<s>
In	O
image	B-Algorithm
registration	I-Algorithm
,	O
inverse	B-General_Concept
consistency	I-General_Concept
measures	O
the	O
consistency	O
of	O
mappings	O
between	O
images	O
produced	O
by	O
a	O
registration	B-Algorithm
algorithm	O
.	O
</s>
<s>
The	O
inverse	B-General_Concept
consistency	I-General_Concept
error	I-General_Concept
,	O
introduced	O
by	O
Christiansen	O
and	O
Johnson	O
in	O
2001	O
,	O
quantifies	O
the	O
distance	O
between	O
the	O
composition	O
of	O
the	O
mappings	O
from	O
each	O
image	B-Algorithm
to	O
the	O
other	O
,	O
produced	O
by	O
the	O
registration	B-Algorithm
procedure	O
,	O
and	O
the	O
identity	O
function	O
,	O
and	O
is	O
used	O
as	O
a	O
regularisation	O
constraint	O
in	O
the	O
loss	O
function	O
of	O
many	O
registration	B-Algorithm
algorithms	O
to	O
enforce	O
consistent	O
mappings	O
.	O
</s>
<s>
Inverse	B-General_Concept
consistency	I-General_Concept
is	O
necessary	O
for	O
good	O
image	B-Algorithm
registration	I-Algorithm
but	O
it	O
is	O
not	O
sufficient	O
,	O
since	O
a	O
mapping	O
can	O
be	O
perfectly	O
consistent	O
but	O
not	O
register	O
the	O
images	O
at	O
all	O
.	O
</s>
<s>
registering	O
a	O
source	O
image	B-Algorithm
to	O
a	O
target	O
image	B-Algorithm
consists	O
of	O
determining	O
a	O
transformation	O
that	O
maps	O
points	O
from	O
the	O
target	O
space	O
to	O
the	O
source	O
space	O
.	O
</s>
<s>
and	O
or	O
,	O
equivalently	O
,	O
and	O
,	O
where	O
denotes	O
the	O
function	B-Application
composition	I-Application
operator	I-Application
.	O
</s>
<s>
Real	O
algorithms	O
are	O
not	O
perfect	O
,	O
and	O
when	O
swapping	O
the	O
role	O
of	O
source	O
and	O
target	O
image	B-Algorithm
in	O
a	O
registration	B-Algorithm
problem	O
the	O
so	O
obtained	O
transformations	O
are	O
not	O
the	O
inverse	O
of	O
each	O
other	O
.	O
</s>
<s>
Inverse	B-General_Concept
consistency	I-General_Concept
can	O
be	O
used	O
as	O
a	O
quality	O
metric	O
to	O
evaluate	O
image	B-Algorithm
registration	I-Algorithm
results	O
.	O
</s>
<s>
The	O
inverse	B-General_Concept
consistency	I-General_Concept
error	I-General_Concept
(	O
)	O
measures	O
the	O
distance	O
between	O
the	O
composition	O
of	O
the	O
two	O
transforms	O
and	O
the	O
identity	O
function	O
,	O
and	O
it	O
can	O
be	O
formulated	O
in	O
terms	O
of	O
both	O
average	O
(	O
)	O
or	O
maximum	O
(	O
)	O
over	O
a	O
region	B-Algorithm
of	I-Algorithm
interest	I-Algorithm
of	O
the	O
image	B-Algorithm
:	O
</s>
<s>
While	O
inverse	B-General_Concept
consistency	I-General_Concept
is	O
a	O
necessary	O
property	O
of	O
good	O
registration	B-Algorithm
algorithms	O
,	O
inverse	B-General_Concept
consistency	I-General_Concept
error	I-General_Concept
alone	O
is	O
not	O
a	O
sufficient	O
metric	O
to	O
evaluate	O
the	O
quality	O
of	O
image	B-Algorithm
registration	I-Algorithm
results	O
,	O
since	O
a	O
perfectly	O
consistent	O
mapping	O
,	O
with	O
no	O
other	O
constraint	O
,	O
may	O
be	O
not	O
even	O
close	O
to	O
correctly	O
register	O
a	O
pair	O
of	O
images	O
.	O
</s>
