Graphics Reference
In-Depth Information
D
C
Figure 4.1.
Square blocks of
feature candi-
dates in an image.
A
B
diagonal directions. If the difference is high in all directions, the block is a good can-
didate to be a feature. Harris and Stephens [
186
] are widely credited with extending
can be derived as follows.
Let
w
(
x
,
y
)
be a binary indicator function that equals 1 for pixels
(
x
,
y
)
inside the
block under consideration and 0 otherwise. Then consider the function
E
that
corresponds to the sum of squared differences obtained by a small shift of the block
in the direction of the vector
(
u
,
v
)
(
)
u
,
v
:
2
E
(
u
,
v
)
=
w
(
x
,
y
)(
I
(
x
+
u
,
y
+
v
)
−
I
(
x
,
y
))
(4.1)
(
x
,
y
)
If we think of
I
(
x
,
y
)
as a continuous function and expand it in terms of a Taylor
series around
(
u
,
v
)
=
(
0, 0
)
, we obtain the approximation
I
2
u
∂
I
∂
v
∂
I
∂
E
(
u
,
v
)
=
w
(
x
,
y
)
(
x
,
y
)
+
x
(
x
,
y
)
+
y
(
x
,
y
)
−
I
(
x
,
y
)
(
x
,
y
)
u
∂
2
I
v
∂
I
=
w
(
x
,
y
)
x
(
x
,
y
)
+
y
(
x
,
y
)
∂
∂
(
x
,
y
)
u
2
∂
2
2
2
uv
∂
v
2
∂
I
∂
x
(
I
∂
x
(
)
∂
I
∂
y
(
I
∂
y
(
=
w
(
x
,
y
)
x
,
y
)
+
x
,
y
x
,
y
)
+
x
,
y
)
(
x
,
y
)
∂
2
∂
(
x
,
y
)
I
(
x
,
y
)
I
)
∂
I
u
v
u
v
w
(
x
,
y
)
x
(
x
,
y
)
w
(
x
,
y
)
x
(
x
,
y
y
(
x
,
y
)
∂
∂
∂
=
∂
∂
2
(
x
,
y
)
(
x
,
y
)
I
)
∂
I
I
w
(
x
,
y
)
x
(
x
,
y
y
(
x
,
y
)
w
(
x
,
y
)
y
(
x
,
y
)
∂
∂
∂
(4.2)
1
While Harris's name is now attached to the idea, other authors proposed very similar approaches
earlier, notably Förstner [
150
].
