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Chapter 5

Off-line Signature Recognition based on

Geometric Centre and Angular Features

5.1 Introduction

Signature is widely used as a means of personal identification,

which emphasizes the need for signature recognition system. In this

chapter, Off-line Signature Recognition using Geometric Centers and

Angular Features are discussed.

In case of Off-line Signature Recognition using Correlation of

Geometric features, the signature images are preprocessed by

resizing, filtering to remove noise, skeletonization and considering

the exact signature area. The pixel density and geometric features are

extracted from the preprocessed signature images. The concept of

correlation is used to compare the sixty geometric feature points of

genuine signature with the test signature. If the value of correlation

coefficient is greater than the predefined threshold correlation value,

the test signature is considered as genuine else forged.

The Off-line Signature Recognition based on Angular Features

(OSRAF) includes skeletonization of the signature image and exact

signature area is obtained by preprocessing. The features are

extracted in two phases. In the first phase, the signature is divided

into 128 blocks using the geometric center of signature by counting

the number of black pixels and the angular feature in each block is

determined to generate 128 angular features. In the second phase,

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the signature is divided into forty blocks from each of the four

corners of the signature to generate forty angular features. Totally

168 angular features are considered from phase one and two to verify

the signature. The difference between the angular features of the

genuine and test signatures is computed and compared with the

threshold value to authenticate the signature.

5.2 Off-line Signature Recognition by Correlation of

Geometric Features

In this section, block diagram of Off-line Signature Recognition

by Correlation of Geometric (OSRCG) features shown in Figure 5.1 is

discussed in detail. The signature images are preprocessed by

resizing and skeletonization. The geometric features are extracted by

vertical and horizontal splitting. The test signature features are

compared with features of signatures in database using correlation.

Figure 5.1: Block diagram of OSRCG system

Signature Database

Preprocessing

Feature Extraction

Correlation

Test Signature

Preprocessing

Feature Extraction

Feature Templates

Match/ Mismatch

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5.2.1 Signature database

The GPDS300 is an off-line handwritten signature database,

which contains 24 genuine signatures and 30 forgeries of varying

sizes from 300 individuals [120, 121] and available in PNG format.

The genuine and forgery samples of GPDS database for a single

person are shown in Figures 5.2 and 5.3 respectively.

Figure 5.2: Genuine samples from GPDS signature database

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Figure 5.3: Forgery samples from GPDS signature database

The signatures are also obtained from persons on a blank

white paper at different timings depending upon the mood and stress

levels and are scanned to get images of 96 dpi resolution in BMP

format to create a local database. The local database consists of 220

signature samples of 11 people, of which 110 signatures are genuine

and 110 signatures are forged. Ten signature genuine samples are

obtained from each person at different time instances to produce

enough intra-signature variations. Ten skilled forgeries are obtained

for each person’s signature. The genuine signature is forged after

sufficient training to generate skilled forgery signature for testing.

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The signature images are of varying sizes. A sample of genuine

signature image is as shown in Figure 5.4.

Figure 5.4: Signature sample from local database

The GPDS database for the proposed OSRCG model is created

by considering first thirty nine persons signature images out of three

hundred persons. The database consists of first twenty samples per

person of the thirty nine persons that is totally seven hundred and

eighty samples. The remaining four samples per person are

considered as test signatures for computing False Rejection Rate

(FRR). The forgery samples are out of database and used for

computing False Acceptance Rate (FAR).

Similarly, the experiment is also performed on a local

database. The database for the proposed model is created by

considering first eight signatures per person of eleven persons. The

other two signatures are used as test signatures for computing FRR.

The forged signatures are used for computing FAR.

5.2.2 Preprocessing

The preprocessing is used to obtain a transformed signature

image with enhanced quality. It includes (i) Noise reduction using

DWT, (ii) Resizing, (iii) skeletonization by morphological operations

and (iv) obtaining the exact signature area.

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(i) Noise reduction using DWT: The dirt on camera or scanner lens,

imperfections in the dirt on camera or scanner lens, imperfections in

the scanner lighting etc., introduces noise in the scanned signature

images. A filtering function is used to remove noise in the images by

applying DWT.

In DWT the rows of an image are convolved with the system

function of low pass filter and high pass filter to get convoluted

signal. These convoluted signals are down sampled by keeping even

indexed columns. They again are convoluted with transfer functions

of low pass filter and high pass filter. The final convoluted signals are

down sampled to rows, to generate the approximation band and

detailed bands. The approximation band contains low frequency

components; thereby the unwanted noise components are eliminated

by the DWT. The Haar wavelet filter is used in the proposed, since its

hardware implementation is cheaper than that of other wavelets.

The signature image after applying the DWT is shown in Figure 5.5.

Figure 5.5: Signature after applying DWT

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(ii) Resize: In this process, frame of the signature images with

different sizes are made into a uniform frame of size 150*450.

Resizing is done by pixel averaging, which gives much better quality

than sub-sampling. The resized signature is as shown in Figure 5.6.

(a) (b)

Figure 5.6: (a) Original signature (b) Resized signature

(iii) Skeletonization: Reducing image to single pixel width. An image

can be represented by its skeleton, which consists of the spines of

the object parts. A two dimensional skeleton may consist of curves

(spines), isolated two dimensional points and possibly, two

dimensional surfaces. The generation of a skeleton is realized by

applying an iterative process which erodes the object layer by layer

until only the object spines remain, which form the skeleton of the

two dimensional image. The skeletonization is done by removing the

pixels on the boundary of the signature image without allowing the

signature image to break apart. This process is achieved by

performing morphological operations on signature image using skel

function. The signature image after skeletonization is as shown in

Figure 5.7.

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Figure 5.7: Signature after skeletonization

(iv) Exact signature area: The signature image might not be present

on the entire frame, so the exact signature area is considered in the

skeletonized image for further analysis. The signature image scanned

from all the four sides to locate first black pixel. Then the new image

frame is formed to obtain exact signature area. This reduces

verification time and is cost effective. The Figure 5.8 shows the image

with exact signature area.

Figure 5.8: Exact signature area

5.2.3 Feature Extraction

The two sets of features are extracted in two-dimensional plane

from the signature image obtained on skeletonization. The vertical

splitting and horizontal splitting are two main steps to retrieve the

features. Each set has thirty features, which represent the stroke

distribution of signature pixels in an image. These sixty features are

computed using geometric centers.

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(i) Feature points based on vertical splitting:

The signature image is scanned to count the number of black pixels.

The number of black pixels is divided by two to locate geometric

centre. The signature image is split into left and right blocks with a

vertical line passing through the geometric centre. Geometric centers

v1 and v2 are computed for left and right parts of the signature

respectively. The left part is split with a horizontal line passing

through v1 to obtain top and bottom parts. The geometric centers v3

and v4 of top and bottom parts of left part are computed. Similarly,

the right part is split with a horizontal line passing through v2 to

obtain top and bottom parts. The geometric centers v5 and v6 of top

and bottom parts of right part computed. Similarly, each block of the

signature image is split to compute thirty geometric centers as shown

in Figure 5.9.

Figure 5.9: Vertical splitting of the signature

(ii) Features based on horizontal splitting: The signature image is

scanned to count the number of black pixels. The total number of

black pixels is divided by two to locate geometric centre. The

signature image is split into top and bottom blocks with a horizontal

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line passing through the geometric centre. Geometric centers h1 and

h2 are computed for top and bottom parts of the signature

respectively. The top part is split with a vertical line passing through

h1 to obtain left and right parts. The geometric centers h3 and h4 of

left and right parts of top part are computed. Similarly, the bottom

part is split with a vertical line passing through h2 to obtain left and

right parts. The geometric centers h5 and h6 of left and right parts of

bottom part computed. Similarly, each block of the signature image

is split to compute thirty geometric centers as shown in Figure 5.10.

Figure 5.10: Horizontal splitting of the signature

5.2.4 Verification

The matching between the genuine signature and test

signature is done based on correlation between the X and Y

components of thirty vertical and thirty horizontal features of

genuine and test signatures. The correlation coefficient R(X,Y) is

calculated using the Equation 5.1.

100

---- (5.1)

where N is total number of features.

The correlation coefficients of X and Y components of vertical

and horizontal features of test and database signatures are compared

with variable threshold values. It is observed that the genuine

signatures are recognized properly for the correlation coefficient

R(X,Y) of 0.94 for local database and 0.824 for GPDS database.

5.2.5 Proposed OSRCG Algorithm

Consider a signature image of a subject whose identity has to be

verified. The objectives are to:

(i) Preprocess the signature image and extract the features by

splitting operation

(ii) Verify the authenticity of the test signature by correlation

technique

(iii) Reduce the error rates

The OSRCG algorithm in which the authenticity of the test

signature image is verified is given in Table 5.1. The signature is

preprocessed to remove the noise contents. The features are

extracted from preprocessed images by vertical and horizontal

2

12

1 1

2

2

1 1

2

111,

N

i

N

iii

N

i

N

iii

N

ii

N

ii

N

iii

YYNXXN

YXYX

YXR

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splitting. The features of test signatures are compared with genuine

signature using correlation.

Table 5.1: OSRCG Algorithm

Input: Signature database and test signatures.

Output: Match/ Mismatch of the test

signature.

1. Signatures are resized and skeletonized

2. Thirty horizontal feature points and thirty

vertical feature points are extracted by

splitting.

4. Extracted features are stored in the database.

5. The test signature features are compared with

the features in database using correlation.

6. If the value of correlation coefficient is greater

than the predefined threshold value, the

signature is declared genuine else forged.

5.2.6 Performance Analysis

The proposed OSRCG model is tested on local and GPDS

databases. The algorithm is simulated on Matlab version 7.8. The

performance parameters FAR and FRR of the proposed model for

local database for different values of threshold correlation are given

in Table 5.2. It is observed that the percentage values of FRR

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increases and percentage values of FAR decreases with the increase

in threshold correlation.

Table 5.2: Variations of FRR and FAR with threshold correlation for

local database

Correlation threshold

%FRR %FAR

0.7 0 78.4

0.8 0 57.85

0.9 0 33.33

0.92 1.66 25.55

0.94 7.76 8.88

0.96 29.40 4.44

0.97 48.5 1.7

0.98 84.2 0

The plot of FAR and FRR with threshold correlation for local

database is shown in Figure 5.11. As threshold correlation increases,

the percentage value of FRR increases and FAR decreases. The value

of EER obtained is 8 for local database corresponding to optimal

correlation threshold of 0.935 at a point where FAR equals to FRR.

The performance parameters FRR and FAR of the proposed

model for different values of threshold correlation for GPDS database

are given in Table 5.3. It is observed that the percentage values of

FRR increases and percentage values of FAR decreases with the

increase in threshold correlation.

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Figure 5.11: FAR and FRR against threshold correlation for

local database

Table 5.3: Variations of FRR and FAR with threshold correlation for

GPDS database

Correlation threshold

%FRR %FAR

0.8 22.3 34.1

0.82 27.2 29.2

0.84 33.2 23.3

0.86 39.1 17.7

0.88 48.1 12.0

0.91 61.4 5.7

0.94 77.5 1.8

The plot of FAR and FRR for the variation of correlation

threshold values for GPDS database is shown in Figure 5.12. As

threshold correlation increases, the percentage value of FRR

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increases and FAR decreases. The value of EER obtained is 27.8

corresponding to optimal correlation threshold of 0.824 at a point

where FAR equals to FRR. The value of EER for GPDS database is

high compared to EER value for local database, since local database

is not standard one.

Figure 5.12: Plot of FAR and FRR v/s threshold for GPDS database

The comparison of EER values of the proposed OSRCG model

with existing models are given in Table 5.4. The EER value of the

proposed model is better compared to existing methods proposed by

Hairong Lv et al., [122], Rekik et al., [123] and Suhail and Manal

[124]. The performance of the proposed algorithm is improved for the

reasons: (i) the exact signature area is considered and (ii) the

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splitting is done by both vertical and horizontal methods to generate

features.

Table 5.4: Comparison of EER values of the proposed model with the

existing models for GPDS database

Method Preprocessing Feature extraction % EER

Hairong Lv et al., [122]

Noise reduction, binarization,

thinning

Moment features, direction, gray and

stroke width distribution

27.9

Rekik et al., [123]

Binarization, histogram,

median filtering

Signature segmentation into

blocks 32.83

Suhail and Manal [124]

Resizeing, binarization,

segmentation, thinning

Eccentricity, skewness, orientation

36

Proposed OSRCG method

Resize, skeletonization, exact signature

area

Geometric features by vertical and

horizontal splitting 27.8

5.3 Off-line Signature Recognition using Angular

Features

In this section block diagram of Off-line Signature Recognition

using Angular Features (OSRAF) shown in Figure 5.13 is discussed

in detail. The signature images are preprocessed by resizing and

skeletonization. The exact signature area is considered for feature

extraction. The angular features are extracted with respect to centre

of the signature by splitting in two phases.

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Figure 5.13: Block diagram of OSRAF system

5.3.1 Signature database

The GPDS300 signature database and local database are

considered as input to the proposed system.

5.3.2 Preprocessing

The signature image is preprocessed to enhance image quality.

The preprocessing includes filtering, resizing, skeletonization by

morphological operations and considering the exact signature area.

(i) Filtering: The noise present in the signature is removed using DWT

technique. The DWT separates low frequency and high frequency

components by filtering. The noise is present in the high frequency

components, and hence the low frequency components of the

Preprocessing

Test Signature

Matching

Decision

N

Signature Database

Preprocessing

Angular Feature Extraction

Feature templates

Y RandomForgery

Angular Feature Extraction

Reject

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signature are considered. The signature image after applying DWT is

as shown in Figure 5.14.

Figure 5.14: Signature after applying DWT

(ii) Resize: The images are resized to 150*450 instead of having

signatures of different dimensions. Algorithm needs all the signatures

to be of same size so that fair comparison is made among the

signatures to produce better results.

(iii) Skeletonization: It is the process of reducing image to single pixel

width, which consists of the spines of the object parts. A two

dimensional skeleton may consist of curves (spines), isolated two

dimensional points and two dimensional surfaces. The generation of

a skeleton is realized by applying an iterative process, which erodes

the object layer by layer until only the object spines remain, which

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form the skeleton of the two dimensional image. The skeletonization

is done by removing the pixels on the boundary of the signature

image without allowing the signature image to break apart. The

process is achieved by morphological operations on signature image.

The Figure 5.15 shows the signature after skeletonization.

Figure 5.15: Signature after skeletonization (iv) Exact signature area: The signature image might not be present

on the entire frame. The exact signature area is considered in the

skeletonized image for further analysis. The signature image is

scanned horizontally from top to get the first black pixel row a1 of the

image and is the value of the row variable i corresponding to first

black pixel. The signature image is scanned from the bottom to get

the last black pixel row a2 of signature and is the value of the row

variable i corresponding to last black pixel. The horizontal scanning

for finding the top row and bottom row of the exact signature area is

given by the Equations 5.2 and 5.3 respectively.

M

i

N

js jiI

1 1

0, ---------------- (5.2)

N

i

M

js jiNI

1 1

0,1 ---------------- (5.3)

where M is the number of rows and N is the number of columns and

Is(i , j) is the skeletonized signature image.

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The signature image is scanned vertically from left to get the

first black pixel column a3 of the image and is the value of the

column variable j corresponding to first black pixel. The signature

image is scanned vertically from right to get the last black pixel

column a4 of the signature and is the value of the column variable

j corresponding to last black pixel. The vertical scanning for finding

exact signature area is given by the Equations 5.4 and 5.5. The

Figure 5.16 shows the image with exact signature area.

M

j

N

is jiI

1 1

0, ----------- (5.4)

M

j

N

is jMiI

1 1

01, ----------- (5.5)

where yxI s . is the skeletonized signature image.

Figure 5.16: Exact signature area

5.3.3 Random Forgery Detection

The random forgery is detected before the feature extraction.

The number of rows ir and columns ic are obtained for all the ten

genuine signatures using the Equations 5.6 and 5.7 respectively.

iii aar 21 ----------- (5.6)

iii aac 43 ----------- (5.7)

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where a1i is the first row containing the black pixel in the ith

signature, a2i is the last row containing the black pixel in the ith

signature, a3i is the first column containing the black pixel in the ith

signature, a4i is the last column containing the black pixel in the ith

signature and i=1, 2, 3, …10.

The average number of rows avgR and columns avgC are

obtained using the Equations 5.8 and 5.9 respectively.

GS

N

ii

avgN

r

R

GS

1

-------------- (5.8)

where ri is the number of rows representing the ith signature and NGS

is the total number of genuine signatures.

GS

N

jj

avgN

c

C

GS

1

----------- (5.9)

where Cj is the number of columns representing the jth signature and

NGS is the total number of genuine signatures.

The number of rows RTi and columns CTi of test signature are

computed and compared with avgR and avgC respectively. If the

absolute value of the difference between Ravg and RTi and the absolute

value of the difference between Cavg and CTi are less than or equal to

predefined threshold, then the test signature is considered as skilled

forgery else random forgery.

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5.3.4 Feature extraction

The angular features are extracted in two phases. In first

phase, the preprocessed signature image is made to undergo vertical

and horizontal splitting. The skeleton of the signature image is

scanned from left to right and top to bottom to count the total

number of black pixels. The total number of black pixels is divided by

two to locate geometric centre. The signature image is split into top

and bottom blocks with a horizontal line passing through the

geometric centre. The geometric centers of top and bottom parts are

located by counting the number of black pixels. The splitting

procedure used to get 128 blocks is shown in Figure 5.17. The angle

of geometric center with respect to top left pixel is computed and the

corresponding diagram is as shown in Figure 5.18. The top block of

the signature is split into left and right parts with vertical line

passing through the geometric center of the top block. The geometric

centers of the left and right parts are located and the corresponding

angles are computed. This process of computing the geometric

centers and the corresponding angles is continued till 128 angles.

Figure 5.17: Horizontal and Vertical splitting of the signature

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The distance between top left reference point and the geometric

centre of signature is obtained by the Equation 5.10.

Distance = 2

122

12 )()( jjii ------------- (5.10)

where ),( 22 ji and ),( 11 ji are the coordinates of two points.

The angle is computed using the Equation 5.11.

AC

ABi

1cos --------------- (5.11)

where 128........4,3,2,1i , adjacent side AB and hypotenuse AC are

given by Equations 5.12 and 5.13 respectively. A(1,1) is the reference

point and C(i, j) is the geometric center.

Figure 5.18: Geometric center angle

22 )1()1( jiAC ------------ (5.12)

1 jAB -------------- (5.13)

The number of blocks can be increased further but there may

be the case where the angle computed would be infinity. As the pixel

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appears on the top left corner of the block, hypotenuse becomes zero,

hence the numbers of blocks are limited to 128.

The second phase consists of division of an image into

dimensions which are predefined. The image is divided into ten

square blocks containing 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100

pixels as shown in the Figure 5.19. The Figures 5.19(a), 5.19(b),

5.19(c) and 5.19(d) correspond to division of the signature image

from top left, top right, bottom left and bottom right respectively.

Each division produces ten blocks, which leads to totally forty blocks.

The angular features for these forty blocks are computed. The total

number of angular features obtained from first and second phase is

one hundred and sixty eight.

(a) (b) (c) (d)

Figure 5.19: Division of signature image

5.3.5 Verification

The comparison between the genuine signature and test

signature is made by computing the difference between the angles in

radians obtained for both the signatures. A threshold is set which

decides the authenticity of the signature. The threshold value of 0.26

radians is considered for verification purpose. The absolute difference

between i th angle Gi of the genuine signature and i th angle Ti of the

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test signature is computed and compared with the predefined

threshold as given in the Equation 5.14.

26.0 TiGi ---------- (5.14)

where 168........4,3,2,1i .

If the number of angles having difference less than or equal to

0.26 radians threshold for minimum of 133 blocks from total of 168

blocks, then the test signature is considered genuine otherwise

forged signature.

5.3.6 Proposed OSRAF Algorithm

Consider a signature image of a person whose identity has to

be verified. The objective is to obtain low FAR, FRR and EER values.

The OSRAF algorithm is given in Table 5.5. The signature is

preprocessed to resize and skeletonize. The angular features are

extracted in two phases. The test signature features are compared

with database signatures to authenticate based on threshold values.

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Table 5.5 OSRAF Algorithm

Input: Signature database and test signatures.

Output: Match/ Mismatch.

1. Preprocess the signature image for efficient feature

extraction.

2. Horizontal and vertical splitting of the signature

image is carried out based on number of black pixels

to obtain 128 blocks. The centre of signature of all

the blocks is computed to determine angular features

in the first phase.

3. The signature is divided into 40 blocks from four

corners of the signature to get angular features in the

second phase.

4. The angular features extracted in two phases are

stored in the database.

5. The features in database are compared with the

feature extracted from the test signature.

6. If the difference in angular features between test and

genuine signatures are less than threshold value for

133 blocks out of 168, then the signature is genuine.

5.3.7 Performance Analysis

For the performance analysis, the local signature database and

GPDS are considered. The MATLAB version 7.8 is used for

implementation of the proposed algorithm.

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The performance parameters FRR and FAR of the proposed

model for local database for different values of threshold are given in

Table 5.6. It is observed that the values of FRR decreases and FAR

increases with the increase in threshold. If the FAR of a system is

same as the FRR then the system is said to be in an optimal state.

The corresponding value of error is EER.

Table 5.6: Variations of FRR and FAR values with threshold for local

database

Threshold %FRR %FAR

0.10 100 0

0.15 85.5 0.25

0.20 45.52 0.50

0.25 11.65 4.75

0.26 4.99 8.50

0.30 1.11 22.75

0.35 0 51.25

0.40 0 75.12

The graph of FAR and FRR in case of local database obtained

for different values of threshold is shown in Figure 5.20. As threshold

increases, the value of FRR decreases and FAR increases. The value

of EER obtained is 7.2 corresponding to optimal threshold of 0.256 at

a point where FAR equals to FRR.

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Figure 5.20: Plot of FAR and FRR v/s threshold for local database

The EER values with local database for the proposed method

OSRAF using angular features is less compared to the proposed

method OSRCG using geometric centre features only. The EER

values for two proposed methods are given in Table 5.7.

Table 5.7: Comparison of EER values for local database

OSRCG 8.0

OSRAF 7.2

The performance parameters FRR and FAR of the proposed

model for different values of threshold for GPDS database are given

in Table 5.8. It is observed that the percentage values of FRR

decreases and FAR increases with the increase in threshold.

118

Table 5.8: Variations of FRR and FAR values with threshold for

GPDS database

Threshold %FRR %FAR

0.10 98.1 0

0.15 85.5 2.2

0.20 53.5 6.5

0.25 35.6 18.7

0.30 12.1 38.7

0.35 2.0 51.2

0.40 0 75.1

The graph of FAR and FRR in case of GPDS database obtained

for different values of threshold is shown in Figure 5.21. As threshold

increases, the value of FRR decreases and FAR increases. The value

of EER obtained is 26.34 corresponding to optimal correlation

threshold of 0.27 at a point where FAR equals to FRR.

The value of EER for GPDS database is high compared to EER

value for local database, since local database is not standard one.

119

Figure 5.21: FAR and FRR v/s threshold for GPDS database

The comparison of EER values of the proposed OSRAF model

with other methods is given in Table 5.9. The EER value of the

proposed model is better compared to existing methods presented by

Hairong Lv al., [122], Rekik et al., [123] and Suhail and Manal [124].

The performance of the proposed algorithm is improved for the

reasons: (i) the exact signature area is considered and (ii) the splitting

is done by both vertical and horizontal scanning to generate angular

features.

120

Table 5.9: Comparison of EER values of the proposed model with

existing systems for GPDS database

Method Preprocessing Feature extraction % EER

Hairong Lv et al., [122]

Noise reduction, binarization,

thinning

Moment features, Direction, gray and

stroke width distribution

27.9

Rekik et al., [123]

Binarization, histogram,

median filter

Signature segmentation into

blocks 32.83

Suhail and Manal [124]

Resize, Binarization, segmentation,

thinning

Eccentricity, skewness, orientation

36

Proposed OSRAF method

Resize, skeletonization, exact signature

area

Angular features in two phases

26.34

5.4 Summary

The proposed OSRCG algorithm which is based on the sixty

geometric centre features is discussed in this chapter. The DWT is

used in the preprocessing stage to remove noise in the signature

image and then skeletonized. The sixty geometric centre features are

determined by horizontal and vertical splitting of signatures. The

matching between test and database signatures is done by

correlation.

The OSRAF algorithm based on the angular features is also

discussed in this chapter. The angular features from preprocessed

signature are extracted in two phases. The angular features are

121

compared using distance formula. It is observed that the error rates

are low in the case of proposed algorithms compared to existing

algorithms.