Image Processing Reference
In-Depth Information
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)-(A(i)-A(i-1)+2*pi);
elseif (A(i)-A(i-1))>pi
G(i)=G(i-1)-(A(i)-A(i-1)-2*pi);
else
G(i)=G(i-1)-(A(i)-A(i-1));
end
end
subplot(3,3,3);
plot(S,G);
axis([0,S(m),-2*pi-1,1]);
%Cumulative angular Normalised
F=G+t;
subplot(3,3,4);
plot(t,F);
axis([0,2*pi,-2*pi,2*pi]);
Code 7.1
Angular functions
2
2
=
1
+
1
∫ ∫
By computing the second integrals of each coefficient, we obtain a simpler form as
b
*
((
L
/ 2
) ) sin(
t
kt dt
)
t
sin(
kt dt
)
0
0
2
= 2 +
1
*
a
((
L
/ 2
) )
t dt
0
2
=
1
*
a
((
L
/ 2
) ) cos (
t
kt dt
)
(7.32)
0
2
= -
2
+
1
∫
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
b
*
((
Lt
/ 2
) ) sin (
kt dt
)
k
0
)
t
. Thus,
