Image Processing Reference
In-Depth Information
N
=1
(
f
- ( +
a
bx
+
cy
+
dx y
))
y
= 0
(9.33)
i
i
i
i
i
i
i
and
N
=1
(
f
- ( +
a
bx
+
cy
+
dx y
))
x y
= 0
(9.34)
i
i
i
i
i
i
i
i
N
Σ
i
since
=1
=
aNa
Equation 9.31 can be reformulated as:
N
N
N
N
f
-
abxcydxy
-
-
-
= 0
(9.35)
i
i
i
ii
i
=1
i
=1
i
=1
i
=1
and Equations 9.32, 9.33 and 9.34 can be reformulated likewise. By expressing the
simultaneous equations in matrix form,
N
N
N
N
a
N
x
y
x y
f
i
i
ii
i
i
=1
i
=1
i
=1
i
=1
N
N
N
N
N
b
x
()
x
2
x y
()
x
2
y
fx
i
i
ii
i
i
ii
i
=1
i
=1
i
=1
i
=1
i
=1
=
(9.36)
N
N
N
N
N
2
2
c
y
x y
()
y
x
()
y
ffy
i
ii
i
i
i
ii
i
=1
i
=1
i
=1
i
=1
i
=1
N
N
N
N
N
2
2
2
2
d
xy
()
xy
xy
()
()()
x y
=1
fxy
i
i
i
i
i
i
i
i
iii
i
=1
i
=1
i
=1
i
=1
i
and this is the same form as Equation 9.22 and can be solved by inversion, as in Equation
9.23. Note that the matrix is
symmetric
and its inversion, or solution, does not impose such
a great computational penalty as appears. Given a set of data points, the values need to be
entered in the summations, thus completing the matrices from which the solution is found.
This technique can replace the one used in the zero-crossing detector within the Marr-
Hildreth edge detection operator (Section 4.3.3), but appeared to offer no significant advantage
over the (much simpler) function implemented there.
9.3
Appendix 3: Example Mathcad worksheet for Chapter 3
The appearance of the worksheets actually depends on the configuration of your system
and of the Mathcad set-up. To show you how they should look, here's a typeset version of
the shortest worksheet. Note that the real worksheet's appearance will depend largely on
your machine's setup.
Chapter 3 Basic Image Processing Operations: Chapter 3. MCD Written by: Mark S.
Nixon, 10/11/95, Last Revision: 7 August 1997
This worksheet is the companion to Chapter 3 and implements the basic image processing
operations described therein. The worksheet follows the text directly and allows you to
process the eye image.
This chapter concerns basic image operations, essentially those which alter a pixel's
value
in a chosen way. We might want to make an image
brighter
(if it is too dark), or to
remove contamination by
noise
. For these, we would need to make the pixel values
larger
(in some controlled way) or to change the pixel's value if we suspect it to be wrong,
respectively. Let's start with images of pixels, by reading in the image of a human eye.
