Graphics Reference
In-Depth Information
λ
1
= 0.53,
λ
2
= 0.15
C = 0.06
λ
1
= 6.35,
λ
2
= 0.19
C = -0.50
λ
1
= 8.04,
λ
2
= 4.24
C = 28.1
λ
1
= 9.37,
λ
2
= 6.00
C = 46.8
80
80
80
80
60
60
60
60
40
40
40
40
20
20
20
20
0
0
0
0
0
v
0
u
0
0
0
0
0
v
v
u
v
u
0
u
Figure 4.2.
Top row: Candidate feature blocks from Figure
4.1
. Middle row: Harris matrix eigen-
values and Harris quality measure
C
with
k
= 0.04. Bottom row: Error surfaces
E
(
u
,
v
)
around
block center.
∂
I
∂
2
∂
I
∂
(
x
,
y
)
(
x
,
y
)
)
∂
I
∂
w
(
x
,
y
)
x
(
x
,
y
)
w
(
x
,
y
)
x
(
x
,
y
y
(
x
,
y
)
H
=
∂
I
∂
∂
I
∂
2
(4.3)
(
x
,
y
)
(
x
,
y
)
)
∂
I
∂
w
(
x
,
y
)
x
(
x
,
y
y
(
x
,
y
)
w
(
x
,
y
)
y
(
x
,
y
)
The eigenvalues and eigenvectors of the Harris matrix can be analyzed to assess
the cornerness of a block. Let these be
(λ
1
,
λ
)
and
(
e
1
,
e
2
)
respectively, with
λ
≥
λ
2
1
Consider the following cases, illustrated in Figure
4.2
:
1. The block is nearly-constant-intensity. In this case,
∂
I
∂
x
and
∂
I
y
will both be
∂
nearly zero for all pixels in the block. The surface
E
(
u
,
v
)
will be nearly flat and
0.
2. The block straddles a linear edge. In this case,
∂
I
∂
thus
λ
≈
λ
≈
1
2
x
and
∂
I
y
will both be nearly
∂
zero for pixels far fromthe edge, and the gradient
∂
I
will be perpendicular
∂
x
∂
I
∂
y
to the edge direction for pixels near the edge. Thus,
λ
1
will be a non-negligible
positive value, with
e
1
normal to the edge direction, while
λ
2
≈
0 with
e
2
along
(
)
the edge direction. The surface
E
u
,
v
will resemble a trough in the direction
of the edge.
3. The block contains a corner or blob. In this case, the surface
E
(
u
,
v
)
will resem-
ble a bowl, since any
(
u
,
v
)
motion generates a block that looks different than
the one in the center. Both
λ
1
and
λ
2
will be positive.
Consequently, we look for blocks where both eigenvalues are sufficiently large. How-
ever, to avoid explicitly computing the eigenvalues, Harris and Stephens proposed
2
This is also sometimes called the
second moment matrix
and is related to the image's local
autocorrelation.
3
Note that both eigenvalues are real and non-negative since the matrix is positive semidefinite.
