CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
IMAGE ENHANCEMENT AND CORRELATION
USING MICROPROCESSORS
A graduate project submitted in partial satisfaction of
the requirements for the degree of Master of Science in
Engineering
by
Morteza Abedini Khorrami
June, 1981
Khorrami is approved:
irman)
California State University, Northridge
Table of Contents
Abstract .
i
Introduction .
ii
Chapter 1
1.1
Geometric and Intensity
Transformation .
1
1.2
Intensity Transformation .
7
1.3
Intensity Transformation by
Karhunen-Loeve Transform .
9
Chapter 2.
Digitizinq a Picture . . .
13
Chapter 3.
Filtering the Picture Array
23
Appendix.
Image Matching by Correlation with a
Microprocessor Development System
27
Bibliography
34
List of Figures
Page
Figure 1.1
8
Figure 1.2
12
Figure 2.1
15
Figure 2.2
16
Figure 2.3
17
Figure 2.4
20
Figure 2.5
20
Figure 2.6
21
Figure 3.1
23
Figure 3.2
24
Figure 3.3
24
ABSTRACT
Imag~
Enhancement and Correlation
Using Microprocessor
by
Morteza A. Khorrami
Master of Science in Engineering
Scene matching refers to the ability to locate or
match a region of a picture with the corresponding region
of another view of the scene often taken with a different
sensor.
In this project the involving problems have been
discussed and with microprocessor's help the filtered
picture has been obtained.
The digitized picture and a
digital low-pass filter are being used in order to get
the gradient picture.
i
Introduction
Analyzing an image of the earth which has been taken
by high and low altitude aircraft is a need today.
This
image information has been used for several purposes such
as geographic and topographic map matching, navigational
guidance, natural resource analysis, weather prediction and
environmental studies.
Scene matching is a common problem
that arises in these applications.
Scene matching refers
to the ability to locate or match a region of a picture
with the corresponding region of another view of the scene
often taken with a different sensor.
The problem of
matching two images of the same scene taken by different
sensors under different viewing geometries is a challenging
problem in the field of image processing and pattern
recognition.
The scenes are usually transformed so
drastically by the different viewing geometries and sensor
characteristics that it is extremely difficult, if not
impossible, to match the original images without the proper
data processing.
Geometric transformation must be performed
on the images to bring the matching elements into one to
one correspondence.
Because of the differences in operating
characteristics of the different sensors, scenes of the same
object taken by different sensors will have a different
intensity value.
The most prominant difference is that an
optical scene is positive \vhile that of a radar scene is
ii
negative.
Therefore, an intensity transformation must be
performed on one scene to match the intensity values of the
other as closely as possible.
The methods vJhich have been used for map matching
include photographic, optical and analog and digital optical
techniques.
The modern trend is definitely toward digital
methods because of increased versatility and robustness, and
economic feasibility.
The standard digital approach is
called the correlation detector.
Scene matching by a
correlation detector is very costly in computation.
A
match is determined by selecting the position of maximum
cross correlation between a window and each possible shift
position of the search region.
For a window of size
~~!.11
')
and a search region size NXN, there are (N-H+l)"" possible
test locations.
For image enhancement and correlation using
microprocessors, first of all each picture is stored in the
memory of the microprocessors as an array of (i.g.) 64 X 64
words each 8 bits long.
Also three dimensional low-pass
filtering is performed through the picture.
filtering has the effect of noise smoothing.
Low-pass
Experiments
performed on edge extraction indicated that considerably
better edge picture is obtained from the lower resolution
picture than that obtained from the high resolution picture.
Since this project is a small part of picture processing,
chapters 1 and 2 are devoted to some definitions and
procedures that provide some background for this subject.
lll
Chapter 1
1.1
GEOMETRIC AND INTENSITY TRANSFORMATION
This chapter involves matching of the two images of
the same scene usually taken by different sensors under
different geometries.
Geometric transformation must be
performed on the images in order to bring the matching
elements into one to one correspondence.
Also scenes taken
by different sensors from the same object have different
intensity, and the most significant difference is between
the optical scene and the radar scene.
An optical scene is
positive while the radar scene is negative.
Thus, an
intensity transformation has to be performed to get the
closest match on the intensity values of the optical and
radar scene.
There are two different methods of geometric
transformation which are the perspective and polynomial.
Perspective transformation requires tracking data to
determine .the positions of sensors at the exposure.
Also
needed are the angles of rotations of one sensor with
respect to the other.
Furthermore, in the polynomial method,
the data needed for the transformation are entirely
contained in the images.
In order to get the coefficients
of the polynomial, prominent features that appear in both
images have to be selected.
The research and experimental
work in determining the relative position and orientations
of one sensor with respect to the other, based on
1
2
information derived from a set of images is described, and
mathematical foundation and theoretical analyses are
presented below.
A geometric rotation of the axes in three
dimensions is required to determine the orientations of one
image with respect to another.
The following relations can
fully express this rotation:
X
=
y
z
X
*
mll
ml2
ml3
m21
m22
m23
y*
m3l
m32
m33
z*
( l.l)
where
x,y,z
Image coordinates of the object
z
=
Focal length
x * ,y * ,z *
=
Another coordinate which may be parallel
to the ground coordinate x,y,z
m .. = Element of the rotational matrix and is
lJ
a function of the three angles of
rotation W,<P,K
Let
x0 , Y0 , z 0
be the sensor position, and
Xj' Yj' zj
be the coordinates of the image conjugate with respect to
the ground coordinates X, Y,
z.
Using the relationship of
similar triangles!
=
X. - xo
J
z. - zo
J
~=
Y. - Yo
J
z. - zo
J
X*
~
z
y
z
*
( l. 2)
3
and from there
X*
=
(X. - x )z *
0
J
z. - zo
( 1. 3)
(Y. - Y )z *
0
J
z. - zo
( 1. 4)
( z . - z )z *
0
z. - zo
J
( 1. 5)
J
y
* =
J
z* =
and with combinations of equations (1.1), 1. 3) ' 1.5)
X
=
X
=
m11x
* +
m12Y
* +
m13z *
y
=
m21x
* +
m22Y
* +
m23z *
z
=
m31x
* +
m32Y * + m33z *
[m11 (Xj - xo) + m12 (Yj. - y 0) + m13 (Zj
(Z. - zo)
-
zo)
Jz *
J
y
=
*
[m21 (Xj - xo) + m22(Yj - y 0 ) + m23(Zj - zo )] z
(Z. - z )
J
z
=
0
[m31 (Xj - xo) + m32 (Y j - Yo) + m33(Zj
( z . - zo)
-
zo)
Jz *
J
X
-
z
y
z
=
(X. - Xo)m11 + (Y. - Yo)m12 + ( z . - 2 o)m13
J
J
J
(X. - Xo)m31 + (Y. - Y0) m32 + ( z . - 2 o)m33
J
J
J
( 1. 6)
=
(X. - Xo)m21 + (Y. - Yo)m22 + ( z . - 2 o)m23
J
J
J
(X. - XO) m31 + (Y. - Yo)m32 + ( z . - zo)m33
J
( 1. 7)
Equations
notation
J
(1.6) and (1.7)
J
can be expressed in determinant
4
X
M X
1
M:X
y
z
M X
2
M X
3
I
=
0
( l. 8)
=
0
( l. 9)
where
X
X
=
y
-
xo
y .·
0
M.
l
=
(mil' mi2' mi3)
z - zo
Given the coordinates of the images and their conjugate
and the focal length, equations
to solve the six unknowns.
(1.6) and
(1.7) can be used
The unknowns are the coordinates
of the sensor positions x , Y , z
and the three angles of
0
0
0
rotation W,¢, K.
To solve these parameters, approximate
values are assumed for these variables and corrections to
the approximations are determined.
For example, let the
' ' ' l approx1mat1on
..
b e W0 , <I> 0 , K0 , x 0 , Y 0 , z 0 and the
1n1t1a
0
0
0
changes in the approximate values be da, de, dB, dx , dY ,·
0
0
and dz .
0
Furthermore, let F be error as a result of the
approximation.
Equation (1.8) then becomes
X
z
( l. 10)
differentiating F with respect to the unknown parameters:
dF
=
()F
()F
ClF
ClF
aw dw + -()¢ d<P + ClK dK + ax
()F
()F
dX
0
0
+
()F
ClF
+ az dz 0 + dX dX + ay dy + az dz
0
ClF
dY
0
ayo
(1.11)
5
or
( 1. 12)
A similar equation can be derived from equation (1.9) as
follows:
dy
=
bl + b 21 dW + b 22
d~
+ b 23 dK - b 24 dX 0
(1.13)
- b24 dYO - b26 ZO + b24 Xj + b25 yj + b26 dZj
The coefficients of equations (1.12) and 1.13) can be
expressed as below:
z
X
y
z
X
z
z
X
z
z
X
z
z
( 1.14)
X
z
y
z
X
z
y
z
6
z
X
=
bl6
b26
ml3
m33
y
z
m23
m33
=
For a rotation of Trv, <P, K
mll
=
cos <P
cos K
ml2
=
cos w sin K + sin
ml3
=
sin w sin K - cos w sin <P cos K
m21
=
-cos <P sin K
m22
=
cos w cos K - sin w sin <P sin K
m23
=
sin w cos K + cos
m31
=
sin <P
vl sin
vl sin
<P cos K
<P sin K
m32 = - sin w cos <P
m33 = cos w cos <P
()M
aw
aM
a<~>
=
=
0
-ml3
ml2
0
-m23
m22
0
-m33
m32
-sin <P cos K
sin w cos <P cos K
-cos w cos ¢
cos K
sin <P sin K
-sin w cos <P sin K
cos w cos ¢
sin K
sin w sin <P
cos <P
m21
m22
m23
ClM = -mll
ClK
-ml2
-ml3
0
0
0
-cos w sin cp
7
aM
aw 3
=
(0, -m33' m32)
(0, -cos
=
w cos
¢, -sin
w cos¢)
Similar expressions can be obtained for the other terms.
Computations begin by assuming the six unknowns W, ¢, K,
x0 ,
Y , z and solving for the six corrections dW, d ¢ , dK, dX ,
0
0
0
dY , dz .
0
0
The iterations continue until the residual error
dF is smaller than a pre-specified value.
l. 2
INTENSITY TRANSI'OR..'IvJATION
Scenes of the same object which have been taken by
different sensors have a different intensity value
because of the differences in operating characteristics of
the different sensors.
The most significant difference is
an optical scene is positive but a radar scene is negative.
Prior to scene matching, an intensity transformation must
be made on one scene to match the intensity values of the
other as closely as possible.
A new intensity matching
technique is based on the Karhunen-Loeve transfbrmation.
In this method first of all the negative radar image is
transformed into a positive image.
This can be done by
simply replacing the amplitude of each picture element
(Pe). . .
(Pe) .. by its complement value
lJ
For a digitized
l]
image with n bits
--
(Pe) ..
l]
=
2
n
-
(Pe) ..
-1
l]
where n is the number of quantization level.
(1.15)
8
•.-.
...
:
·..
-
- ....
~
.
. ..
': _: -: ·. · .'·, ·.
' .\
i .
'
.
-
,:
.'
.
l.l(a)
l.l(c)
Original radar
Geometric
corrected optical
t-~.
••
-
l.l(b)
l.l(d)
..
"
- .'
. . .. .
. ~
") '
.
',
.
'
~-
~
.·•
..
i \
;..
~~- -
~
'
~
. ·.•
I
{
t
'
.
.· .. •' -,.,..-._
;-
... ·, • . •. f
.
.
'
-~r-- .J ~--.\.
•
l
.....;
,6
.
~ ·,
)
.
,,,r'
I
.
I
r~
Intensity reversed
Intensity transformation (Karhunen-Loeve
Transform)
9
Figure l.l(a) shows the original radar image.
An
intensity reversal was performed on this image by applying
the equation (1.15)
in order to get the figure l.l(b).
It
can be seen that the contrast of the image is low, and
intensity modification is required to match as closely as
possible the intensity values of the optical image shown in
figure 1.1 (c) .
1.3
INTENSITY
TRANSFOR~~TION
BY KARHUNEN-LOEVE TRANSFORM
Let's assume that R is the radar image of size
and 0 is the optical image of size MXM.
MX~1
Let R and 0 be
scanned row-by-row such that:
R = Radar Image
and
0 = Optical Image
=
(01,
•••
I
0 MXM )
Each of window pair (rK, OK), 1
2
........K ~ M , is examined.
~
-..;::
Assuming thar rK has the quantization level y , OK has a
1
quantization level of y , and n is the number of bits used
2
in the quantization, an intensity pairing function
f(y 1 , Y2 ) 0 ~y 1 , y 2 .:::;2n- 1 is incremented by one.
f(y 1 , y 2 ) for y 1 = y 2 takes the value of the numbers of
window pairs which are matched in intensity and f(y , y )
2
1
for y
1
t
y
2
takes the value of the numbers of window pairs
that are mismatched in intensity.
If R and 0 were identical:
10
0
M(y , y )is the number of window pairs with intensity y in
1
1
2
R and Y in 0.
2
A covariance matrix L
can be formed to indicate the
y
relative correlation between the two images:
L
where
y
= E[(Y- My ) (Y- My )T]
denotes expected value
E[
=
[:: l
M =
y
[:::l
y
M
= expected values of y 1
yl
M
= expected values of y 2
y2
Karhunen-Loeve transform can then be performed to obtain a
new set of coordinates ¢ 1 and ¢ as follows:
2
LA
=
¢ L ¢T
=
A
y
and
A= Diagonal matrix with the eigenvalues A· of
l
L
y
as the diagonal elements, i = 1,2.
11
¢ = matrix whose columns are the ordered
eigenvectors of L
- ¢_
y
= ¢1, ¢2~-for ~\y2: .\2
The transformed coordinates ¢
1
and ¢
2
are as shown in the
and ¢ , intensity correlations can
2
1
now be made by scaling the intensity profile of the radar
figure 1.2.
Based on ¢
image such that the resulting coordinates ¢ '
1
orthogonal and the angle between ¢ '
1
is approximately 45 degrees.
and ¢ '
2
and ¢ '
2
and the x
are
1
axis
Figure l.l(d) shows the image resulting from the
application of the intensity transformation.
Considerable
details which are not visible in the original radar image
have been made visible by the intensity transformation.
There are some other methods for intensity transformation
which are not discussed in this project.
12
y
</>
(optical)
2
I
</>
2
</>
I
l
""' corrected
intensity
2
y
1
(radar)
I
I
I
I
...... .......
I
I
I
I
Figure 1.2
I
Intensity coordinate transformation
13
Chapter 2
DIGITIZING A PICTURE
To analyze an ordinary picture using a digital computer
requires some kind of representation in order to make a
suitable picture for the machine.
For a black and white
picture, which is what we are concerned about, simply black
and white can be realized as a real valued function of two
variables.
A picture that occupies a plane with coordinates
x and y can be defined as a picture function f
(x, y) , which
is proportional to the light intensity at the point (x, y)
on the picture.
The intensity of a picture at a point is
also called the gray level or the brightness.
From a
mathematical point of view, a picture could be defined by
specifying its picture function.
Furthermore, considering
pictures as functions, any means for representing a function
in a digital computer can be used to represent a picture.
For example, polynomials are usually represented by storing
their coefficients, but not all interesting picture
functions have low degree polynomials.
Generally, a picture
function merely has a simple analytic form; therefore, its
representation is usually accomplished by sampling the
picture function at a discrete number of points in the x-y
plane and storing the sample values.
The process is
called sampling or measuring at discrete point.
To
define a quantization procedure we have to specify where
14
the samples are to be taken.
The simplest specification is
to partition the picture plane by a quadruled grid and to
sample the picture function at the center of each cell.
In
general, the picture function can assume any value between
some minimum (black) and maximum (white), while the digital
computer can represent only a finite number of values.
Therefore, we have to partition the range of amplitudes of
the picture function into a finite number of cells.
By
doing this we have specified an algorithm for representing
the original picture function as an array of integers where
each element of the array specifies the approximate gray
level of the picture in the corresponding cell.
Partition-
ing the gray scale into a set of discrete cells can be done
by simply dividing the range of picture intensities, from
black to white, into uniform intervals.
To do this, we
have only to specify the number of cells, or, in other words,
the fineness of the partition.
Sometimes we are not
constrained to make the quantization cells uniform in size,
and the main reason is if we have a nonuniform picture that
most of the detail in the picture occurred in the dark
regions.
If we were constrained to use at most a given
number of cells, it would make sense to quantize nonuniformly.
We could quantize the dark portion of the gray
scale into relatively fine cells, and quantize the light
portion of the gray scale into relatively coarse ones.
~lso,
we
mig~1·t
if we have no prior
kno~ledge
about the picture,
taJ:e as our c;uide the construc·tion of
eye-brain combination,
\';J~'licll.
seems to be
logarithmic in its response to liaht.
·t~J.e
:::lUr:;an
a?~1roxir.:-~a·tely
This nhenomenon
suggests that we first take the logarithn of the nicture
function and quantize log f(x,y)
uniformly.
For convenience,
a picture can be represented by an ordinary :::;-\aJcrix whose
real entries define the (approxinate)values of the picture
function in the corresponding region of the picture plane.
When we speak of f as a digital picture function the (i,j)
then is called the element of this matrix f(i,j).
The
unquantized picture 2unction f(x,y) will be referred to as
the analog picture function.
Also, the low and high values
:':'.,igure 2.1
1 r
..Lei
?ic:ure :2.2
of the quantized ?icture function nean, res9ectively , dark
a n d li g ht levels of intensity .
discussed,
As an e x a mDle of what we
let's consider f igures 2 .1 and 2.2.
Figure 2.1
shows a simple three - dimensional scene containing elesentar:;r
geometrical objects.
The p icture was
from an ordinary television n onitor.
photogra~hed
Figure 2.2 shows a
q uantized re p resentation of ficrure 2.1 .
.:."":. a uadruled
q uantization grid with 1 2 0 cells on a side have
here and have quantized the qray scale into 16
s 1.;aced levels.
a
~) recess
of
The p rocess of scene
sim:~ lification--a.
a~al y sis
~een
used
unifor~ l y
is generall y
con?lica·ted obj ec·::, t h e
original picture, is converted i n to a
sequence of steps.
directly
si ~, ler
fo r~
by some
I n sucl-: a sequen ce, o ::e natur al s ·t.ep is
to convert the q i v en nict ure i :1to a :1 out 2.i ne d :;:-a-;,"i :-:g .
7his
17
step would hopefully preserve the important features of the
original picture, but would reduce the computational
requirements imposed on subsequent steps.
As experiments
have shown, human beings concentrate most of their attention
on the borders between more or less homogeneous regions.
In
reducing a picture to a line drawing, obviously there are
certain hazards.
The reduced picture generally contains
less information than the original, and there is no guarantee that the lost information is irrelevant.
However, in
some circumstances the reduction of a picture to an outline
drawing is useful.
An outline drawing of a picture can be
produced by emphasizing regions containing abrupt dark-light
transitions, and de-emphasizing regions of approximately
homogeneous intensity.
In other words, the outlines are
edges, and edges are by definition transitions between two
markedly dissimilar intensities.
In terms of the picture
function, an edge is a region of the x-y plane, where f(x,y)
Figure 2.3
18
has a gradient with a large magnitude.
To produce an
outline drawing the requirement would_be estimating the
magnitude of the gradient of the function.
The gradient
can be estimated if the directional derivatives of the
function along any two orthogonal directions are known. Now
the only step would be selection of a pair of orthogonal
directions and an approximation to a (one-dimensional)
derivative in order to have the essential ingredients of an
algorithm for producing outline drawings.
As an example,
let's approximate the magnitude of the gradient at picture
point (i,j) by
IV'f(i,j)l
~
R(i,j)
=
V[f(i,j) - f(i+l, j+l) ]
+ [f(i,j+l) - f(i+l,j)]
2
2
diagrammatically, at cell (i,j) a 2x2 window could be
considered whose diagonal elements are associated by
subtraction:
i,j
i+l,j
/
' ""'
/
i 'j+l
i+l,j+l·
The directional derivative in each direction is approximated
by simply subtracting adjacent elements.
The operator
(R(i,j) is sometimes called the Roberts cross operator.
the point (i,j) is in a region of uniform intensityi the
value of R(i,j) is zero.
If there is a discontinuity in
intensity between column j and column (j+l), then R(i,j)
If
19
has a large value, and similarly if there is a discontinuity
between row i and row (i+l).
The Roberts cross operator is
often simplified for computational efficiency by using
absolute magnitudes rather than squares and square roots.
Thus G(i,j) by definition would be
G(i,j) = lf(i,j) - f(i+l, j+l)j +jf(i,j+l) - f(i+l,j)l
Obviously, R(i,j) ~ G(i,j) ~
/2
R(i,j) and G(i,j)
behaves qualitatively very much like R(i,j).
In figure 2.3 it is shown that the result of applying
G to the digital picture of figure 2.2 and displaying the
(i,j) cell if G(i,j)
>
2.
The most obvious shortcoming is
that the back edge of the wedge has been lost, but there is
only one gray level difference between the intensities on
each side of the lost line.
If such a difference were
considered significant and the threshold of 2 lowered, we
would discover unacceptably large numbers of "spurious"
lines in the floor and wall.
The picture shown in figure
2.3 is usually called a gradient picture.
The process of
obtaining the gradient picture is variously known as
spatial differentiation, edge enhancement, sharpening or
simply taking the gradients.
gradient picture.
Figure 2.3 shows a threshold
Since thresholding a gradient picture is
fairly common, the unthresholded gradient picture is loosely
called the analog gradient picture.
Because of the
existence of noise there is a difficulty for taking the
20
gradient.
In the language of communication theory, it could
be said that the digital picture function f(i,j)
of two picture functions:
is the sum
an "ideal" picture, or signal,
s(i,j) and a pure noise picture n(i,j).
The only problem
that comes up is that we really want to estimate the
gradient not of f but of the ideal picture s.
To illustrate
this for simplicity let us consider the one-dimensional and
analog case.
In figure 2.4 it has been shown a
one-
dimensional ideal picture function s(x) that undergoes an
It could be interabrupt change in the vicinity of x .
0
preted that a one-dimensional picture could be the intensity
s (x)
XQ
Figure 2.4.
X
An idealized edge
f (x)
X
Figure 2.5.
An actual edge
21
function of the two-dimensional picture along some oneNow the f(x) = s(x)
dimensional cut in the picture plane.
+ n(x)
is available (figure 2.5).
The reasonable procedure for estimating the location
of x
0
from f(x)' is some kind of averaging.
For this the
function f should be smoothed enough to average out the
worst of the noise, but not smoothed so much that it causes
the jump in s to get blurred completely.
estimation operator
D(X)
=
D(X)
x+wl
l
)
A derivative
might be defined by
l
f(u)du - -w2
X
fx-w
f(u)du
2
As shown in figure 2.6, this operator places windows
of length w
2
and w just before and after x, averages the
1
function f over each of these windows, and takes the
I
difference of the averages.
Similarly, the estimation of
the gradient in the two-dimensional case requires some
f (x)
X
Figure 2.6.
X
Averaging windows
22
combination of averaging and differencing.
This fact has
led to the development of a number of gradient estimators
using windows of various sizes.
23
Chapter 3
FILTERING THE PICTURE ARRAY
The process of obtaining the gradient picture is
called edge enhancement or simply taking the gradient.
Filtering a picture using a low-pass filter implies that a
low-pass filter attenuates high spatial frequencies and
passes low spatial frequencies.
High spatial frequencies
are introduced by the occurrence of sharp edges in the
original picture and low-pass filtering is to remove the
In a complementary fashion, a high-pass
sharp edges.
spatial filter attenuates low frequencies and passes high
frequencies.
Since high spatial frequencies correspond to
Figure 3.1
sharp edges, high-pass filtering enhances edges.
represents some digital low-pass filters.
1
I6
1
9
u
2
[~
1
4
2
1
1
~]
1
10
~]
4
1
[~
~]
1
2
1
[
:]
Figure 3.1
The coefficients of the filters are to normalize the filters
to unit weighting so that the low-pass filtering process
does not generate a brightness bias in the processed image.
24
In the field of pattern recognition the whole idea of
this process is to match the optical images with the radar
images.
The standard digital
approach
of
scene
matching is called the correlation detector and is very
costly in computation.s.
A match is determined by select-
ing the position of maximum cross-correlation between a
window and each possible shift position of the search
region.
=
(m,n)
(1,1)~~·~-----.~(m,n)
= (l,N)
(m,n)
Figure 3.2.
S (m1,n)
=
=
M,l)
----~~
reference scene
(m,n)
= M,N)
Scene Reference
Intensity of picture element at
(m~,,n)
= 0 to 255 for 8-bit quantization
=
(i,j)
(l,l)~~~~~~(i,j)
= (I,l)
~
------ reference window
w
= (l,J)
(i,j)
Figure 3.3.
(i,j)
= (I,J)
Window Reference
Obviously the reference window is smaller than the
reference scene.
W(i,j) = Intensity of picture element at (i,j) in w
25
J
I
2
2 i=l
R(m,n) =
S(m+i-1, n+j-1) W(i,j)
j=l
vvhere
R(m,n) = correlation
and
S(m+i-1, n+j-1) = Intensity of picture element at
(m+i-1, n+j-1)
And
R(x,y) = max[R(m,n)]
'if;m,n
Declares (x,y) is the best match location.
Also the cross-correlation could be defined as the
J
RN
(m,n)
=
I
2 .2 S(m+i-1, n+j-1) w(i,j)
S (m+i-1, n+j-1)
2
i=l
l=l
I
2
X
] l/2
l
I
i~l
2
] l/2
w (i' j)
The perfect matching gives a value of (l)
for cross-
correlation and a value of (0) simply means no match at all.
Now for a low-pass filter
1/9
[~ ~
n
and a picture array of 64 x 64 using the microprocessor
6502, the following program has been written.
This program
26
simply tells that first we call the nine locations from the
memory and then multiply them by the digital filter element
by element, then call the division subroutine in order to
divide the sum by 9 and put the result back into the first
location.
The formula which is used for nine different
locations of array is
[
N
N+l
N+64
N+65
N+2
N+66
N+l29
N+l30
N+l28
J
and for simplicity the picture array contains only l's and
O's.
For a more developed system,parallel multi-processing
procedure could be used.
The following example is to
accomplish the above single processor low-pass filtering
and the decimal point on the output array was disregarded.
The asterisk (*) means 1, and in addition to the program
the input and output (result)
on the print-out paper.
array plus filter is included
Iraage ~1aJcching by Correla:tion >;,;Ji e1 a
I1icroprocessor Develo;11T1.ent. Sys-tem
5
PRI'\lT
CHR$ <4); "BLOAD TE:1P.
-
OBJ~"
10
HOME
20 ADDR = 8192
100 ~OR I = 0 TO 4224 STEP 54
~:~2
~RIN7
!1~
~DKE
:
+
F'O~
....
'-MO.
_·(.;
:
~DDR
+
I, 1: ~OKE ADDR + : + 1,1: POKE ADDR
qooR + : ~52,:: POKE ADD?+ I •
5!, 1:
~OK~
.J
~C
\:=:XT
;"iiNI
-
Sl2):
~c~<C:
ADDR
CHR$ !4); ""R#l":
-J..:
:oq:NT
+
.;1
.~..Jt
.~ND
CHR$
21~
C27); ~HR$ (56)
PRINT "FE. TER: ": ?RINT : ?RINT "1 1 1": PRINT
CALL 4095
220
PRINT: PRINT
~
!
+ 2,1:
~OKE
ADDR +
6~.:
(:)
2):
--";:=-y:
CHR$
'29):
0
~HR$
2(1)2
CHR$ (4);"PR#0"
PRINT
11<1
J.
"'
..:.
...
RINT
28
7EMP
NEXT CBJEC7 FILE NAME
SOURCE F:!....E:
:
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$10!2!0
EQU $FDED
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14 **********
.. ..; NSTARTL EQU $1Z)I2)
16 NSTARTH EQU $20
17 **********
18 ROWCOUNT EQU $02
19 NBRROWS EQU 64
20 **********
21 COLUMNCOUNT EQU $03
22 NBRCOLUMNS EQU 62
iZlli'JIZIIZl:
1~
....
1000:
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12l021Zl:
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**********
24 OFFSET EQU
25 **********
26
JSR
27 ******"'"'"'*
LDA
28
STA
29
LDA
30
31
STA
..,..., ..............................
LDA
33
STA
34
35 "'"'**"'"'*"'**
36 NEXT ROW LDA
STA
37
38 SAME ROW LDY
LDA
39
40
LDY
41
CLC
ADC
42
LDY
43
44
CLC
45
ADC
46
LDY
47
CLC
48
ADC
49
LDY
CLC
50
ADC
51
52
LDY
CLC
53
54
ADC
55
LDY
56
CLC
ADC
57
02
PRINT
*+NSTARTL
MATRIX
*+NSTARTH
MATRIX+!
·.J~
121121
02
121121
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00
1211Zl
1211
121121
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<MATRIX),Y
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#F4
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#F5
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#F6
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29
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ss
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1 03F: A0
112141:91
1043:E6
1045:00
1047:£6
1049:E6
104B:A5
104D:C9
104F:F0
1051 :4C
"""
2)0
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51
52
00
00
00
1210
63
54
55
56
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112179:A9
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111181:1219
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1089:2121
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111195:E6
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111199:A5
11119B:C9
11219D:F0
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74
75
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FD
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FD
10
FD
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
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101
11212
11113
11214
11215
11116
11117
11218
109
11121
111
112
113
114
115
116
117
118
119
120
121
122
123
!_DY
fi:F8
CLC
ADC (MATRIX),y
LDY #F9
CLC
ADC (MATRIX),Y
LDY #F1
STA (MATRIX),y
INCMATRIX INC MATRIX
BNE TESTCOLUMN
INC MATRIX+l
TESTCOLUMN INC CDLUMNCOUNT
LDA CDLUMNCOUNT
CMP #N8RCOLUMNS
SEQ TEST ROW
JMP SAME ROW
TEST ROW INC rtOWCOUNT
LDA ROWCOUNT
CMP #N8RROWS
BEQ PRINT
LDA MATRIX
CLC
ADC #OFFSET
sec Tl
INC MATRIX+!
T1
STA MATRIX
JMP NEXT ROW
,.............................
PRINT
,..
JSR
LDA
STA
LDA
STA
8ELLI\B
#NSTARTL
MATRIX
l*NSTARTH
MATRIX+!
...........................
LDA
STA
l*$1110
ROWCOUNT
,.. ...........................
PRINTNEXTROW LDA #$1110
STA COLUMNCOUNT
PRINTSAMEROW LDY #Fl
LDA <MATRIX),y
ORA #$80
CMP #$89
BNE PRINTIT
LDA #$AA
PRINTIT JSR VIDEO
LDA #$Alii
JSR VIDEO
PRINTINCMATRIX INC MATRIX
PRINTTESTCOLUMN
1 BNE
INC MATRIX+!
PRINTTESTCOLUMN INC COLUMNCOUNT
LDA COLUMNCOUNT
CMP l*NBRCOLUMNS+2
BEG! PRINTTESTROW
JMP PRINTSAMEROW
PRINTTESTROW INC ROWCOUNT
LDA ROWCOUNT
CMP #NBRROWS
BEG! PRINTOUT
LDA #$8D
JSR VIDEO
JMP PRINTNEXTROW
PRINTOUT LOA #$8D
JSR VIDEO
RTS
30
1088:A0 50
:0BR:A3 0£
::z!Bc :20 R8 FC
~0BF:AD 312l CIZl
1.0C2:88
128
10C3:012l F5
10C5:AD Q!IZl CIZI
11ZlC8: 112l EE
11ZlCA:8D 11Zl Ctzl
112JCD:512l
1:29
***
1:24 8E!....LhB
.-.c:.J.....:......J BELL
LDY
LDA
1:25
J"SR
1:27
I...DA
DEY
BNE
LDA
BPL
STA
RTS
-1
1312l
131
132
133
#$60
#$05
$FCR8
$C0312l
BELL
$Ctzl1Zl0
BELU<B
$C010
SUCCESSFUL ASSEMBLY: NO ERRORS
r;
-~
31
FILT=:R::
:1L / 9
....
...;
32
1 : 1 ~.1 1 : 1 a .Q-0 ~-c: a 1 1 1 1 a a 1 a : a 1 0 : a 1 a : 1 1 1 1 1 g ~ 0 : a : a 1 1 0 ~ 1 1 1 ~ 1 1 1 : : ~ 1 0 : : 1 1 1
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34
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