| Image
Processing Articles
Index |
 |
| Why
Using Moments of Area? |
| It
is seen that the usage
of moments of area
highly supports for
the systems using
Artificial intelligence.
The reason behind
the fact is that these
moments tend to be
more specific about
the original shapes
of the Ligatures(blobs).
The main property
of moments is that
they are Rotation,
translation and Scaling
independent and that's
why they are highly
used for the recognition
process. These moments
along with other features
are then usually passed
to Neural Nets to
get the result..... |
|
| It
is highly recommended
to study the last
article before proceeding
next... Implementation
of Labeling Connected
Components |
|
| Moments
of Area |
| Consider
now a two dimensional
light intensity function
g(x,y) (the pattern
or visual input) normalized
so that the volume
under the function
is equal to one. For
our purposes it then
behaves just like
a bi-variate probability
density function.
For such a function
of two variables the
moments are defined
as follows: |
|
| mjk=
ò ò x jyk f(x, y)dxdy |
| for
j, k = 0,1,2,.... |
|
| In
this way we now are
able to obtain a countably
infinite number of
shape measurements
for describing g(x,y).
As in the one dimensional
case, an infinite
number of measurements
yields an impractical
system. Luckily, in
practice, even if
the shape of g(x,y)
is quite complicated
not many moments are
needed to adequately
describe it. |
|
| Affine
Transformations |
| Consider
designing a character
recognition system
for machine printed
characters. Two characters
such as A and A are
still considered A’s
and therefore quite
similar even though
one is bigger than
the other. Such patterns
would still be considered
A’s even if they differed
in location, stretching,
squeezing, and shearing.
Rotation is a rather
special transformation
and depending on the
context it may or
may not be desirable
to treat patterns
that are invariant
under rotation as
belonging to the same
pattern class. This
may result, for example,
in the system’s inability
to discriminate between
M and W or p and d.
Transformations such
as these are special
cases of affine transformations
and are treated in
detail in [Ry86].
Let R2 denote the
two-dimensional Euclidean
plane. |
|
| Definition:
A mapping T of R2
onto R2 is called
an affine transformation
if there exists an
invert as a pattern
P and three of its
collapsing projections
on the x, y and x+y
axes. |
|
| How
this method of Moments
came into existance
was in fact Sigfried.
He opened the book
and quickly noticed
that different shapes
had different formulas
and gave different
values even if the
shapes had the same
height, width or area.
He was now getting
excited. He turned
to the next page and
was electrified. Here
was a page full of
letter shapes, exactly
his field of interest.
In the book they were
called I-beams, X-beams
and L-beams and what
have you, but to him
they were just letters
of the alphabet and
they all had their
formulas for the moments.
Sigfried realized
he had stumbled on
a new and different
method for extracting
shape features from
patterns. He put the
dynamics book back
on the shelf, kissed
his worn-out paperback
copy of de Bono’s
Lateral Thinking and
rushed back to his
office to tell his
room mate he had found
a topic for his thesis,
feature extraction
for character recognition
by the method of moments. |
|
| Guidelines
for Use: |
| To
illustrate RTS invariant
moments, we start
with a simple image
containing some distinct
artificial objects(
specifically text) |
 |
|
| Now
we apply Grayscale
conversion to the
image to convert it
to Grayscale image. |
|
 |
|
| Now,
we will convert the
image into binary
so only two intensities
will be present in
the image..... Black
and white or in other
words 0 and 1. |
|
 |
|
| After
scanning this image
and labeling the distinct
pixels classes with
a different grayvalue,
we obtain the labeled
output image. |
|
 |
|
| C#
Sample Program: |
|
| The
algorithm is coded
in C# using unsafe
so the quality and
speed of the program
may not be affected.
The class BitmapData
is used to read and
process the pixels
in the image. This
is the speicality
of C# to provide such
a speed even on image
processing applications.
There is a set of
modules that are designed
to implement the algorithm.
The program scans
the image to convert
the image into grayscale
Levels.Then it converts
the image into binary.This
binary image will
be subjected to spliting
it into components.Here
we can us 4-Connected
or 8-Connected Algorithm
but we used 8-Connected
Algorithm for finding
the Blobs in the image
as described above. |
|
| In
order to understand
the basic functionality
of the program, you
must consider my previous
articles <give
reference here>.
The program consists
of a set of classes
that illustrate the
basic functionality
of the Moments of
area. Let us see how
these classes work
together to get the
values of the invariant
moments. The diagram
below explains the
hierarchy of the classes. |
|
 |
|
| There
are three classes
here that can be seen
in the image above.
Please refer to the
article "Connected
Components" to
learn about the functionality
of the class ConnectedComponents.
Here we will discuss
how does the classes
Object and Feature
works at all. |
|
| Class
Object: |
| It
is a collection of
objects having the
following information
about each object
obtained during the
process of finding
the connected components. |
|
private
int startX=0,startY=0;
private
int finalX=0,finalY=0;
public
image.Features feature;
(startX,startY): the
top left position
of the object.
(finalX,finalY): the
bottom right position
of the object
feature: an object
of type Features. |
|
| Process: |
| In
the previous article,
we have seen that
we get an array of
objects when we pass
an image to the instance
of the class ConnectedComponents.
Now, we want to get
some important information
from these objects.
When recognition of
objects is made, we
segment the objects
from the image first
and then get Features
from these objects.
Some of the features
that we calculate
are RTS invariant
Moments. |
|
| Class
Features: |
| public
Features (int
startX,int
startY,int
width,int
height,int
l) |
|
| The
constructor takes
the top left position
of the object, the
width and height and
the label i.e., intensity
value of the object
so the object can
be reached easily. |
|
| private
void
calcAreaCenter() |
|
 It
calculates the area
of the object.
It
calculates the central
position of the object
along horizontal axis.
It
calculates the central
position of the object
along vertical axis. |
|
public
double normCentralMoment
(int
p, int
q,int
objectId)
p: which moment to
be calculated as directed
on the vertical axis
q: which moment to
be calculated as directed
on the horizontal
axis
object id: The intensity
value of the object. |
|
| The
function calculates
the normalized central
moment with respect
to the center. |
|
| public
double centralMoment
(int
p, int
q, int
objectId) |
|
p:
which moment to be
calculated as directed
on the vertical axis
q: which moment to
be calculated as directed
on the horizontal
axis
object id: The intensity
value of the object. |
|
| The
function calculates
the central moment
of each of the pixel
value. |
|
| The
final output is a
colored image showing
separate colors for
every blob.... An
array named objects
of Type Class Objects
contains the sizes
of each blob or object
being segmented and
the object also contains
the features of the
objects yet obtained... |
|
| Output:
A word file containing
the feature list for
the RTS invariant
Moments. |
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