Blue Ballpoint Pen Inks Differentiation using Multivariate Image Analysis of Digital Images Captured with PhotoMetrix PRO®

. In Forensic Documentoscopy, it is frequently questioned if a particular document was written with one or more pens. Different methods have been developed to distinguish pen inks from each other, but some of these techniques require the ink extraction, destructing the document, and other techniques uses high cost instruments. PhotoMetrix PRO ® , an app for mobile devices, is a qualitative and colorimetric analysis tool that applies uni-and multivariate analysis. Amongst them, Principal Component Analysis (PCA), Hierarchical Cluster Analysis (HCA) and Partial Least Squares Discriminant Analysis (PLS-DA) can be obtained from digital images’ decomposing data. It is a non-destructive and a simple method, of easily use and low cost. Chemometric knowledge is important for results interpretation. This study aims to evaluate the PhotoMetrix PRO ® capacity on blue ballpoint pens differentiation. Three experiments were performed with different ballpoint pens, including colorful pens as an app functionality


Introduction
Forensic Documentoscopy aims to analyze information concerning a document history, its authenticity or inauthenticity and different kinds of alterations. Considering handwriting examination, sometimes it is necessary to demonstrate if a particular document was written with one or more pens, and this information may be related to fraud by writing in two different moments. In order to detect this kind of fraud, it is necessary to analyze the documents' pen inks 1 .
Ink analysis has a great importance in Forensic Science. In Brazil, documentoscopy experts are frequently requested to solve questions regarding differentiation of pen inks, and about 80% of cases involve ballpoint pens 2 .
There is not a pattern formula for pen inks fabrication. For this reason, the inks' components vary in their quantities between different brands and also between different regions in the world 1,3 . In this context, it is important to develop appropriate methods to differentiate pen inks from each other, and both the cost and the simplicity of the method should be evaluated. Sometimes, proving that two different pens were used in a document can provide answers in specific judicial cases, when a document has been scribed and re-written with a pen of similar color, or in a case with writing addition on the original document 4 . For example, a medical certificate can be altered on its days' quantity, a bank check could have additional numbers and text to increase its value, and work contracts might have altered information for retirement purposes.
In the past few years, many methods have been developed for ink characterization 5 . Some of those methods were designed as destructive for the document, when it is necessary to cut a part of the document to extract the pen ink, which is not the best option for Forensic Science. Some of the published papers describing pen inks differentiation using destructive techniques included HPLC (High performance liquid chromatography) 6,7 , Orbitrap Mass Analyzer 8,9 ; UV-Vis (UV-Vis Spectroscopy) 10 26,27 and food analysis 28,29 .
Therefore, the objective of this study is to evaluate the PhotoMetrix PRO ® capacity on differentiating blue ballpoint pen inks, using common pens brands in Brazil.
The app is a simple non-destructive method that can provide useful information to discriminate samples in the Forensic field; also, it is a fast, easy-handling and a lowcost tool. also with singular value decomposition using NIPALS algorithm.

Inks collection
Initially, all inks were applied on paper -blank paper sheets of same brand, with 75g of weight. The inks were applied by filling in squares, using lines of same pressure, and by writing a random word ("pen"), as represented in Figure 1a and Figure 1b ( Figure 1). All inks were applied on paper by the same writing fist and then the inks were allowed to dry for one day. The ink deposition was set this way in order to uniform the ink quantity for all pen brands and types. The experiments were conducted on images collection from the squares (set as an uniform pattern for each ink) and from the graphisms (simulating real cases), and then compared.
(a) (b) Figure 1. Pen inks application on paper, so that images could be captured with the PhotoMetrix PRO ® app. All the different brands are also described, as well as their codes for PCA and HCA graphics. a) colorful ballpoint pens; b) blue ballpoint pens.
First, six ballpoint pens of different colors (navy blue, light blue, violet, pink, red and light green) were analyzed as a preliminary study, to evaluate the app functionality and to define the images capturing conditions. Figure 1a shows all the colors, the codes used for data display, and the template used for inks collection.
After establishing the app capability of distinguish different visual colors, twelve blue ballpoint pens, of nine different brands, were tested. The intention of this work was to evaluate different blue ballpoint pen brands, and those pens were chosen considering their availability in the Brazilian market (specifically stores located in Porto Alegre city, state of Rio Grande do Sul). For Bic and Pilot brands, more than one type of pen was found. Also, two pens of identical types of Bic pens were used to evaluate the behavior of inks from the same brand and type. Figure 1b shows all pen brands and types used in this study, their codes for data display and the template utilized for inks collection.

Images collection
All the images were obtained using two different mobiles devices: a G5 Motorola ® smartphone operating with Android 8.1.0 system, with a 13MP rear camera, and a Samsung ® Galaxy A8 smartphone, operating with Android 9 system, and a 16MP rear camera. Figure 2 shows the established parameters for images capturing. After programing the number of samples and the region of interest size (defined at 32x32 in this study) at Settings, we chose Multivariate Analysis, PCA Analysis, Sampling, and then mean method. Concerning single channels parameters, using all channels but luminosity was the best condition in this study. All images were collected in triplicates in the exact same spot on paper, as an internal control for each pen brand. In order to collect three images of the same spot, the mobile device was positioned on a stable platform. Different heights (6 and 8cm) were tested for image capturing, and no influence of height was observed. However, the same height (8cm) was established for both mobile devices to maintain a pattern, and this distance was appropriated to focus the camera for taking the pictures. All the images were collected under natural ambient luminosity. After collecting all the pictures, PCA graphs scores are provided and it is possible to take a screen shot of the results, for both PCA score graphs and PCA loadings graphs. HCA analysis can be performed with the same data, by choosing HCA Analysis and Re-Processing. All the experiments were performed at least five times, at the same day and at different days for both devices, to evaluate the app repeatability. There is a small variability concerning each sample position in the PCA graph, considering a possible variability for image capturing. The best graphs scores were chosen considering the triplicates proximities, demonstrating adequate images collection for each pen brand.
Qualitative pen brands differentiation is evaluated considering the distances between each brand triplicates in the PCA graph score.

Method confirmation
After PCA and HCA analysis, the PLS-DA method was applied to confirm PhotoMetrix PRO ® capability to discriminate different pen brands, separated at the PCA graph score. The PLS-DA method was conducted as follows ( Figure 3): a) calibration model: two sets of five images of each pen brand were collected, using "0" for images not belonging to the class and "1" for images belonging to the class in question; b) validation: sample collection with known classes, using "0" and "1" in the same way as above; c) blind samples: collecting the same samples without informing their classes.
Both validation and blind samples collection should also be positioned as "0" and "1" in the plot graph, as the calibration model. Sample sets distance and its calculated errors will show the difference between the two analyzed colors. All confirmation tests were performed using image capturing from the squares, described at Figure 1b.

Results
For colorful pens, both squares and graphism images showed similar results. Figure 4 shows the results for image collection from the graphism "pen", using three images from the same region represented in Figure 4a, for the colorful pens (figure 1a). We can observe a great differentiation between those pens in the score chart, which was expected, and it is also shown that inks of similar color grouped together (red, pink and purple close to each other; navy blue, light blue and green separated). Those results were obtained using both mobiles devices, Motorola® and Samsung®, even though some differences can be observed between them. Both graphics of two principal components (PC1xPC2) explains 99% of the experimental variation ( figure 4b and 4c).     Figure 6 shows the results for image collection from the graphism "pen", using three images from the same region represented in Figure 6a, for all blue ballpoint pens.
Using Motorola® device, the differentiation between pens became harder in this experiment, but it is possible to differentiate some brands, like Molin® from Pilot® brand (as shown in Figure 6b), for example. Also, analyzing different pairs of triplicates, it is possible to differentiate some other brands too, like Paper Mate® (G) from Unisa-S® (M). When analyzing graphisms, the pressure between each written word is different even when performed by the same writing fist, which could be influencing the amount of ink deposited on paper and, consequently, the color captured by the mobile device camera. However, when the Samsung® device was used, a better differentiation was observed. In this model, it were captured five images of Bic® samples, five images from Pilot® samples and five images of Molin® samples, all named as "0". Then, five images of Tris® samples were collected as "1". Figure 9 shows the graphs for the calibration model for this experiment (Figure 8a), for the validation model, informing the app about their codes (Figure 8b) and for the blind sampling, without informing any code to the app (Figure 8c), and it is possible to observe that Tris® samples are closer to "1" in the sampling graphs (Figures 8b and 8c), while all the other brands does not belong to this class, being closer to "0" in the graphs. Figure 9 shows an experiment performed with two Bic® pens, to demonstrate when two pens cannot be differentiated from each other. Figure 9a shows the calibration model, using five images of a Bic® pen named as "0" and five images from another Bic® pen, named as "1". At figure 9b and 9c it is possible to observe that the app could not distinguish the images from each other, as it can be seen for different pen brands at Figures 7 and 8.    Figure 8b). Adding more pens as not belonging to Tris® class showed a similar RMSEC value (0,03805), but it increased RMSEP value (0.1926), which it is expected considering that there are three different pens tagged as "0" (Figure 8b). Analyzing the prediction graphs (Figures 7c and 8c), it can be seen that Tris® samples are separated from the others, closer to "1". Comparatively, when analyzing two pens of the same brand (Bic®), RMSEC was 0.02538, while RMSEP was 0.2771, which demonstrates a high error for prediction and indicates that the pen colors could not be differentiated from each other ( Figure 9b). Also, all Bic® samples are positioned together in the graph, close to "0" (Figure 9c).

Discussion
Given the results we have found when studying nine different pen brands, it is possible to infer that some pen brands can be distinguished from each other using PhotoMetrix PRO ® app, but not all of them at the same time. Also, Samsung® mobile device camera has shown better discrimination, when compared to Motorola® device camera, which can be explained by the higher quality of Samsung®'s camera. Furthermore, different mobiles devices should be studied for its capability of differentiate blue ballpoint pens.
To evaluate the collected data, the proximity of each image in a triplicate indicates how this sample is differentiated from another sample triplicate in the visual space of PCA. As closer as the samples of the same triplicate are in the PCA graphs, it means that the image collection was correctly proceeded; otherwise, the image collection should be re-done. In some cases, it will be easy to delimitate a categorical conclusion; however, in some cases it will be necessary to proceed with another technique for ink analysis, to avoid false positives or negatives results. rollerball and felp-tip pens, than pens of same kind but different brands, such as different ballpoint pen brands. Therefore, our study tried to distinguish blue ballpoint pens from each other, and also to apply the method in writings, in an attempt to reproduce real cases.
Innovatively, our study showed that the differentiation between blue ballpoint pens, using MIA of digital images captured with PhotoMetrix PRO ® , is possible between some pen brands. It showed some limitations, but it also opened a space for future research. It is important for those results to be replicated by different analyzers, also including a larger number of pen brands. As the pressure for graphisms had an influence on the images capture, even for a same person writing it, a bigger study involving different writers and graphisms should be performed, considering that the amount of ink applied on paper could be an interference. It is important to highlight the importance of testing those results with different mobiles phones. Thus, considering the long time between a document forgery and its analysis by a forensic expert, a study involving ink`s age should also be considered.

Conclusion
PhotoMetrix PRO ® is a free app for download in different phones devices, and it is an easy tool to manipulate, which allows multivariate analysis in several areas. By applying this method for colorful ballpoint pens, our results showed a great differentiation from each other, as expected. Considering blue ballpoint pens, it is possible to differentiate between some of the studied brands, while there is some limitation to distinguish between others pen brands. For blue pens of different brands, but visually similar color, it was not possible to discern it from each other using this technique. However, PhotoMetrix PRO ® use is very interesting to obtain validated results in specific cases. Besides its limitations, this technique could be further studied, with different pens and mobile devices, so it can be possibly applied in some specific cases in Forensic Documentoscopy. Also, this method could be studied in other forensic areas. Forense". The authors wish to thank these institutions.