Feature Extraction and Image Processing

Object description 263

bLtktdttktdt

k

*

0

2

0

2

=

1

(( /2 ) ) sin( ) +

1

sin( )

By computing the second integrals of each coefficient, we obtain a simpler form as

aLtdt

0

*

0

2

= 2 +

1

(( /2 ) )

aLtktdt

k

*

0

2

=

1

(( /2 ) ) cos ( )

(7.32)

b

k

Lt ktdt

k

*

0

2

= –

2

+

1

(( /2 ) ) sin ( )

In an image, we measure distances, thus it is better to express these equations in arc-length

form. For that, we know that s = (L/2 )t. Thus,

Code 7.1 Angular functions

plot(S,A);

axis([0,S(m),-1,2*pi+1]);

%Cumulative angular G(s)=-2pi

G=zeros(1,m);

for i=2:m

d=min(abs(A(i)-A(i-1)),abs(abs(A(i)-A(i-1))-2*pi));

if d>.5

G(i)=G(i-1);

elseif (A(i)-A(i-1))<-pi

G(i)=G(i-1)Ð(A(i)-A(i-1)+2*pi);

elseif (A(i)-A(i-1))>pi ...