<s>
Affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
is	O
a	O
methodology	O
for	O
iteratively	O
adapting	O
the	O
shape	O
of	O
the	O
smoothing	O
kernels	O
in	O
an	O
affine	O
group	O
of	O
smoothing	O
kernels	O
to	O
the	O
local	O
image	O
structure	O
in	O
neighbourhood	O
region	O
of	O
a	O
specific	O
image	O
point	O
.	O
</s>
<s>
Equivalently	O
,	O
affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
can	O
be	O
accomplished	O
by	O
iteratively	O
warping	O
a	O
local	O
image	O
patch	O
with	O
affine	O
transformations	O
while	O
applying	O
a	O
rotationally	O
symmetric	O
filter	O
to	O
the	O
warped	O
image	O
patches	O
.	O
</s>
<s>
In	O
the	O
area	O
of	O
computer	B-Application
vision	I-Application
,	O
this	O
idea	O
has	O
been	O
used	O
for	O
defining	O
affine	O
invariant	O
interest	O
point	O
operators	O
as	O
well	O
as	O
affine	O
invariant	O
texture	O
analysis	O
methods	O
.	O
</s>
<s>
The	O
interest	O
points	O
obtained	O
from	O
the	O
scale-adapted	O
Laplacian	O
blob	B-Algorithm
detector	I-Algorithm
or	O
the	O
multi-scale	O
Harris	O
corner	B-Algorithm
detector	I-Algorithm
with	O
automatic	O
scale	O
selection	O
are	O
invariant	O
to	O
translations	O
,	O
rotations	O
and	O
uniform	O
rescalings	O
in	O
the	O
spatial	O
domain	O
.	O
</s>
<s>
The	O
images	O
that	O
constitute	O
the	O
input	O
to	O
a	O
computer	B-Application
vision	I-Application
system	O
are	O
,	O
however	O
,	O
also	O
subject	O
to	O
perspective	O
distortions	O
.	O
</s>
<s>
Affine	O
invariance	O
can	O
be	O
accomplished	O
from	O
measurements	O
of	O
the	O
same	O
multi-scale	O
windowed	O
second	O
moment	O
matrix	O
as	O
is	O
used	O
in	O
the	O
multi-scale	O
Harris	O
operator	O
provided	O
that	O
we	O
extend	O
the	O
regular	O
scale	B-Algorithm
space	I-Algorithm
concept	O
obtained	O
by	O
convolution	B-Language
with	O
rotationally	O
symmetric	O
Gaussian	O
kernels	O
to	O
an	O
affine	O
Gaussian	O
scale-space	B-Algorithm
obtained	O
by	O
shape-adapted	O
Gaussian	O
kernels	O
(	O
;	O
)	O
.	O
</s>
<s>
Disregarding	O
mathematical	O
details	O
,	O
which	O
unfortunately	O
become	O
somewhat	O
technical	O
if	O
one	O
aims	O
at	O
a	O
precise	O
description	O
of	O
what	O
is	O
going	O
on	O
,	O
the	O
important	O
message	O
is	O
that	O
the	O
affine	O
Gaussian	O
scale-space	B-Algorithm
is	O
closed	O
under	O
affine	O
transformations	O
.	O
</s>
<s>
This	O
overall	O
process	O
is	O
referred	O
to	O
as	O
affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
(	O
;	O
;	O
;	O
;	O
;	O
)	O
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
process	O
described	O
here	O
is	O
often	O
combined	O
with	O
interest	O
point	O
detection	O
automatic	O
scale	O
selection	O
as	O
described	O
in	O
the	O
articles	O
on	O
blob	B-Algorithm
detection	I-Algorithm
and	O
corner	B-Algorithm
detection	I-Algorithm
,	O
to	O
obtain	O
interest	O
points	O
that	O
are	O
invariant	O
to	O
the	O
full	O
affine	O
group	O
,	O
including	O
scale	O
changes	O
.	O
</s>
<s>
Besides	O
the	O
commonly	O
used	O
multi-scale	O
Harris	O
operator	O
,	O
this	O
affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
can	O
also	O
be	O
applied	O
to	O
other	O
types	O
of	O
interest	O
point	O
operators	O
such	O
as	O
the	O
Laplacian/Difference	O
of	O
Gaussian	O
blob	O
operator	O
and	O
the	O
determinant	O
of	O
the	O
Hessian	O
(	O
)	O
.	O
</s>
<s>
Affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
can	O
also	O
be	O
used	O
for	O
affine	O
invariant	O
texture	O
recognition	O
and	O
affine	O
invariant	O
texture	O
segmentation	O
.	O
</s>
<s>
Closely	O
related	O
to	O
the	O
notion	O
of	O
affine	B-Algorithm
shape	I-Algorithm
adaptation	I-Algorithm
is	O
the	O
notion	O
of	O
affine	O
normalization	O
,	O
which	O
defines	O
an	O
affine	O
invariant	O
reference	O
frame''	O
as	O
further	O
described	O
in	O
Lindeberg	O
(	O
,,	O
:Appendix	O
I.3	O
)	O
,	O
such	O
that	O
any	O
image	O
measurement	O
performed	O
in	O
the	O
affine	O
invariant	O
reference	O
frame	O
is	O
affine	O
invariant	O
.	O
</s>
