<s>
Harmonic	B-Algorithm
phase	I-Algorithm
(	O
HARP	B-Algorithm
)	O
algorithm	O
is	O
a	O
medical	O
image	O
analysis	O
technique	O
capable	O
of	O
extracting	O
and	O
processing	O
motion	O
information	O
from	O
tagged	O
magnetic	O
resonance	O
image	O
(	O
MRI	O
)	O
sequences	O
.	O
</s>
<s>
The	O
method	O
uses	O
spectral	O
peaks	O
in	O
the	O
Fourier	O
domain	O
of	O
tagged	O
MRI	O
,	O
calculating	O
the	O
phase	O
images	O
of	O
their	O
inverse	O
Fourier	O
transforms	O
,	O
which	O
are	O
called	O
harmonic	B-Algorithm
phase	I-Algorithm
(	O
HARP	B-Algorithm
)	O
images	O
.	O
</s>
<s>
The	O
motion	O
of	O
material	O
points	O
through	O
time	O
is	O
then	O
tracked	O
,	O
under	O
the	O
assumption	O
that	O
the	O
HARP	B-Algorithm
value	O
of	O
a	O
fixed	O
material	O
point	O
is	O
time-invariant	O
.	O
</s>
<s>
However	O
,	O
suffered	O
from	O
long	O
imaging	O
and	O
post-processing	O
times	O
,	O
tagged	O
MRI	O
was	O
slow	O
in	O
entering	O
into	O
routine	O
clinical	O
use	O
until	O
the	O
HARP	B-Algorithm
algorithm	I-Algorithm
was	O
developed	O
and	O
published	O
in	O
1999	O
.	O
</s>
<s>
HARP	B-Algorithm
processing	O
uses	O
a	O
bandpass	O
filter	O
to	O
isolate	O
one	O
of	O
the	O
spectral	O
peaks	O
.	O
</s>
<s>
where	O
is	O
called	O
the	O
harmonic	O
magnitude	O
image	O
and	O
is	O
called	O
the	O
harmonic	B-Algorithm
phase	I-Algorithm
image	O
.	O
</s>
<s>
And	O
the	O
harmonic	B-Algorithm
phase	I-Algorithm
image	O
in	O
(	O
d	O
)	O
contains	O
the	O
motion	O
of	O
the	O
myocardium	O
in	O
horizontal	O
direction	O
.	O
</s>
<s>
Notice	O
that	O
the	O
harmonic	B-Algorithm
phase	I-Algorithm
images	O
are	O
computed	O
by	O
taking	O
the	O
inverse	O
tangent	O
of	O
the	O
imaginary	O
part	O
divided	O
by	O
the	O
real	O
part	O
of	O
,	O
such	O
that	O
the	O
range	O
of	O
this	O
computation	O
is	O
only	O
in	O
.	O
</s>
<s>
Either	O
or	O
might	O
be	O
called	O
a	O
harmonic	B-Algorithm
phase	I-Algorithm
(	O
HARP	B-Algorithm
)	O
image	O
,	O
but	O
only	O
can	O
be	O
directly	O
calculated	O
and	O
visualized	O
.	O
</s>
<s>
It	O
is	O
the	O
basis	O
for	O
HARP	B-Algorithm
tracking	O
.	O
</s>
<s>
For	O
a	O
fixed	O
material	O
point	O
with	O
a	O
HARP	B-Algorithm
value	O
,	O
only	O
one	O
of	O
the	O
points	O
sharing	O
the	O
same	O
HARP	B-Algorithm
value	O
in	O
a	O
later	O
time	O
frame	O
is	O
the	O
correct	O
match	O
.	O
</s>
<s>
The	O
result	O
of	O
HARP	B-Algorithm
tracking	O
of	O
one	O
frame	O
of	O
cardiac	O
MRI	O
is	O
shown	O
in	O
the	O
figure	O
.	O
</s>
<s>
The	O
entire	O
HARP	B-Algorithm
algorithm	I-Algorithm
takes	O
only	O
a	O
few	O
minutes	O
to	O
perform	O
on	O
a	O
normal	O
computer	O
and	O
the	O
motion	O
tracking	O
result	O
is	O
accurate	O
(	O
with	O
a	O
typical	O
error	O
range	O
of	O
pixel	O
)	O
.	O
</s>
