Submitted:
09 July 2024
Posted:
11 July 2024
Read the latest preprint version here
Abstract

Keywords:
1. Introduction
2. Materials and Methods
3. Results and discussion
3.1. Metrics in Practice
3.1.1. Image-Based Metrics: L*a*b*
3.1.2. Image-Based Metrics: Skewness
3.1.3. Appearance-Based Metrics: Colour and Gloss
3.1.4. Spectral-Based Metrics: HSI
3.1.5. Spectral-Based Metrics: FTIR
3.1.6. Spectral-Based Metrics: SEM-EDX
3.2. Evaluating Soiling Removal Scores Using the Metrics
4. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Additional Methodological Details
| Incident Light | Raking Light | ||
|---|---|---|---|
| Image Capture | Image Capture | ||
| ISO | 100 (ground); 200 (paint) | ISO | 160 (ground); 200 (paint) |
| Exposure | 1/125 s | Exposure | 1/125 s |
| Aperture | f/2.8 | Aperture | f/2.8 |
| SetupGeometries | SetupGeometries | ||
| Camera height | 73 cm | Camera height | 73 cm |
| Light quantity | 2 (left and right) | Light quantity | 1 (right) |
| Lights height from plane | 39 cm | Lights height from plane | 16 cm |
| Lights angle from plane | 45o | Lights angle from plane | 60o |
| Lights to lens distance | 45 cm | Lights to lens distance | 75 cm |
| HSI Cameras | VNIR1800 | SWIR384 | Lights | Tungsten-Halogen | |
|---|---|---|---|---|---|
| Spectral range, nm | 407-998 | 951-2505 | Spectral coverage, nm | c. 320-2600 | |
| Spectral bands | 186 | 288 | Quantity | 2 | |
| Spectral intervala, nm | 3.26 | 5.45 | Room lighting | Darkness | |
| Pixels acquired | 1800 | 384 | Geometryb | 45o, h: 130 cm, d: various | |
| Focal length, m | 0.30 | 0.30 | Spectral reflectance | Spectralon white (99%) | |
| Field-of-viewc, cm | 8.60 | 8.60 | standard | and grey (50%) diffuse | |
| Spatial resolution, μm | 50 | 220 | |||
| Mount | Fixed, perpendicular to surface | Mount | Fixed to stage | ||
| Acquisition Parameters | |||||
| HSNRd | 0 | 0 | |||
| Integration time, μs | |||||
| for exposed ground | 25000 | 6900 | |||
| for oil paint | 39000 | 10800 | |||



Appendix B. Discussion of Unsupervised Unmixing for Soiling Removal Mapping

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| Scoring Criteria | ||||
|---|---|---|---|---|
| Score Rating |
Cleaning Efficacy |
Cleaning Homogeneity |
Pigment Swelling | Selectivity (Pigment Loss) |
| 1 | No effect | Uneven removal (<30%) | Extreme, visible swelling | Unacceptable loss |
| 2 | Little effect | Inconsistent removal (<50%) | Moderate, visible swelling | Notable loss |
| 3 | Moderate effect | Consistent removal (<80%) | Sensation of swelling, invisible | Microscopic loss |
| 4 | Effective removal | Complete removal (100%) | No swelling | No loss |
| Mock-Up | Stratigraphy | Application | Ageing and Soilinga | Surface Propertiesb |
|---|---|---|---|---|
| Chalk-Glue Ground |
Canvas: washed linen, twill weave, stretched Size: rabbit skin glue Ground: chalk, in rabbit skin glue |
Hog’s hair brushes | 6 months ambient drying 3 weekly cycles of accelerated ageing: Memmert ICH110L chamber; light: 4 fluorescent lamps (6 500 K (D56), 500 W); irradiance: 70 Wm-2; total energy: 169 330 kJm-2; 40oC (CHT); and fluctuating RH (15–65%) 3 spraying campaigns (2 for oil paint) of artificial soiling adapted for the Aula Soiling layer: 27.1 ±2.4 µm Min particle size: 0.095 µm Max particle size: 10 µm |
Thickness: 122.3 ±39.2 µm Water sensitivity: 14 rolls Chalking: ISO 2 pH: 6.5 Conductivity: 1 500 µS cm-1 |
|
Composite Half-Chalk Ground |
Canvas: ibid. Size: ibid. Ground: chalk, zinc white, lead white in rabbit skin glue and boiled linseed oil emulsion |
Thickness: 104.9 ±40.2 µm Water sensitivity: 10 rolls Chalking: ISO 3 pH: 6.4 Conductivity: 500 µS cm-1 |
||
|
Chromium Oxide Green Oil Paint |
Canvas: ibid. Size: ibid. Ground: half-chalk ground Pigment-binder: undiluted chromium oxide green in linseed oil |
Thickness: 114.9 ±26.4 µm Water sensitivity: 5 rolls Chalking: ISO 1 pH: 6.4 Conductivity: 530 µS cm-1 |
| Supplier | Material | Composition | Quantity | Dry Weight |
|---|---|---|---|---|
| g or mL | % | |||
| Rublev | Lamp black (oil furnaces) | C | 0.62 | 1.00 |
| Kremer | Vine black (organic source) | C | 0.62 | 1.00 |
| Burgundy ochre (fine) | Fe2O3·H2O | 1.45 | 2.34 | |
| Wheat starch powder | Polysaccharide (C6H10O5)n | 10.00 | 16.14 | |
| Gelatin powder | Proteins and peptides | 10.00 | 16.14 | |
| Merck | Sodium nitrate | NaNO3 | 2.50 | 4.03 |
| Kaolin | Al2Si2O5(OH)4 | 18.00 | 29.06 | |
| Portland cement (Type I) | CaO·SiO2 Fe, Al, MgO | 17.00 | 27.45 | |
| Silica, quartz | SiO2 | 1.75 | 2.83 | |
| Mineral oil | Hydrocarbons | 5.0 | - | |
| Filippo Berio | Olive oil | Mainly triacylglycerols | 2.5 | - |
| Kremer | Shellsol D40 | Hydrocarbons | 1000 | - |
| Cleaning Solution |
Concentration | Chalk-Glue Ground | Half-Chalk Ground | Chromium Oxide Green |
|---|---|---|---|---|
| Deionised water |
- | pH 7.2, 20 µS cm-1 | pH 7.2, 20 µS cm-1 | pH 7.2, 20 µS cm-1 |
| Adjusted watera (ammonium acetate) |
Conductivity-related | pH 5.5, 1 500 µS cm-1 | pH 5.5, 500 µS cm-1 | pH 5.0, 500 µS cm-1 |
| Chelatorb (citric acid / sodium hydroxide) |
0.5% w/v (0.026M) CA in 10% w/v (2.5M) NaOH | pH 5.0, 4 240 µS cm-1 | pH 4.5, 3 240 µS cm-1 | pH 4.5, 3 240 µS cm-1 |
| Chelatorb (citric acid / ammonium hydroxide) |
0.5% w/v (0.026M) CA in 10% w/v (5.0M) NH4OH | pH 5.0, 5 320 µS cm-1 | pH 4.5, 4 270 µS cm-1 | pH 4.5, 4 270 µS cm-1 |
| Clearancec (ammonium acetate) |
Conductivity-related | pH 6.5, 500 µS cm-1 | pH 6.5, 500 µS cm-1 | pH 6.5, 500 µS cm-1 |
| Metrica | Rangeb | Data Typec | Concept | Equipmentd | Post-Processinge | |
|---|---|---|---|---|---|---|
|
Cleaning homogeneity |
VNIR /SWIR |
2D spectral maps |
Image homogeneity from grey-level co-occurrence matrix (GLCM) | DLSR camera HSI camera |
Change image type to 8-bit depth for GLCM Texture plug-in in ImageJ |
|
| Cleaning efficacy | ||||||
| Image-based |
L*a*b* images | VIS | 2D RGB images |
Thresholded pixels representing soiling |
DLSR camera Mobile phone |
Conversion to CIELAB space; image thresholding |
| Histogram skewness |
VIS | 2D RGB images |
Histogram distribution asymmetry as function of darker soiling on lighter substrate | Spreadsheet/statistical calculations |
||
| Appearance | Glossimetry | VIS | 1D point measurements |
Perceived surface texture under direct light source |
Glossmeter | Spreadsheet/statistical calculations |
| Colorimetry (from HSI) |
VNIR | 2D L*a*b* images (from 3D datacube) |
Colour difference, ΔE2000, before and after soiling removal |
HSI camera | Conversion to CIELAB space; colorimetric and statistical calculations | |
| Spectral-based | HSI: spectral unmixing |
VNIR /SWIR |
3D datacube | Spectral reflectance similarity (compared to unsoiled areas, or soiling) |
HSI camera | Spectral calibration; algorithm pre- and post-processing |
| HSI: NDI mapping |
SWIR | 2D normalised difference images |
SWIR marker bands for soiling and surface |
HSI camera | Spectral calibration; PCA; image processing | |
| FTIR mapping | MIR | 2D chemical maps |
MIR spectra (or marker bands) for soiling | FTIR spectrometer |
Atmospheric correction; correlation map profiles | |
| SEM-EDX mapping |
(XR) | 2D chemical maps |
Element signal for soiling | SEM | TruMap processing; element selection |
| Cleaning Efficacy Metric | Value for xBT | Value for xAT | |
|---|---|---|---|
| Image-based |
L*a*b* images | Number of black pixels before treatment (black pixels represent soiling) | Number of black pixels after treatment (black pixels represent soiling) |
| Histogram skewness | Difference in skewness between unsoiled (CT) and soiled (BT) mock-up (ΔskewnessCT,BT) |
Difference in skewness between unsoiled (CT) and cleaned (AT) mock-up (ΔskewnessCT,AT) |
|
| Appearance | Glossimetry | Difference in gloss between the unsoiled (CT) and soiled (BT) mock-up (ΔglossCT,BT) | Difference in gloss between the unsoiled (CT) and cleaned (AT) mock-up (ΔglossCT,AT) |
| Colorimetry (from HSI) | CIE2000 colour difference between the unsoiled (CT) and soiled (BT) mock-up (ΔE2000(CT,BT)) |
CIE2000 colour difference between the unsoiled (CT) and cleaned (AT) mock-up (ΔE2000(CT,AT)) |
|
| Spectral-based | HSI: spectral unmixing | Mean pixel value from 100 pixel x 100 pixel area taken from unsoiled (CT) mock-up, or soiling control (sCT), in unmixing map (CT, or sCT) | Mean pixel value from 100 pixel x 100 pixel area taken from cleaned (AT) mock-up, in unmixing map (AT) |
| HSI: NDI mapping | Mean pixel value from 100 pixel x 100 pixel area taken from unsoiled (CT) mock-up, or soiling control (sCT), in NDI map (CT, or sCT) | Mean pixel value from 100 pixel x 100 pixel area taken from cleaned (AT) mock-up, in NDI map (AT) | |
| FTIR mapping | Number of white pixels before treatment (white pixels represent soiling) | Number of white pixels after treatment (white pixels represent soiling) | |
| SEM-EDX mapping | Number of element-rich areas as counted by Analyse particles function in ImageJ before cleaning |
Number of element-rich areas as counted by Analyse particles function in ImageJ after cleaning |
| CleaningEfficacyMetrics | MeanValues | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Image-Based | Spectral-Based | |||||||||||||
| Cleaning Solution | L*a*b* | Skewness | Supervised (VNIR) | NDI (SWIR) | FTIR (MIR) | Image-Based | Spectral-Based | |||||||
| Deionised water | 0.76 | 0.81 | 0.95 | 0.85 | 0.39 | 0.79 | 0.73 | |||||||
| Adjusted water | 0.78 | 0.79 | 0.91 | 0.84 | 0.58 | 0.79 | 0.78 | |||||||
| Chelator (NaOH) | 0.79 | 0.70 | 0.91 | 0.88 | 0.46 | 0.75 | 0.75 | |||||||
| Chelator (NH4OH) | 0.84 | 0.68 | 0.96 | 0.96 | 0.57 | 0.76 | 0.80 | |||||||
| Scoring criteria | ||||||||||||||
| CleaningSolution | CleaningEfficacya |
Cleaning Homogeneityb |
Colour Integrityc |
Gloss Integrityc |
Selectivityd | Residue Absenced | ||||||||
| Deionised water | 0.76 | 0.23 | 0.75 | 0.17 | 1.00 | 1.00 | ||||||||
| Adjusted water | 0.78 | 0.22 | 0.69 | 0.64 | 1.00 | 1.00 | ||||||||
| Chelator (NaOH) | 0.75 | 0.33 | 0.72 | 0.62 | 0.60 | 1.00 | ||||||||
| Chelator (NH4OH) | 0.78 | 0.57 | 0.82 | 0.86 | 0.80 | 1.00 | ||||||||
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