DISTINGUISHING LIQUID AND VISCOUS BLACK INKS USING

RGB COLOUR SPACE

Dasari Haritha and Chakravarthy Bhagvati

Dept. of Computer and Information Sciences, University of Hyderabad, Hyderabad, India 500046

Keywords:

Questioned Document Examination, Black inks, Image processing, MLR.

Abstract:

Analysis of inks on Questioned documents is often required in the ﬁeld of document examination. This paper

provides a novel approach for ink type recognition for black inks. Ink types Liquid ink or Viscous ink will

be derived from the colour properties of ink, by extracting its amount of blackness. This classiﬁcation helps

in distinguishing Gel and Roller pens versus Ball pens. Different types of inks exhibit different absorption

characteristics that causes colour and distribution of colour pixels to change. We observed that the RGB

colour space is useful to reveal the differences in ink types. We used multiple linear regression to model the

RGB data points of the writings to a plane. The distance from the origin (pure black) to that plane is calculated

to classify inks i.e. liquid inks and viscous inks. The distance measures in RGB and HSV colour spaces are

used to identify the particular ink. The accuracy of identiﬁcation is analysed using Type I and Type II errors.

1 INTRODUCTION

Forensic examination of documents is fast emerging

as a challenging ﬁeld of research with the prolifera-

tion of fake documents using computers or computer-

based technologies. A document is labeled ques-

tioned document if its authenticity is in doubt. The

main goal of examining questioned documents is to

determine whether they are genuine or fake by detect-

ing alterations if any. Alterations occur primarily in

three forms: addition of new text, obliterations, and

erasures.

The conventional methods used by expert ques-

tioned document examiners are varied and sophisti-

cated involving both destructive and non-destructive

means. References (Brunelle, 1982), (Ellen, 1997)

and (Hilton, 1993) offer excellent overviews. Mi-

croscopy, study of colour variations under chang-

ing illumination (Hilton, 1993), ﬁlters for improv-

ing colour contrasts (Bauer, 1966), ultraviolet ﬂuores-

cence, infrared absorbance (Godown, 1964), infrared

luminescence (Hardcastle, 1978) and Fourier trans-

form infrared spectrometry (Brunelle, 1982) have all

been used for examining questioned documents. A

special instrument, called the video spectral compara-

tor, is often used for the above non-destructive test-

ing methods. The destructive chemical procedures

include solubility tests, thin layer chromatography

and high performanceliquid chromatography(HPLC)

(Tappolet, 1983).

The use of image processing techniques in foren-

sic document examination is relatively new (Ellen,

1997). Image processing techniques offer signiﬁcant

cost beneﬁts by eliminating or at least minimizing the

need for expensive instruments and destructive test-

ing methods. A majority of image processing tech-

niques applied to forensic examination of documents

thus far are quite primitive and usually imply some

form of contrast enhancement. For the image process-

ing community,the forensic domain opens a new area

of research where new operations need to be deﬁned

and developed.

Of particular importance in document examina-

tion is identifying the writing instrument and the type

of ink used in writing. Viscous ink (a thick pastelike

material) is used in ball pens and liquid ink (water

soluble) is used in fountain, gel and roller pens. In

this paper, we study the problem of identifying dif-

ferent ink types using colour image processing tech-

niques. The underlying principle is to detect colour

394

Haritha D. and Bhagvati C. (2007).

DISTINGUISHING LIQUID AND VISCOUS BLACK INKS USING RGB COLOUR SPACE.

In Proceedings of the Second International Conference on Computer Vision Theory and Applications - IFP/IA, pages 394-397

 SciTePress

differences that correspond to the varying absorption

and colour characteristics of different ink types. For

example, a gel black ink appears more blacker than

black viscous ink. In our previous analysis, we show

that the HSV colour space is especially useful as ab-

sorption is revealed in the saturation values in bring-

ing out the differences in blue and blueblack pens

(Haritha, 2005). For black writings, hue is distrib-

uted over the entire range (0, 360

◦

) and hence HSV

colour space is not suitable. In this paper, we use

RGB colour space to reveal the differences in colour

characteristics of black inks.

The rest of the paper is organized as follows. Sec-

tion 2 is a brief description of Multiple Linear regres-

sion and modeling black writings using MLR. Section

3 describes different distance measures in RGB and

HSV colour spaces. Section 4 explains our methodol-

ogy used for ﬁtting the RGB data into a plane in cubi-

cal space and use of distance measures to distinguish

different inks. Results are presented and discussed in

Section 5 with conclusions in Section 6.

2 MODELING BLACK WRITINGS

USING MLR

Multiple Linear Regression model (MLR) is the most

commonly applied statistical technique for relating a

dependent variable and a set of two or more indepen-

dent variables (Siegel, 1996). Using MLR, the RGB

data of black writings is ﬁtted into the plane given by

+ b

×red + b

×blue+ b

×green = 0

It is very interesting to know how much black is

a black writing. To quantify the blackness of a black

writing, the distance of the ﬁtted plane of the data of

a black writing to pure black point (0,0,0) i.e. the

center of RGB cube is calculated. The distance is

√

. It is observed that this distance of the

ﬁtted plane from the pure black (0,0,0) can be used

to classify the viscous black inks versus liquid black

inks. We know that the ball pens use viscous ink

where as gel/roller pens use liquid ink. Several re-

gression statistics are computed as functions of the

sums-of-squares terms. The explanatory power of re-

gression is summarized by its “R −squared” value,

also called the coefﬁcient of determination, is often

described as the proportion of variance “described”

by regression. If the regression is “perfect”, R

is 1.

If the regression is failure, R

equals zero.

3 DISTANCE MEASURES IN RGB

AND HSV COLOUR SPACES

Identiﬁcation of the particular ink/writing instrument

used is the next step to classiﬁcation in forensic

examination of documents. We use distance mea-

sures to identify the particular ink/writing instrument

used. Black colour can be treated as a dark shade

of any colour. Two black colours can be distin-

guished by their mean R, G, B colour vectors. This

section describes various distance measures existing

for discriminating two colours and the two new de-

rived distance measures namely WeightedL1 HSV

distance measure and Geodesic HSV distance mea-

sure (Chakravarthy, 2005).

In Table 1 the expressions for RGB distance mea-

sures and new HSV distance measures between two

colour vectors are given. The expressions for L1

HSV, L2 HSV, Canberra HSV, Cosine Angle HSV

and Czekanowski HSV distances are similar to that

of RGB distances except that r is to be replaced by h,

g by s and b by v.

Table 1: Distance Measures in RGB and HSV colour

spaces.

DISTANCE

MEASURE

EXPRESSION FOR D(X,Y)

L1 RGB ((|r

−r

|)+(|g

−g

|)+(|b

−b

|))

L2 RGB ((r

− r

)

+ (g

− g

)

+ (b

−

)

Canberra

RGB

−r

−g

−b

Cosine An-

gle RGB

cos

−1

(

√

)

Czeknowski

RGB

1−

2(min(r

)+min(g

)+min(b

))

Weighted

Euclidean

HSV

−v

)

+ s

−2s

cos(h

di f f

)

Weighted

L1 HSV

S×h

di f f

+ |s

−s

|+ |v

−v

Geodesic

HSV

−s

)

+ s

−h

)

+ (v

−v

)

Statistical evaluation The validity of performance

of the distance measures in identiﬁcation of writing

instrument is analyzed on statistical basis. We take

the distance of feature vectors between writings of

the same writing instrument and call it as a within

writing instrument distance denoted by d

. The be-

tween writing instrument distance d

is obtained by

measuring the distance between two different writing

instruments.

= d(f

− f

) where i = 1 to n and j, k=1 to m.

= d(f

− f

) where i, k= 1 to n and j, l=1 to m.

where n is the number of writing instruments, m

is the number of sample images written by each writ-

ing instrument, f

etc. are the feature vectors of the

corresponding images, and d is the distance between

two feature vectors of an image. Let n

and n

are the

sizes of within and between writing instrument dis-

tance classes respectively. If n writing instruments

provide m writings, there are n

= m

×n within

writing instrument distance data and n

= m×m×n

In our data collection we have taken 15 ball pens and

15 gel and roller pens. For each pen 15 images are

taken.

= 30 x 15

= 3150 data.

= 15 x 15 x 30

= 97,875 data.

A good descriptive way to represent the relation-

ship between two classes is calculating overlaps be-

tween two distributions. It can be done with two types

of errors. Type I error occurs when the images of

same writing instrument are identiﬁed as of different

writing instruments. The type II error occurs when the

images of different writing instruments is classiﬁed as

of same writing instrument.

4 METHODOLOGY

Twenty Five black pens including ball,roller,gel and

fountain pens with different manufactures were taken.

A page containing 100 words was written by each of

these pens on A4 size white xerox paper and from that

page selected samples (20) were scanned at high opti-

cal resolution i.e,1200 dpi. Algorithm for classifying

inks is comprising of the following steps.

1. Select suitable threshold values of R, G and B

from the RGB histograms to seperate background

and foreground pixels.

2. Fit the foreground data into a plane in the RGB

cube.

3. Find the distance d from the ﬁtted plane to the

pure black point (0,0,0). Find R

coefﬁcient of

determination and MSE.

4. Classify liquid and Viscous Inks using the dis-

tance from the pure black (if d is ≥ 15, it is vis-

cous ink otherwise it is liquid ink) .

Figure 1: Writings of sample image of cello ball and Add

roller pens.

Algorithm for identiﬁcation of inks comprises the fol-

lowing steps.

1. Seperate background and foreground pixels.

2. Find the feature vector (mean colour) (r,g,b) of the

foreground pixels. Find its equivalent h, s, v val-

ues. Find the distance d between the mean colour

vectors of two images.

3. Label the distance as within writing instrument

distance, if the two images belong to the same pen

or as between writing instrument distance, if two

images belong to different pens.

4. Repeat the above step for all the images of the

database. Find the Type I and II errors from the

distributions of within and between writing instru-

ment distances.

5 RESULTS AND DISCUSSION

Figure 1 shows the sample images taken using Cello

ball, Add roller pen. The data from the sample writ-

ings of different pens is ﬁtted into a corresponding

plane in the RGB cube. Figure 2 shows the ﬁtted data

of ball pen, actual data in to the corresponding planes

in the RGB cubic space. The green coloured plane in-

dicates the ﬁtted plane of the data. The red coloured

pixels indicate actual data of the scanned image. The

blue coloured pixels indicated the estimated pixels.

The coefﬁcient of determination ”R-Squared ratio” in

ﬁtting the data of Cello ballpen image using regres-

sion is 0.999268 and MSE is 14.7248. The R

ratio in

ﬁtting the data of Add roller pen image using regres-

sion is 0.999586 and MSE is 7.6987. We can observe

that R

ratio is closure to 1 indicating that regression

is ”good”.

We have taken two datasets, one for training and

analysis and another for testing purpose.The ﬁrst

dataset comprises of 15 ball pens and 10 roller/gel

pens each of 20 sample images. The second dataset

testset comprises of 10 ball pens and 10 gel/roller

pens each of 10 sample images. The results were

analysed using False Acception Ratio (FAR) and

False Rejection Ratio (FRR). The FAR and FRR are

calculated for classiﬁcation of liquid inks and viscous

Figure 2: Data ﬁtting of Cello ball pen using MLR.

inks based on distance of the ﬁtted plane from pure

black and is shown in Table 2.

Table 2: FAR and FRR errors for Ballpens and Gel/Roller

pens training and test sets.

PEN

TYPE

DATA

SET

FAR % FRR %

Ball pens training 02.34 1.35

test 1.87 1.09

Gel/Roller

pens

training 01.35 02.34

test 1.09 1.87

After classifying the inks, we must be able to iden-

tify the writing instrument. For each handwritten

image, the mean vector of foreground pixels is ob-

tained. The distance between these mean vectors of

two images is calculated. For analysis the distribu-

tions of within the same writing instrument distance,

between different writing instrument distances is plot-

ted. We have taken 15 ball pens and 15 gel/roller

pens and each pen with 15 images. Table 3 shows

the TYPE I and TYPE II errors of identiﬁcation.

Type I error is minimum for our two new distance

measures Weighted L1 HSV and Geodesic HSV dis-

tances. However, the overall accuracy is more for L1

HSV and L2 HSV distances.

6 CONCLUSIONS

In this paper, we have shown the use of RGB colour

space in classiﬁcation of black inks. An approach for

ﬁtting the black writings into a plane in RGB space,

using MLR is given. This work is useful as the ﬁrst

step in identiﬁcation of alterations in forged docu-

ments. The use of distance measures in identiﬁca-

tion of particular writing instrument is explored. This

work can be further extended to distinguish gel ver-

Table 3: Type I and II errors for HSV and RGB distance

measures.

DISTANCE MEASURE TYPE I

ERROR

TYPE II

ERROR

L1 HSV 7.176 6.595

L2 HSV 6.82 08.33

Cosine HSV 12.16 11.94

Canberra HSV 14.04 7.15

CzeknowskiHSV 8.432 11.28

Euclidean HSV 10.608 10.067

WeightedL1 HSV 6.55 11.59

Geodesic HSV 5.46 16.767

L1 RGB 16.22 14.71

L2 RGB 12.16 15.27

Canberra RGB 9.929 21.47

Cosine RGB 16.802 17.39

CzeknowskiRGB 9.672 22.6

sus roller pens and to classify printed documents. It

can also be further extended to develop a system that

can be used to classify and identify black writings or

printings for forensic examination of documents.

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