<s>
Phase	B-Algorithm
congruency	I-Algorithm
is	O
a	O
measure	O
of	O
feature	O
significance	O
in	O
computer	O
images	O
,	O
a	O
method	O
of	O
edge	B-Algorithm
detection	I-Algorithm
that	O
is	O
particularly	O
robust	O
against	O
changes	O
in	O
illumination	O
and	O
contrast	O
.	O
</s>
<s>
Phase	B-Algorithm
congruency	I-Algorithm
reflects	O
the	O
behaviour	O
of	O
the	O
image	O
in	O
the	O
frequency	O
domain	O
.	O
</s>
<s>
Phase	B-Algorithm
congruency	I-Algorithm
compares	O
the	O
weighted	O
alignment	O
of	O
the	O
Fourier	O
components	O
of	O
a	O
signal	O
with	O
the	O
sum	O
of	O
the	O
Fourier	O
components	O
.	O
</s>
<s>
where	O
is	O
the	O
local	O
or	O
instantaneous	O
phase	O
as	O
can	O
be	O
calculated	O
using	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
and	O
are	O
the	O
local	O
amplitude	O
,	O
or	O
energy	O
,	O
of	O
the	O
signal	O
.	O
</s>
<s>
Several	O
ways	O
of	O
implementing	O
phase	B-Algorithm
congruency	I-Algorithm
have	O
been	O
developed	O
,	O
of	O
which	O
two	O
versions	O
are	O
available	O
in	O
open	O
source	O
,	O
one	O
written	O
for	O
Matlab	O
and	O
the	O
other	O
written	O
in	O
Java	O
as	O
a	O
plugin	O
for	O
the	O
ImageJ	O
software	O
.	O
</s>
<s>
The	O
square-wave	O
example	O
is	O
naive	O
in	O
that	O
most	O
edge	B-Algorithm
detection	I-Algorithm
methods	O
deal	O
with	O
it	O
equally	O
well	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
first	B-Algorithm
derivative	I-Algorithm
has	O
a	O
maximal	O
magnitude	O
at	O
the	O
edges	O
.	O
</s>
<s>
However	O
,	O
there	O
are	O
cases	O
where	O
the	O
perceived	O
edge	O
does	O
not	O
have	O
a	O
sharp	O
step	O
or	O
a	O
large	O
derivative	B-Algorithm
.	O
</s>
<s>
The	O
method	O
of	O
phase	B-Algorithm
congruency	I-Algorithm
applies	O
to	O
many	O
cases	O
where	O
other	O
methods	O
fail	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
the	O
phase	B-Algorithm
congruency	I-Algorithm
map	O
has	O
a	O
single	O
line	O
.	O
</s>
<s>
Calculating	O
the	O
phase	B-Algorithm
congruency	I-Algorithm
map	O
of	O
an	O
image	O
is	O
very	O
computationally	O
intensive	O
,	O
and	O
sensitive	O
to	O
image	O
noise	O
.	O
</s>
