<s>
An	O
image	B-Algorithm
gradient	I-Algorithm
is	O
a	O
directional	O
change	O
in	O
the	O
intensity	O
or	O
color	O
in	O
an	O
image	O
.	O
</s>
<s>
The	O
gradient	O
of	O
the	O
image	O
is	O
one	O
of	O
the	O
fundamental	O
building	O
blocks	O
in	O
image	B-Algorithm
processing	I-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
the	O
Canny	B-Algorithm
edge	I-Algorithm
detector	I-Algorithm
uses	O
image	B-Algorithm
gradient	I-Algorithm
for	O
edge	B-Algorithm
detection	I-Algorithm
.	O
</s>
<s>
In	O
graphics	B-Application
software	I-Application
for	O
digital	B-Application
image	I-Application
editing	I-Application
,	O
the	O
term	O
gradient	O
or	O
color	O
gradient	O
is	O
also	O
used	O
for	O
a	O
gradual	O
blend	O
of	O
color	O
which	O
can	O
be	O
considered	O
as	O
an	O
even	O
gradation	O
from	O
low	O
to	O
high	O
values	O
,	O
as	O
used	O
from	O
white	O
to	O
black	O
in	O
the	O
images	O
to	O
the	O
right	O
.	O
</s>
<s>
Mathematically	O
,	O
the	O
gradient	O
of	O
a	O
two-variable	O
function	O
(	O
here	O
the	O
image	O
intensity	O
function	O
)	O
at	O
each	O
image	O
point	O
is	O
a	O
2D	O
vector	O
with	O
the	O
components	O
given	O
by	O
the	O
derivatives	B-Algorithm
in	O
the	O
horizontal	O
and	O
vertical	O
directions	O
.	O
</s>
<s>
Since	O
the	O
intensity	O
function	O
of	O
a	O
digital	O
image	O
is	O
only	O
known	O
at	O
discrete	O
points	O
,	O
derivatives	B-Algorithm
of	O
this	O
function	O
cannot	O
be	O
defined	O
unless	O
we	O
assume	O
that	O
there	O
is	O
an	O
underlying	O
continuous	O
intensity	O
function	O
which	O
has	O
been	O
sampled	O
at	O
the	O
image	O
points	O
.	O
</s>
<s>
With	O
some	O
additional	O
assumptions	O
,	O
the	O
derivative	B-Algorithm
of	O
the	O
continuous	O
intensity	O
function	O
can	O
be	O
computed	O
as	O
a	O
function	O
on	O
the	O
sampled	O
intensity	O
function	O
,	O
i.e.	O
,	O
the	O
digital	O
image	O
.	O
</s>
<s>
Approximations	O
of	O
these	O
derivative	B-Algorithm
functions	O
can	O
be	O
defined	O
at	O
varying	O
degrees	O
of	O
accuracy	O
.	O
</s>
<s>
The	O
most	O
common	O
way	O
to	O
approximate	O
the	O
image	B-Algorithm
gradient	I-Algorithm
is	O
to	O
convolve	B-Language
an	O
image	O
with	O
a	O
kernel	O
,	O
such	O
as	O
the	O
Sobel	B-Algorithm
operator	I-Algorithm
or	O
Prewitt	B-Algorithm
operator	I-Algorithm
.	O
</s>
<s>
Image	B-Algorithm
gradients	I-Algorithm
are	O
often	O
utilized	O
in	O
maps	O
and	O
other	O
visual	O
representations	O
of	O
data	O
in	O
order	O
to	O
convey	O
additional	O
information	O
.	O
</s>
<s>
GIS	B-Application
tools	O
use	O
color	O
progressions	O
to	O
indicate	O
elevation	O
and	O
population	O
density	O
,	O
among	O
others	O
.	O
</s>
<s>
Image	B-Algorithm
gradients	I-Algorithm
can	O
be	O
used	O
to	O
extract	O
information	O
from	O
images	O
.	O
</s>
<s>
Gradient	O
images	O
are	O
created	O
from	O
the	O
original	O
image	O
(	O
generally	O
by	O
convolving	O
with	O
a	O
filter	O
,	O
one	O
of	O
the	O
simplest	O
being	O
the	O
Sobel	B-Algorithm
filter	I-Algorithm
)	O
for	O
this	O
purpose	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
common	O
uses	O
is	O
in	O
edge	B-Algorithm
detection	I-Algorithm
.	O
</s>
<s>
One	O
example	O
of	O
an	O
edge	B-Algorithm
detection	I-Algorithm
algorithm	O
that	O
uses	O
gradients	O
is	O
the	O
Canny	B-Algorithm
edge	I-Algorithm
detector	I-Algorithm
.	O
</s>
<s>
Image	B-Algorithm
gradients	I-Algorithm
can	O
also	O
be	O
used	O
for	O
robust	O
feature	O
and	O
texture	O
matching	O
.	O
</s>
<s>
is	O
the	O
derivative	B-Algorithm
with	O
respect	O
to	O
y	O
(	O
gradient	O
in	O
the	O
y	O
direction	O
)	O
.	O
</s>
<s>
The	O
derivative	B-Algorithm
of	O
an	O
image	O
can	O
be	O
approximated	O
by	O
finite	B-Algorithm
differences	I-Algorithm
.	O
</s>
<s>
If	O
central	B-Algorithm
difference	I-Algorithm
is	O
used	O
,	O
to	O
calculate	O
we	O
can	O
apply	O
a	O
1-dimensional	O
filter	O
to	O
the	O
image	O
by	O
convolution	B-Language
:	O
</s>
<s>
where	O
denotes	O
the	O
1-dimensional	O
convolution	B-Language
operation	O
.	O
</s>
