| Image
Processing Articles
Index |
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| Background |
| The
AND binary operation
takes two binary inputs
and outputs 1 only
when both the inputs
are 1 else produces
0. The NAND binary
operator is the complete
inverse of the AND
binary operation.
NAND outputs 0 when
both the inputs are
1, else it produces
0. The functionality
of AND and NAND is
clarified by the help
of the truth tables: |
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| AND
NAND |
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| Using
AND and NAND boolean
algebra allows you
to represent things
like: |
|
| The
sky is high and blue. |
|
| Understanding
AND & NAND Mathematically: |
| The
ANDing of two images
is carried out by
performing AND operation
to the corresponding
images of the two
images to produce
the output pixel value.
For instance, suppose
that we wish to AND
the integers 167 and
211 together using
8-bit integers. 167
is 10100111 in binary
and 255 is 11010011.
ANDing these together
in bitwise fashion,
we have 10000011 in
binary or 131 in decimal. |
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| This
is the method adopted
in the sample implementation,
but not at all the
only implementation
of this of the logical
operators rather you
can implement the
logical ANDing and
NANDing using some
thresholding to transform
the digital image
data into the binary
format, or simply
by taking the 0 pixel
value as the logical
0 and the non-zero
pixel values as the
logical 1 value. |
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| General
Working |
| The
AND and NAND operations
are performed through
a single pass module
which during operation
passes through the
each pixel of each
image and calculates
the pixels of the
output image by doing
the respective operation
on the corresponding
pixels to calculate
the output pixels.
It is necessary to
have two images of
the identical size.
In the sample program,
if two images are
not identical in size,
then they are made
of the same size (
explained below).
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| Guidelines
for Use |
| The
most obvious application
of AND is to compute
the intersection of
two images. We illustrate
this with an example
where we want to detect
those objects in a
scene which did not
move between two images,
i.e. which are at
the same pixel positions
in the first and the
second image. We illustrate
this example using |
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| and |
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| If
we simply AND the
two images in a bitwise
fashion we obtain: |
|
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| and
if we simply NAND
the two images in
a bitwise fashion,
we obtain the result
as: |
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| AND
can also be used to
perform so called
bit-slicing on an
8-bit image. To determine
the influence of one
particular bit on
an image, it is ANDed
in a bitwise fashion
with a constant number,
where the relevant
bit is set to 1 and
the remaining 7 bits
are set to 0. For
example, to obtain
the bit-plane 8 (corresponding
to the most significant
bit) we AND the image
with 128 (10000000
binary) and threshold
the output at a pixel
value of 1. |
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| C#
Sample Program: |
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| 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 expects
that the input images
are grayscaled. Then
it takes the BitmapData
objects of the two
input images. It determines
which image is bigger
in width as well as
in height. Then it
scales the smaller
image to acquire the
size of the bigger
image to make the
sizes of both the
images equal. Then
the algorithm calculates
the ANDed image in
the single pass through
the image. The final
output is an image
showing the result
of the AND operator
on the two input images
which is then displayed
on the screen in the
down most picture
box. |
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