Image Processing Reference
In-Depth Information
considering changes along a particular direction in the image
P
itself. This is the basic idea
of
Moravec's corner
detection operator. This operator computes the average change in
image intensity when a window is shifted in several directions. That is, for a pixel with co-
ordinates, (
x
,
y
), and a window size of 2
w
+ 1 we have that
w
w
2
E
(
xy
, ) =
[
P
-
P
]
(4.53)
u
,
v
xiy j
+, +
x i uy j
+ + , + +
v
i
=-
w
j
=-
w
(a)
κ
ϕ
(b)
-ϕ
(c)
κ
⊥ ϕ
(d)
-⊥ ϕ
Figure 4.34
Comparing image curvature detection operators
This equation approximates the
autocorrelation
function in the direction (
u
,
v
). A measure
of curvature is given by the minimum value of
E
u
,
v
(
x
,
y
) obtained by considering the shifts
(
u
,
v
) in the four main directions. That is, by (1, 0), (1, 1), (0, 1) and (-1, -1). The minimum
is chosen because it agrees with the following two observations. First, if the pixel is in an
edge defining a straight line, then
E
u
,
v
(
x
,
y
) is small for a shift along the edge and large for
a shift perpendicular to the edge. In this case, we should choose the small value since the
curvature of the edge is small. Secondly, if the edge defines a corner, then all the shifts
produce a large value. Thus, if we also chose the minimum, then this value indicates high
curvature. The main problem with this approach is that it considers only a small set of
possible shifts. This problem is solved in the
Harris
corner detector
(Harris, 1988) by
