to identify theetic pigment pigments represented tend to be broad. In an by an absorption. Qualitative and quantitative determinations become difficult. LFEPRFor this spectrum, reason, three these different absorption identification widths algorithms can were be comparable examined for the to analy- the sweep width of B and siscan of thebe painting cut off to in determine the spectrum if one performed at the best mi onnimum spectra and with baselinemaximum uncertainty. B sweep values. Figure 3 Theypresents are referred examples to as the of matrix, three least first squares, derivative and interior-point LFEPR algorithms. absorptions. These algo-The spectral baseline be- rithms were chosen because they represent a range of computational speed and complexity incomes the order more listed. difficult to ascertain as the absorption width increases. The lack of a clear spectral baseline creates a challenge for algorithms used to identify the pigment represented by an absorption. Qualitative and quantitative determinations become difficult.

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FigureFigure 3. 3.Simulated Simulated ﬁrst first derivative derivative EPR EPR absorptions absorptions with with different different widths. widths. Uncertainty Uncertainty in the in baselinethe base- locationline location increases increases as the as linewidth the linewidth increases. increases.

EachFor this algorithm reason, assumesthree different the painting identificati is composedon algorithms of i pigments, were examined each with for a the unique anal- EPRysis spectrumof the painting (Ri). Theto determine total EPR if spectrum one performed (S) from best a on location spectra in with the paintingbaseline isuncer- the weightedtainty. They sum are of thereferred spectra to fromas the the matrix, pigments, least where squares,Ai is and the weightinginterior-point factor. algorithms. These algorithms were chosen because they represent a range of computational speed and complexity in the order listed. S = ∑ Ri Ai (2) Each algorithm assumes the painting isi composed of i pigments, each with a unique EPRThe spectrum matrix ( algorithmRi). The total is based EPR onspectrum the premise (S) from that ai equationslocation in are the needed painting to solveis the i forweightedi Ai values. sum Deﬁningof the spectraSm and fromRi,m the, respectively, pigments, where as the A total is the and weighting pigmentEPR factor. signals at magnetic ﬁeld value m, Equation (2) becomes 𝑆=𝑅 𝐴 (2) Sm = ∑ Ri,m Ai (3) The matrix algorithm is based on the premisei that i equations are needed to solve for i Ai values.Writing Defining Equation Sm (3) and in R matrixi,m, respectively, form as the total and pigment EPR signals at magnetic field value m, Equation 2 becomes

[Sm] = [Ri,m][Ai] (4) 𝑆 =𝑅, 𝐴 (3) and solving for [Ai] −1 Writing Equation (3) in matrix[A formi] = [Ri,m] [Sm] (5) −1 where [Ri,m] is the inverse of matrix [[RSmi,m] =]. [ OurRi,m][ systemAi] of four pigments (i = RC, HB,(4) TR, and BV) requires spectral values at four ﬁeld values (m=1, 2, 3, and 4). The expanded versionand of solving Equation for (5) [A becomesi] -1 [Ai] = [Ri,m] [Sm] (5)    −1  ARC RRC,1 RHB,1 RTR,1 RBV,1 S1 where [Ri,m]-1 is the inverse of matrix [Ri,m]. Our system of four pigments (i = RC, HB, TR,  AHB   RRC,2 RHB,2 RTR,2 RBV,2   S2  and BV) requires spectral =  values at four field values (m=1, 2, 3, and 4). The expanded. ver- (6)  ATR   RRC,3 RHB,3 RTR,3 RBV,3   S3  sion of Equation (5) becomes ABV RRC,4 RHB,4 RTR,4 RBV,4 S4 𝐴 𝑅, 𝑅, 𝑅, 𝑅, 𝑆 Our matrix algorithm is the⎡ simplest of the three and⎤ placed no constraints on 𝐴 𝑅, 𝑅, 𝑅, 𝑅, 𝑆 Ai solutions. =⎢ ⎥ . (6) 𝐴 ⎢ 𝑅, 𝑅, 𝑅, 𝑅, ⎥ 𝑆 The least squares algorithm determines which Ri is closest to S. It assumes one pigment 𝐴 ⎣ 𝑅, 𝑅, 𝑅, 𝑅, ⎦ 𝑆 per image location and disregards Ai by requiring all spectra be initially normalized. The outputOur is thematrixi value algorithm that yields is the the simplest minimum of of the the three expression and placed no constraints on Ai solutions. 2 The least squares algorithm determines∑(Ri,m − whichSm) Ri is closest to S. It assumes one pig-(7) m ment per image location and disregards Ai by requiring all spectra be initially normalized. The output is the i value that yields the minimum of the expression

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The interior-point [27] algorithm ﬁnds the best Ai values that minimize the difference between Ai,Ri,m, and Sm at all points m in the spectrum. This algorithm is the most computationally intense of the three. Each algorithm is applied to spectra from locations on a grid in the painting to create m pigment maps of the painting. Both the matrix and interior-point algorithms are capable of producing pigment maps proportional to the amount of pigment, Ai. However, this is not possible to achieve with an impasto painting. Although the sampling region is a 3.5 × 5 mm ellipse, the pole pieces of the unilateral magnet yoke and surrounding MOUSE housing create a 9 cm diameter circular ﬂat surface, which is placed against the painting. Depressions in the topography of the painting possess a lower signal than high points in contact with the RF coil. The ability to detect a signal from the MOUSE diminishes to approximately 20% by 500 µm from the RF coil [20,28]. For these reasons, all pigment maps were binary, where the largest Ai value for a grid location is assigned a value of one in its pigment map.

3. Materials and Methods As a test of the proposed method, a simple four-color 10 × 10 cm impasto painting on canvas was prepared using linseed oil paints (see Figure1). The impasto painting was chosen because it presented a challenging test of the algorithms and for convenience. The paint was hand mulled using boiled linseed oil (Houston Art) and the pigments blue vitriol (CuSO4·5H2O, J.T. Baker), Han blue (BaOCuO(SiO2)4, Kremer Pigments), terracotta red 3+ (from fired red clay containing Fe ), and rhodochrosite (MnCO3, Kremer Pigments). as previously described [22]. The painting, Palm Tree on a Beach at Twilight, is of a palm tree growing in sand against a dark blue sky. The palms of the tree were painted with blue vitriol, which attains a green color when mixed with the oil and dried, the tree trunk with terracotta red, the sky with Han blue, and the sand with rhodochrosite. A contact profilometer was used to characterize the pigment thickness variations in the painting. Composite images were created from the results to enable comparison to the original painting. A composite image is a color image created from a pigment’s component map and its red, green, and blue (RGB) values. Since only one pigment is assigned to a pixel, there is no overlap of colors, and the composite image contains only pixels of four colors. The collection of the LFEPR signals in the painting was performed using the EPR MOUSE. The painting was attached to an acrylic bed of a two-axis positioning system with 0.1 mm resolution. The positioning system moves the painting over the MOUSE to the various sampling positions on the ZX grid and lowered it onto the MOUSE. The grid is relative to the MOUSE magnetic resonance coordinate system where B is along Z and the RF polarized along Y [20]. The center of the elliptical sampling region was positioned on a square grid, with a 3.33 mm spacing between horizontal and vertical grid lines, to produce a 29 × 30 point sampling space on the painting. A finer grid is unnecessary, as resolution is limited by the 3.5 × 5 mm elliptical sampling region. Locations on the painting are referred to by their (z,x) location. Some overlap between adjacent sampled grid locations existed. Figure1 presents the grid and a few of the elliptical sampling regions superimposed onto the painting. This image shows the smaller Z and larger X overlap of adjacent ellipses, as exemplified by the ellipses at (24,8), (25,8) and (25,7), (25,8), respectively. When the ellipse spans more than one pigment, as in the ellipse on grid (21,12), fractional sampling occurs, and the EPR spectrum is a weighted sum of spectra from the pigments in the ellipse. LFEPR spectra were acquired at each grid point using the acquisition parameters presented in Table1. Acquisition of data from the 870 points on the 29 × 30 grid took approximately 14.5 hours. Parameters were chosen to record in a short amount of time a discernable spectrum upon which a determination of the pigment could be made. Spectra were recorded of the four pure pigments and used as reference spectra for the various identification algorithms. Pigments with more similar spectral g-factors and absorption line shapes and widths should be recorded slower with more spectral points to capture their subtle differences, which would take more time. Heritage 2021, 4 FOR PEER REVIEW 6

were recorded of the four pure pigments and used as reference spectra for the various identification algorithms. Pigments with more similar spectral g-factors and absorption line shapes and widths should be recorded slower with more spectral points to capture their subtle differences, which would take more time.

Table 1. LFEPR acquisition parameters.

Parameter Value Frequency (ν) 388.5 MHz Magnet sweep width 51 mT Scan time 13 s Number of spectral points 100 Modulation frequency 10 kHz Heritage 2021, 4 Modulation amplitude 1187 2 mT Time constant 0.1 s

Table 1. LFEPR acquisition parameters.Number of averages 1

Parameter Value This gridFrequency and (ν )the ellipses were used to 388.5 create MHz a digital truth image of the dominant pigmentMagnet at each sweep location. width Dominance was dete 51 mTrmined through visual assessment of the Scan time 13 s surfaceNumber area offraction spectral points of a pigment in the ellipse. 100 Those locations covering a surface area Modulation frequency 10 kHz fraction Modulationgreater amplitudethan 0.6 were assigned the pigment 2 mT with the larger fraction. Those locations with fractionsTime constant between 0.6 and 0.4 were 0.1assigned s the thicker pigment. The truth im- Number of averages 1 age is an approximate representation of the visual amount of pigment at each location. AlthoughThis grid andthe the EPR ellipses signal were is used not to equal create a to digital the truthvisual image amount of the dominant owing to variations in the thick- pigmentness of at eacha paint location. and Dominance its dependence was determined on throughthe concentration visual assessment in of a the volume, the top surface of surface area fraction of a pigment in the ellipse. Those locations covering a surface area fractionwhich greater is only than 0.6visible, were assigned it is the the pigment closest with available the larger fraction. indication Those locations of the presence of a pigment. A withcomposite fractions between truth 0.6image and 0.4 was were assignedcreated the using thicker th pigment.e dominant The truth pigment image is map and the RGB frac- an approximate representation of the visual amount of pigment at each location. Although thetional EPR signal values is not of equal BV(0.59, to the visual 0.73, amount 0.53), owing HB(0.00, to variations 0.00, in 0.10), the thickness RC(0.89, of 0.73, 0.50), and TR(0.47, a0.23, paint and0.14). its dependence This image on the is concentrationpresented in in a volume,Figure the 4. top surface of which is only visible,The it sampling is the closest availableprocedure indication created of the presencea 29 × of30 a pigment.× 100-point, A composite spatial–spatial–spectral set of truth image was created using the dominant pigment map and the RGB fractional values ofdata. BV(0.59, Each 0.73, 0.53),of the HB(0.00, spatial 0.00, points 0.10), RC(0.89, was 0.73, analyzed 0.50), and by TR(0.47, three 0.23, algorithms 0.14). This for identification of the imagepigment is presented at the in Figurepoint.4. The matrix, least squares, and interior-point algorithms were imple- The sampling procedure created a 29 × 30 × 100-point, spatial–spatial–spectral set ofmented data. Each in of theMATLAB spatial points (Mathworks). was analyzed by All three algorithms algorithms for identificationproduced of four pigment maps where theeach pigment grid at location the point. Thewas matrix, single least valued. squares, andThe interior-point final step, algorithms presentation, were was equivalent for each implemented in MATLAB (Mathworks). All algorithms produced four pigment maps wherealgorithm. each grid locationThe four was singlepigment valued. maps The final were step, presentation,converted was into equivalent a single for composite image by first eachcolorizing algorithm. each The four pigment pigment maps map were with converted its RGB into avalu singlees. composite The four image layers by representing each pig- firstment colorizing map eachwere pigment then map combined with its RGB to values. show The the four loca layerstions representing of all four each pigments in a single RGB pigment map were then combined to show the locations of all four pigments in a single RGBimage. image. Creating Creating the the composite composite image was image also realized was also in MATLAB realized code. in MATLAB code.

FigureFigure 4. Truth 4. Truth image representingimage representing the dominant pigment the dominant at each sampling pigment location. at each sampling location. .

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Heritage 2021, 4 Four metrics assessed the ability of each algorithm to segment the1188 pigments: true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN) [29]. TP are the number of correctly identified pigment grid points. FP are the number of grid pointsFour incorrectly metrics assessed identified the ability as the of pigment. each algorithm TN are to segmentthe number the pigments: grid points true correctly iden- tifiedpositives as (TP),not truebeing negatives a pigment. (TN), false FN positives are the (FP), number and false of negatives pigment (FN) grid [29 ].points TP are that were not identifiedthe number as of correctlythe pigment. identified Because pigment the grid number points. FP of are pigment the number grid of points grid points (P) and non-pig- incorrectly identified as the pigment. TN are the number grid points correctly identified as mentnot being grid a pigment.points (N) FN differ are the for number each of pigment, pigment grid ratios points were that used were notto identifiedfacilitate asthe comparison ofthe an pigment. algorithm’s Because ability the number to identify of pigment a pigment. grid points The (P) andratios non-pigment are the true grid positive points rate (TP/P), false(N) differ negative for each rate pigment, (FN/P), ratios true were negative used to facilitaterate (TN/N), the comparison and false of anpositive algorithm’s rate (FP/N). ability to identify a pigment. The ratios are the true positive rate (TP/P), false negative rate (FN/P), true negative rate (TN/N), and false positive rate (FP/N). 4. Results and Discussion 4. ResultsFigure and 5 Discussionpresents a plot of pigment thickness along the vertical Z = 9 grid line 3 cm fromFigure the left5 presents edge of a plotthe ofpainting. pigment thicknessThe three along broad the verticalflatter regions Z = 9 grid with line 3a cm thickness of ~0.8 mmfrom correspond the left edge ofto the the painting. blue vitriol The three in the broad palm flatter tree regions foliage. with The a thickness topography of ~0.8 of the impasto mm correspond to the blue vitriol in the palmμ tree foliage. The topography of the impasto paintingpainting variedvaried by by as as much much as 600as 600µm, makingm, making it impossible it impossible to perform to perform quantitative quantitative de- terminationsdeterminations with with thethe algorithms. algorithms. For For this reason,this reason, all pigment all pigment maps were maps binary. were binary.

FigureFigure 5.5.The The pigment pigment thickness thickness along along a line ina theline painting in the correspondingpainting corresponding to Z grid line 9.to The Z grid line 9. The thicknessthickness plot plot is is color color coded coded to the to paint’s the paint’s RGB pigment RGB pigment color. color. For spectral identification, it is preferable that the sweep width be wide enough for the signalFor spectral to start and identification, end at zero signal. it is However, preferab becausele that these the are sweep LFEPR width spectra be where wide enough for thethe signal absorption to start widths and can end be comparableat zero signal. to the However, sweep width because and the these signal are greater LFEPR than spectra where thezero absorption at the start of widths the scan, can a method be comparable of reproducibly to the overlaying sweep width spectra and was necessary.the signal greater than The decided-upon method was one where all spectra were offset to start at zero signal zeroat zero at magneticthe start field of the and scan, normalized a method such that of reproducibly the largest negative overlaying signal values spectra in the was necessary. Thespectra decided-upon were equal. The method offset, thenwas normalized,one where EPRall spectr spectraa forwere the fouroffset pigments to start are at zero signal at zeropresented magnetic in Figure field5. The and four normalized spectra present such the similarities that the and largest differences negative in the spectra,signal values in the spectraand the challengeswere equal. of identifying The offset, them. then These normalized, spectra are the EPRRi spectra spectra introduced for the infour the pigments are m presentedbackground in section. Figure For 5. the The matrix four algorithm, spectra thepresen fourt magnetic the similarities field values and for differences= 1, 2, 3, in the spec- and 4 in Equation (6) were 8.69, 12.79, 17.39, and 28.64 mT in these spectra. The vertical tra,dashed and lines the inchallenges Figure6 indicate of identifying the location them. of these These field values. spectra These are field the values Ri spectra were introduced in thechosen background to give unique, section. non-zero For pointsthe matrix in the spectra.algorithm, They the are sufficientfour magnetic to perform field the values for m = 1,identification, 2, 3, and 4 but in may Equation not be optimal. 6 were 8.69, 12.79, 17.39, and 28.64 mT in these spectra. The vertical dashed lines in Figure 6 indicate the location of these field values. These field values were chosen to give unique, non-zero points in the spectra. They are sufficient to perform the identification, but may not be optimal.

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Figure 6. LFEPR reference spectra of the four pigments in the painting. Spectra are offset to start at zero signal and normalized such that the largest negative signal values were equal. Dashed vertical lines indicate the ﬁeld values used in the matrix algorithm.

Figure7 presents the segmented images by the three pigment identification algorithms. Also presented in this figure are discrepancy images where there is a difference between the truth image (Figure4) and an algorithm image. Image pixelation is a consequence of the 29 × 30-point sampling grid. The algorithms prevented a pixel from belonging to more than one pigment class. All three algorithms presented a recognizable image that is comparable to the original painting and the truth image. Differences between the outputs of the algorithms in the pixels identified as a certain pigment were less than five pixels in all cases. Incorrectly identified pixels were primarily associated with boundary locations where two or more pigments occupied a sampling region and a consequence of the algorithm picking the larger signal over the larger visible surface area pigment. This can be seen at the BV–HB and HB–RC boundaries. One exception can be found at grid location (z,x) = (21,19) by the least squares algorithm. The truth image presents this location as BV, but it was identified as TR. Since there is no TR in the painting at this point, the discrepancy is attributed to the simplicity of this algorithm and the portions of RC and BV present being interpreted as TR by the algorithm. The matrix and interior-point algorithms identified this location correctly as BV. The metrics for the four pigments by the three algorithms are summarized in Table2. Of the 870 grid locations on the painting, 210, 343, 270, and 47 are, respectively, assigned to BV, HB, RC, and TR in the truth image. All algorithms had a true positive rate of 0.95 or better and a true negative rate of 0.98 or better for all pigments. These numbers are an indication of the high sensitivity and specificity of all three algorithms. These two metrics varied little between the algorithms for a given pigment. Similarly, there was very little discrepancy between the algorithms in the number of false positives and false negatives for a given pigment. In general, rhodochrosite was the most correctly identified pigment by all the techniques. This was followed by terracotta red and blue vitriol. Han blue was incorrectly identified the most with a false positive rate of 0.01 and a false negative rate of 0.04 to 0.05 by the algorithms. Heritage 2021, 4 FOR PEER REVIEW 9 Heritage 2021, 4 1190

Figure 7. ColorizedFigure 7. composite Colorized (rowcomposite one) and (row grayscale one) and discrepancy grayscale di (rowscrepancy two) images(row two) from images the least from squares the least (left ), matrix (center), andsquares interior-point (left), matrix (right )(center algorithms.), and interior-point (right) algorithms.

The metricsTable for 2.theEvaluation four pigments metrics by for the identificationthree algorithms algorithms. are summarized in Table 2. Of the 870 grid locations on the painting, 210, 343, 270, and 47 are, respectively, assigned to BV, HB, RC, and TR in the truth image. All algorithms had a truePigment positive rate of 0.95 Algorithm Metric or better and a true negative rate of 0.98 orBlue better Vitriol for all pigments. Han Blue These Rhodochrosite numbers are an Terracotta Red indication of the high sensitivity andTP/P specificity 0.98 of all three algorithms. 0.95 These 1.00 two metrics 1.00 varied little between the algorithmsFP/N for a give 0.02n pigment. Similarly, 0.01 there was 0.01 very little 0.00 Matrix discrepancy between the algorithmsFN/P in the number 0.02 of false positive 0.05s and false 0.00 negatives 0.00 for a given pigment. In general, rhodochrositTN/Ne 0.98was the most correctly 0.99 identified 0.99 pigment 1.00 by all the techniques. This was followedTP/P by terracotta 0.97 red and 0.95 blue vitriol. Han 1.00 blue was 1.00 FP/N 0.02 0.01 0.01 0.00 incorrectly identifiedLeast the Squares most with a false positive rate of 0.01 and a false negative rate of 0.04 to 0.05 by the algorithms. FN/P 0.03 0.05 0.00 0.00 TN/N 0.98 0.99 0.99 1.00 Table 2. Evaluation metrics for the identificationTP/P algorithms. 0.98 0.96 1.00 1.00 FP/N 0.01 0.01 0.01 0.00 Interior-Point Pigment Algorithm Metric FN/P 0.02 0.04 0.00 0.00 Blue TN/NVitriol Han 0.99 Blue Rhodochrosite 0.99 Terracotta 0.99 Red 1.00 TP/P 0.98 0.95 1.00 1.00 FP/N 0.02 0.01 0.01 0.00 Matrix Similarities between the less than perfect metrics from an algorithm for a given pigmentFN/P are attributed0.02 to EPR spectral 0.05 imperfections 0.00 from noise. 0.00 Since most discrepancies are seenTN/N at the boundaries0.98 between 0.99 pigments, 0.99 where two pigments 1.00 occupy the elliptical samplingTP/P region,0.97 we attribute them 0.95 to variations 1.00 in the topography 1.00 of the surface of the paintingFP/N and the0.02 use of a flat RF 0.01 sample coil 0.01 mounted in a flat 0.00 housing approximately Least Squares equalFN/P to the size of0.03 the painting. 0.05 Since the limit 0.00 of detection increases 0.00 as distance from the sampleTN/N coil increases,0.98 i.e., the coil 0.99 creates less signal 0.99 the further away 1.00 the sample is from its surface, the pigment closest to the sample coil will have the dominant signal of the two. TP/P 0.98 0.96 1.00 1.00 We estimated that the signal from a pigment covering as little as 40% of the ellipse area FP/N 0.01 0.01 0.01 0.00 Interior-Pointand in contact with the coil would dominate over a pigment offset from the surface and FN/P 0.02 0.04 0.00 0.00 occupying 60% of the ellipse. The results indicate that this may be too conservative an estimate.TN/N 0.99 0.99 0.99 1.00 For this four-pigment painting, it is possible with the matrix method to scan the painting at just four magnetic field values rather than 100. The protocol would be to raster

Heritage 2021, 4 1191

the mouse over the grid locations at four B value instead of incrementing the MOUSE location and scanning the entire sweep width. This would signiﬁcantly decrease the data acquisition time.

5. Conclusions The results of this study present art conservators and historians with another analytical technique for identifying paramagnetic pigments and mapping their spatial distribution in a painting. The EPR MOUSE can noninvasively collect LFEPR spectra from grid points on a painting either by moving the painting over the MOUSE or the MOUSE over the painting. These spectra can identify the pigment at each grid location on the painting. A dense grid of identified pigments can be presented as a spatial map or color image of the pigments in the painting. All three spectral identification algorithms produced in an unsupervised manner images that closely resembled the original painting and very closely matched the truth image. The metrics used to compare the pigment maps from the three algorithms to the truth image were exceptionally good. For all pigments by all algorithms, the true positive rate was at least 0.95, and the true negative rate 0.98. Similarly, the false positive and false negative rates were less than or equal to 0.02 and 0.05, respectively. We believe the interior-point was the most robust algorithm followed by the least squares and matrix algorithms. The matrix method was least robust because it depended on only four spectral points and was the most sensitive to spectral noise. The least squares algorithm was the simplest and worked surprisingly well. All three algorithms are scalable to a larger number of pigments; however, performance will depend on the uniqueness and quality of the spectra. Quantitative results should be possible with flatter (less impasto) painting surfaces or the redesign of the MOUSE surface. This study is part of a methodical approach to developing LFEPR spectroscopy for noninvasively studying paintings. Earlier studies focused on identifying single pigments [21], mixtures of two pigments [22], pigment layers [22], imaging of one component [23], and now mapping the spatial distribution of four pigments. The presented analytical technique is promising for application in topics related to the preservation of cultural her-itage, since it is non-destructive and the designed system can operate automatically. In the future, we intend to examine underpaintings, expand mapping to more pigments, and apply our techniques to paintings with cultural heritage significance.

Author Contributions: Conceptualization, J.P.H. and H.W.; methodology and software, S.M. and H.W.; validation, S.M. and H.W.; formal analysis, S.M., H.W. and J.P.H.; painting, H.W.; writing— original draft preparation, J.P.H.; writing—review and editing, S.M., H.W. and J.P.H.; supervision, J.P.H. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Acknowledgments: The authors thank Olivia Kuzio for helpful comments during the preparation of the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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