International Journal of Computers, Communications & Control
Vol. I (2006), No. 1, pp. 17-24

Novel Features for Off-line Signature Verification

Banshider Majhi, Y Santhosh Reddy, D Prasanna Babu

Abstract: In this paper a novel feature extraction scheme has been suggested for offline
signature verification. The proposed method used geometric center for feature extraction.
Euclidean distance model was used for classification. This classifier is well suitable for fea-
tures extracted and fast in computation. Method proposed in this paper leads to better results
than existing offline signature verification methods. Threshold selection is based on statistical
parameters like average and standard deviation (σ ).
Keywords: Feature Extraction, Geometric Center, Euclidean Distance Model, Standard De-
viation and Off-line Signature Verification.

1 Introduction

Signature verification is an important research area in the field of person authentication. We can generally
distinguish between two different categories of verification systems: online, for which the signature signal is
captured during the writing process, thus making the dynamic information available, and offline for which the
signature is captured once the writing processing is over and, thus, only a static image is available[8]. The objective
of the signature verification system is to discriminate between two classes: the original and the forgery, which are
related to intra and interpersonal variability. The variation among signatures of same person is called Inrea Personal
Variation. The vatiation between originals and forgeries is called Inter Personal Variation[7].
In this paper we concentrated on Offline Verification System. Upto now many signature verification methods
proposed based on different strategies but no verification system classified near forgeries which were classified by
this method. And the main advantage of this algorithm is efficiency and computational complexity. For general
purpose applications like smart cards we want quick and efficient verification system[2]. This method is based on
the Geometric Center and signature strokes distribution. Section 2 discusses the feature extraction from signature.
This is a recursive method which applying on signature recursively. A lot of work has been done in the field of
automatic off-line signature verification. While a large portion of work is focused on random forgery detection,
more efforts are still needed to address the problem of skilled forgery detection[6]. Our method will be the first
verification system which seperates some skilled forgeries from originals.
This paper organized in the following sections: Section 1.1 provides the different types of forgeries. Section 2
introduces new feature extraction method. Section 3 discusses classification based on Euclidean distance model.
Section 4 discussed about threshold selection. Section 5 shows training, testing and results and Section 6 gives
conclusion and furthure working directions.

1.1 Types of forgeries

There are three different types of forgeries to take into account. The first, known as random forgery which
writtn by the person who don’t know the shape of original signature. The second, called simple forgery, is
represented by a signature sample which written by the person who know the shape of original signature with-
out much practice. The last type is skilled forgery, represented by a suitable imitation of the genuine signature
model[3]. Each type of forgery requires different types of verification approach[4]. Hybrid systems have also been
developed[9] Fig. 1 shows the different types of forgeries and how much they are varies from original signature[5].

Figure 1: (a) Random Forgery (b) Simple Forgery (c) Skilled Forgery (d)Original Signature

By using this method we can easily eliminate random and simple forgeries. Some of the skilled forgeries also
eliminated.

Copyright c© 2006 by CCC Publications



18 Banshider Majhi, Y Santhosh Reddy, D Prasanna Babu

Figure 2: (a) Before adjustment of signature (b) After adjustment of signature

2 Feature Extraction

The geometric features proposed by this paper are based on two sets of points in two-dimentional plane. Each
set having six feature points which represent the stroke distribution of signature pixels in image. These twelve
feature points are calculated by Geometric Center[1]. Vertical Splitting and Horizontal Splitting are two main
steps to retrieve these feature points. Vertical Splitting is discussed in Section 2.2 and Horizontal Splitting is
discussed in Section 2.3.
Before finding feature points we have to do some adjustments to the signature image. That is moving signature
strokes to the center of the image which discussed in Section 2.1.

2.1 Moving signature to the center of image

In this step signatures are moving to the center of image. Because of this we can reduce intra-personal vari-
ations. Here first we have to find out the geometric center of the image and move the signature pixels such that
the geometric center should reside at center of image. Fig. 2 shows the signature images before moving and after
moving.

2.2 Feature points based on vertical splitting

Six feature points are retrieving based on vertical splitting. Here feature points are nothing but geometric
centers. The procedure for finding feature points by vertical splitting is mentioned in Algorithm.

Algorithm

This is the procedure for generating feature points based on verical splitting.
Input: Static signature image after moving the signature to center of image
Output: v1, v2, v3, v4, v5, v6 (feature points)
(a)Split image with vertical line at the center of image then we will get left and right parts of image.
(b)Find geometric centers v1 and v2 for left and right parts correspondingly.
(c)Split left part horizontal line at v1 and find out geometric centers v3 and v4 for top and bottom parts of left part
currespondingly.
(d)Split right part horizontal line at v2 and find out geometric centers v5 and v6 for top and bottom parts of left part
currespondingly.

Fig. 3 shows the feature points retrieved from signature image and O is the center of image. These features we
have to calculate for every signatrure image in both training and testing.

2.3 Feature points based on horizontal splitting

Six feature points are retrieving based on horizontal splitting. Here feature points are nothing but geometric
centers. The procedure for finding feature points by horizontal splitting is mentioned in Algorithm.



Novel Features for Off-line Signature Verification 19

Figure 3: Feature points based on vertical splitting

Figure 4: Feature points based on horizontal splitting

Algorithm

This is the procedure for generating feature points based on horizontal splitting.
Input: Static signature image after moving the signature to center of image
Output: h1, h2, h3, h4, h5, h6 (feature points)
(a)Split image with horizontal line at the center of image then we will get top and bottom parts of image.
(b)Find geometric centers h1 and h2 for top and bottom parts correspondingly.
(c)Split top part with vertical line at h1 and find out geometric centers h3 and h4 for left and right parts of top part
currespondingly.
(d)Split bottom part with vertical line at h2 and find out geometric centers v5 and h6 for left and right parts of left
part currespondingly.

Fog. 4 shows the feature points retrieved from signature image and O is the center of image. These features we
have to calculate for every signatrure image in both training and testing. Now total twelve feature points (v1, ..., v6
and h1, ..., h6) are calculated by vertical and horizontal splittings. In Section 4 we will see how each feature point
can classify.

3 Classification

In this paper features are based on geometric properties. So we used euclidean distance model for classifi-
cation. This is the simple distance between a pair of vectors of size n. Here vectors are nothing but feature points,
so the size of vector is 2. How to calculate distance using eucliden distance model is descibed in Section 3.1. In
threshold calculation these distances are useful.

3.1 Euclidean distance model

Let A(a1, a2, ..., an) and B(b1, b2, ..., bn) are two vectors of size n. We can calculate distance(d) by using
equarion 1.

distance(d) =

√
n

∑
i=1

(ai −bi)2 (1)



20 Banshider Majhi, Y Santhosh Reddy, D Prasanna Babu

In our application, vectors are points on plane. So d is the simple distance between two points.

4 Threshold

Individual thresholds for vertical splitting and horizontal splitting. Here we proposed one method for threshold
selection which used in Section 5.1. Fig. 5 shows the variations in single curresponding feature points of training
signatures. Let n is the number of training signatures and x1, x2, ..., xn are curresponding single feature points of
training signatures(taking one curresponding feature point from each signature). xmedian is the median of n features
from n signatures. Let d1, ..., dn are distances defined here,

d1 = distance(xmedian, x1)
d2 = distance(xmedian, x2)

...

dn = distance(xmedian, xn) (2)

Two main parameters we used in threshold calculation are davg and σ . Equations 3 and 4 shows the calculation

d avg + σ
x i

x 2

x n−1

x 1

x 3

d avg

x n

σ

Figure 5: davg (average distance) and σ (standard deviation) derivation from distances

of these two parameters.
davg = average(d1, d2, ..., dn) (3)

σ = SD(d1, d2, ..., dn) (4)

Like this total six different feature points are there for both vertical and horizontal splitting based on average
distance (davg) and standard deviation (σ ). Equation 5 shows the main formula for threshold.

threshold(t) =

√√√√ 6∑
i=1

(davg,i + σi)2 (5)



Novel Features for Off-line Signature Verification 21

5 Experiments & Results

For experiment we took 30 original signatures from each person and selected 9 for training. These original
signatures are taken in different days. Forgeries taken by three persons and 10 from each. Total 21 originals and 30
forgeries for each person signature are going to be tested. There are two thresholds (one based on vertical splitting
and another based on horizontal splitting) for each person signature.

5.1 Training

Let n signatures are taking for training from each person. There are 12 feature points from each original signa-
ture, 6 are taken by vertical splitting (Section2.2) and 6 are taken by horizontal splitting (Section2.3). Individual
thresholds and patterns are calculating for vertical splitting and horizontal splitting. Pattern points based on vertical
splitting are shown below.

vpattern,1 = median(v1,1, v2,1, ..., vn,1)
vpattern,2 = median(v1,2, v2,2, ..., vn,2)
vpattern,3 = median(v1,3, v2,3, ..., vn,3)
vpattern,4 = median(v1,4, v2,4, ..., vn,4) (6)
vpattern,5 = median(v1,5, v2,5, ..., vn,5)
vpattern,6 = median(v1,6, v2,6, ..., vn,6)

Where vi,1, vi,2, ..., vi,6 are vertical splitting features of i
th training signature sample. Threshold based on vertical

splitting is shown below.

vthreshold =

√√√√ 6∑
i=1

(vdavg,i + σv,i)2 (7)

In equation 9 vdavg,i is same as average distance and σv,i is same as standard deviation shown in Section 4. Pattern
points based on horizontal splitting are shown below.

hpattern,1 = median(h1,1, h2,1, ..., hn,1)
hpattern,2 = median(h1,2, h2,2, ..., hn,2)
hpattern,3 = median(h1,3, h2,3, ..., hn,3)
hpattern,4 = median(h1,4, h2,4, ..., hn,4) (8)
hpattern,5 = median(h1,5, h2,5, ..., hn,5)
hpattern,6 = median(h1,6, h2,6, ..., hn,6)

Where hi,1, hi,2, ..., hi,6 are horizontal splitting features of i
th training signature sample. Threshold based on hori-

zontal splitting is shown below.

hthreshold =

√√√√ 6∑
i=1

(hdavg,i + σh,i)2 (9)

We will store pattern points and thresholds of both horizontal splitting and vertical splitting. These values are
useful in testing.

5.2 Testing

When new signature comes for testing we have to calculate features of vertical splitting and horizontal splitting.
Feature points based vertical splitting are vnew,1, vnew,2, vnew,3, vnew,4, vnew,5, vnew,6. Distances between new signature



22 Banshider Majhi, Y Santhosh Reddy, D Prasanna Babu

features and pattern feature points based on vertical splitting are shown below.

vdnew,1 = distance(vpattern,1, vnew,1)
vdnew,2 = distance(vpattern,2, vnew,2)
vdnew,3 = distance(vpattern,3, vnew,3)
vdnew,4 = distance(vpattern,4, vnew,4) (10)
vdnew,5 = distance(vpattern,5, vnew,5)
vdnew,6 = distance(vpattern,6, vnew,6)

For classification of new signature we have to calculate vdistance and compare this with vthreshold . If vdistance is less
than or equal to vthreshold then new signature is acceptable by vertical splitting.

vdistance =

√√√√ 6∑
i=1

vd2new,i (11)

Feature points based vertical splitting are hnew,1, hnew,2, hnew,3, hnew,4, hnew,5, hnew,6. Distances between new signa-
ture features and pattern feature points based on vertical splitting are shown below.

hdnew,1 = distance(hpattern,1, hnew,1)
hdnew,2 = distance(hpattern,2, hnew,2)
hdnew,3 = distance(hpattern,3, hnew,3)
hdnew,4 = distance(hpattern,4, hnew,4) (12)
hdnew,5 = distance(hpattern,5, hnew,5)
hdnew,6 = distance(hpattern,6, hnew,6)

For classification of new signature we have to calculate hdistance and compare this with hthreshold . If hdistance is less
than or equal to hthreshold then new signature is acceptable by horizontal splitting.

hdistance =

√√√√ 6∑
i=1

hd2new,i (13)

New signature features have to satisfy both vertical splitting and horizontal splitting thresholds.

5.3 Results

False Acceptance Rate (FAR) and False Rejection Rate (FRR) are the two parameters using for measuring
performance of any signature verification method. FAR is calculated by equation 14 and FRR is calculated by
equation 15.

FAR =
number o f f orgeries accepted

number o f f orgeries tested
×100 (14)

F RR =
number o f originals re jected

number o f originals tested
×100 (15)

Table 1 shows the False Acceptance Rate of our method for different types of forgeries. Table 2 shows the False
Rejection Rate for original sigature.

Table 1: False Acceptance Rate (FAR)
Forgery Type FAR(%)

Random Forgeries 2.08
Simple Forgeries 9.75
Skilled Forgeries 16.36

In general there are different thresholds for different types of forgery detections. But here threshold is same for
random, simple and skilled forgeries. Because this method is mainly eliminating random and simple forgeries.



Novel Features for Off-line Signature Verification 23

Table 2: False Rejection Rate (FRR)
Signature FRR(%)

Original Signatures 14.58

6 Conclusion

This method performs much better than any other off-line signature verification methods. Future direction in
this is classifying the skilled forgeries correctly. For this we have to approach novel classification method.

Figure 6: Feature points based on vertical splitting of depth 2

Figure 7: Feature points based on horizontal splitting of depth 2

For better classification we can again split the sub-parts of Fig.3 using vertical splitting and Fig.4 using hor-
izontal splitting. Then instead of six featire points we can get 24 feature points for each vertical and horizontal
splittings. Fig.6 shows the vertical splitting of depth 2. Fig.7 shows the horizontal splitting of depth 2.

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24 Banshider Majhi, Y Santhosh Reddy, D Prasanna Babu

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Banshider Majhi, Y Santhosh Reddy, D Prasanna Babu
Department of CSEA

NIT Rourkela
India 769008

E-mail: ysantosh@rediffmail.com