Radial Sector Coding at SCIS & ISIS 08

A Novel Algorithm for Translation, Rotation and Scale Invariant Character Recognition

Asif Iqbal, A. B. M. Musa, Anindya Tahsin, Md. Abdus Sattar, Md. Monirul Islam, and K. Murase

SCIS & ISIS 08

Overview• Introduction• Advantages over existing methods• Radial Sector Coding

– Center of Mass– Axis of Reference– Line of Reference– Feature vector generation

• Classifier• Experimental Results• Analysis• Conclusion

Introduction

• Invariant Character Recognition (ICR) is recognition of characters independent of translation, rotation and scaling

• It is still a hard problem in computer vision• Most of the existing algorithms are

computationally too expensive or cannot perform well under all three transformations

• Here we propose a simple and inexpensive algorithm for ICR which performs well under all three transformations

Advantages over existing methods

Our Radial Sector Coding (RSC) is simple and inexpensive

• Moment Based Methods:– Invariant moments are used– Computationally too expensive– Examples: Cartesian moment, Zernike

moment, Pseudo-Zernike, Orthogonal Fourier-Mellin moments

Advantages over existing methods

RSC do not sample whole character for feature extraction

• Projection Methods:– Projection is taken for whole character– Data redundancy exists

Advantages over existing methods (contd.)

RSC consider whole area of characterfor feature extraction

• Boundary Methods:– Sample boundary of character only– Good for solid object recognition– Not good for character recognition as they

have much topological information inside

Advantages over existing methods (contd.)

RSC uses only single circle and its radiifor feature extraction

• Radial Coding and SAFER:– Use multiple concentric circles – Small circles create erroneous features

Radial Sector Coding

Center of Mass

x y

qppq yxfyxm ),(A

CoM locates the character independent of location in the Image

Center of Mass (CoM)If is the CoM then ),( yx CC

00

01

00

10 and m

mC

m

mC yx

Here is the Cartesian Moment of order (p+q)

pqm

Axis of Reference (Symmetric Characters)

AAxis of Reference is the Axis of Symmetry of symmetric characters

Enclosing Circle

Radii deviding the circle into n sectors

Cutpoints

Cutpoints with maximum distance

Is it Axis of Reference (AoR) ?

Not Equal Almost Equal ! Not Equal

It is not AoR as pair wise max cutpoint distances are not

equal in most of the cases

Is it Axis of Reference (AoR) ?

Almost Equal !

It is AoR as pair wise max cutpoint

distances are equal in most of the cases

Hence the name Radial Sector CodingCutpoint is the pixel of intensity change

Axis of Reference (Symmetric Characters) [contd.]• For Symmetric characters the summation of

absolute difference of maximum cutpoints distances for each pair of lines having same angular distance from Axis of Symmetry/Axis of Reference will be very small

• We can exploit this fact to find AoR/AoS• As we do not know the actual AoR/AoS we can

consider each axis as a potential AoR/AoS and the one having minimum summation is the actual AoR/AoS

Axis of Reference (Symmetric Characters) [contd.]

111 , . . . ,, , . . . ,, inii ddddd

),( ii yx

odd) is(n , . . . ,,, 21 no dddd

2

1

1 )1)%(2

1(

||n

i

ik nn

kk dd

Let denotes maximum cut-point distance along each radius and initial sampling starting at 0 degree is

Now there exists an ordering

where

is minimum with respect to all other orderings

id

Now let the points for id2

1n

idand are ),( ii yx and ),(

2

1

2

1

ni

ni

yx

The line connecting ),(2

1

2

1

ni

ni

yxand is the AoR

Axis of Reference (Non-symmetric Characters)• The Axis found with the minimum

summation criteria is a rotation invariant feature for non-symmetric characters also

• So with minimum sum criteria we are getting Axis of Reference which is the Axis of Symmetry for symmetric characters and a rotation invariant feature for all characters

Axis of Reference Examples

AoR of Symmetric Character A

AoR of Non-symmetric Character F

Line of Reference

• Line of Reference is one of the two radii on Axis of Reference which has the largest cutpoint distance compared to other one

),( yx CC ),( ii yx ),(2

1

2

1

ni

ni

yxIf is the CoM and ,

are end points of AoR then line connecting ),( yx CC

),( ii yx

,

Is the LoR if it has greater cutpoint distance

Line of Reference Examples

LoR of Symmetric Character A

LoR of Non-symmetric Character F

Feature vector generation

• Feature vector size 18 is used

• Line of Reference is considered as 0° line

• Average distances of cutpoints on 18 radii is calculated starting with LoR

• Feature vector consists of these 18 values

Radial Sector Coding in Brief • Step 1: Find Center of Mass (CoM)• Step 2: Find radius r of enclosing circle• Step 3: Draw n radii at equal angular distance to

divide the circle into n sectors• Step 4: Find cutpoints on each radius• Step 5: Calculate maximum and average

cutpoint distances• Step 6: Find Axis of Reference (AoR)• Step 7: Fine Line of Reference (LoR)• Step 8: Consider LoR as 0° line and generate

feature vector of size n/2

Classifier

• Multilayer feed-forward ANN is used as classifier

• ANN has good noise tolerance

• ANN has good generalization ability

Experimental Results

• Experimental Setup– Matlab is used for feature generation and

experimental evolution– Three layer feed-forward ANN is used for

experimentation– Two widely used fonts Arial and Tahoma is

used– Large sample of 26 uppercase English

characters from both fonts are used

Experimental Results (contd.)Character Accuracy Character Accuracy

A 100 N 100

B 100 O 100

C 100 P 100

D 100 Q 100

E 100 R 100

F 94.44444 S 100

G 91.66667 T 100

H 100 U 100

I 100 V 100

J 100 W 100

K 97.22222 X 100

L 100 Y 100

M 100 Z 100

Average 99.35897

Recognition rate for Arial font. 40x40 pixel 0° to 90° rotated characters at 10° gap are used for training. 40x40 pixel 0° to 350° rotated characters at 10° gap are used for testing. Total number of training characters is 26x10 = 260. Total number of test characters is 26x36 = 936


A 98.611111 N 100

B 100 O 100

C 100 P 100

D 100 Q 97.222222

E 100 R 100

F 88.888889 S 100

G 98.611111 T 100

H 100 U 98.611111

I 100 V 100

J 100 W 97.222222

K 94.444444 X 97.222222

L 100 Y 97.222222

M 100 Z 100

Average 98.77137



A 100 N 100

B 91.666667 O 100

C 100 P 100

D 100 Q 97.222222

E 100 R 100

F 97.222222 S 97.222222

G 100 T 100

H 100 U 100

I 100 V 100

J 100 W 100

K 100 X 100

L 100 Y 100

M 100 Z 83.333333

Average 98.71795



A 100 N 100

B 100 O 100

C 94.444444 P 100

D 100 Q 97.222222

E 100 R 100

F 100 S 83.333333

G 88.888889 T 100

H 97.222222 U 100

I 97.222222 V 100

J 100 W 100

K 97.222222 X 97.222222

L 94.444444 Y 100

M 100 Z 100

Average 97.97009



A 100 N 100

B 100 O 100

C 100 P 100

D 100 Q 100

E 100 R 100

F 100 S 100

G 100 T 100

H 97.222222 U 100

I 97.222222 V 100

J 100 W 100

K 100 X 100

L 100 Y 100

M 100 Z 100

Average 99.78632



A 100 N 100

B 55.555556 O 100

C 100 P 100

D 100 Q 100

E 100 R 91.666667

F 91.666667 S 100

G 100 T 100

H 100 U 97.222222

I 100 V 100

J 100 W 88.888889

K 100 X 97.222222

L 100 Y 100

M 100 Z 100

Average 97.00855

Recognition rate for Tahoma font. 40x40 pixel 0° to 90° rotated characters at 10° gap are used for training. 50x50 pixel 0° to 350° rotated characters at 10° gap are used for testing. Total number of training characters is 26x10 = 260. Total number of test characters is 26x36 = 936


A 99.7685185 N 100

B 91.20370383 O 100

C 99.074074 P 100

D 100 Q 98.611111

E 100 R 98.61111117

F 95.37037033 S 96.75925917

G 96.52777783 T 100

H 99.074074 U 99.3055555

I 99.074074 V 100

J 100 W 97.68518517

K 98.148148 X 98.611111

L 99.074074 Y 99.537037

M 100 Z 97.22222217

Average 98.60221

Average recognition rate for all characters considering previous tables

Analysis

• Correlation of Features

RSC generates highly correlated features under different rotation

Analysis (contd.)• Discrimination capability for similar characters

RSC generates enough distinctive features for similar characters

Analysis (contd.)• Double Mirror Symmetry

– Characters like H, I, O has double Axis of Symmetry

Double Mirror Symmetry can be exploited in future

Analysis (contd.)• Double Reverse Mirror Symmetry

– Characters like N, S, Z are symmetric if we reverse the mirror reflected part

Double Reverse Mirror Symmetry can be exploited in future

Horizontal Reverse

Mirror Symmetry

Vertical Reverse

Mirror Symmetry

Analysis (contd.)

• Inherent Difficulties– Finite Resolution

• Sampling is limited by finite resolution of image

– Round Up Error• Any measure required to be mapped to image

requires rounding up

– Boundary Distortion• Rotation introduces unavoidable boundary

distortion

Conclusion

• RSC is simple and inexpensive

• Experimental results prove its effectiveness

• Use of more sophisticated classifier in future may improve its performance

• Double mirror and reverse mirror symmetry can be exploited in future

Thanks !

Education

Radial Sector Coding at SCIS & ISIS 08