Manipulation of pixel data

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Manipulation of pixel data

• Simple geometric transformations
• Arithmetic combinations of images
• done on a pixel-by-pixel basis
• images must be the same size
• Image addition and averaging
• averaging multiple noisy images reduces the noise
  level
• scene must be static
• Image subtraction
• used for motion detection and tracking
• use a threshold to ignore insignificant changes

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Pixel Values
Each of the pixels that represents an image
stored inside a computer has a pixel value which
describes how bright that pixel is, and/or what
color it should be. In the simplest case of
binary images, the pixel value is a 1-bit number
indicating either foreground or background. For a
grayscale images, the pixel value is a single
number that represents the brightness of the
pixel. The most common pixel format is the byte
image, where this number is stored as an 8-bit
integer giving a range of possible values from 0
to 255. Typically zero is taken to be black, and
255 is taken to be white. Values in between make
up the different shades of gray. To represent
color images, separate red, green and blue
components must be specified for each pixel
(assuming an RGB colorspace), and so the pixel
value' is actually a vector of three numbers.
Often the three different components are stored
as three separate grayscale' images known as
color planes (one for each of red, green and
blue), which have to be recombined when
displaying or processing. Multi-spectral images
can contain even more than three components for
each pixel, and by extension these are stored in
the same kind of way, as a vector pixel value, or
as separate color planes.
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Levels of computation
We can consider image processing algorithms from
the viewpoint of locality of computation. (levels
of computation) Consider each algorithm is terms
of its input-output characteristics. Here our aim
is to characterize operations so that we can
discuss the nature of input and output and how
best to implement these operations .
There is a variety of ways to classify and
characterize image operations. The reason for
doing so is to understand what type of results we
might expect to achieve with a given type of
operation or what might be the computational
complexity associated with a given operation.
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Types of image operations
The types of operations that can be applied to
digital images to transform an input image Am,n
into an output image Bm,n (or another
representation) can be classified into three
categories as shown in Table 1.
 
 
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Types of image operations
Types of image operations. Image size N x N
neighborhood size P x P. Note that the
complexity is specified in operations per pixel.
This is shown graphically in Figure 1.
Figure 1 Illustration of various types of image
operations
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Point level operations
In a point operation, each output pixel
corresponds directly to the input pixel having
the same coordinates fB(x,y) O point
fA(x,y) where fA and fB are input and output
images , respectively
The simplest and most widely used segmentation
method is thresholding. It consists of setting
background values for pixels below a threshold
value T and a different set values for the
foreground. If the input image is f(x,y) and
thresholded image is g(x,y), the equation of the
thresholding operator is given by
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Experiment - Thresholding
Shown below are the original image and the
results after applying different thresholds
values (118, 128) to it.
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Local level operations - neighbourhood operations
Local level operation produces an output image
in which the intensity at a point depends on the
neighborhood of the corresponding points in the
input image
fB(x,y) Olocal fA(xk,yl) (xk,yl) ? Nx,y)
Local operations produce an output pixel value
bmmo,nno based upon the pixel values in the
neighborhood of Ammo,nno. Some of the most
common neighborhoods are the 4-connected
neighborhood and the 8-connected neighborhood in
the case of rectangular sampling and the
6-connected neighborhood in the case of hexagonal
sampling illustrated in Figure 2.
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Masks, filters, kernels, templates
Figure 2a Figure 2b Figure 2c Rectangular
sampling Rectangular sampling hexagonal sampling
4-connected 8-connected 6-connected
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Smoothing and edge detection are local
operations
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Global level operations
The output of certain operators depends on the
whole image. A histogram of intensity values and
Fourier transform are global operations. P
Oglobalf(x,y)
Object Level - Size, average intensity, shape,
and other characteristics of an object must be
computed for the system to recognize this object.
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Mathematics-based Operations

• Binary operations
• Arithmetic-based operations

In the binary case there are two brightness
values "0" and "1". In the ordinary case we begin
with 2B brightness values or levels but the
processing of the image can easily generate many
more levels. For this reason many software
systems provide 16 or 32 bit representations for
pixel brightnesses in order to avoid problems
with arithmetic overflow.

• Arithmetic combinations of images
• - done on a pixel-by-pixel basis
• - images must be the same size

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Arithmetic-based operations
The gray-value point operations that form the
basis for image processing are based on ordinary
mathematics and include
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Arithmetic-based operations
Output images Usually it will be necessary to
pre-define the type or range of the resultant
image. For example, if two 256 grey level images
are multiplied together, the result for any pixel
is highly likely to be outside the 0 to 255
range! Depending on the application, it might be
preferable to define the result as a floating
point number so that any value is recorded, or a
new range of 0 to 255² (i.e. effectively 216 so
that we would now have a 16-bit image) so that
all the results are within the range.
Alternatively a smaller range could be defined,
and any results which were outside that range
would be clipped, i.e. if the range is A to B,
any pixel where the result of the operation was
less than A would be given the value A and any
pixel where the result was greater than B would
be given the value B.
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Arithmetic-based operations
Image - Image Multiplication This can only be
done on two images which have the same
dimensions. The value of each pixel in one image
is multiplied by the value of the corresponding
pixel in the other image.
Image - Image Division The values in the first
image are divided by those in the second. Image -
Image Addition The values in the two images are
added. Image - Image Subtraction The values in
the two images are added. Note that this should
be used with care as it easily results in
negative values which are undefined for a gray
level image.
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Pixel Addition -How It Works
The addition of two images is performed
straightforwardly in a single pass. The output
pixel values are given by
Or if it is simply desired to add a constant
value C to a single image then
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Arithmetic-based operations
Image - Image Combining This is similar to
addition but proportions of the corresponding
pixels of the two images are added together. For
example, 0.6 of image 1 could be added to 0.4 of
image 2. We may wish to give more emphasis to one
image than the other. This can be done by 'alpha
blending'
g(x,y) ?f1(x,y) (1- ?) f2(x,y)
When ? in this Equation is 0.5, g(x,y) becomes a
simple, evenly-weighted average of the two input
images. It is possible for a ? to vary, every
pixel of an image can have its own ?, stored in a
separate ' alpha channel'.
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Image Combining
a)Image A b)Image B
c)0.5 A 0.5 B
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The main application of image averaging is noise
removal
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Subtraction of images
The difference between two images f1(x,y) and
f2(x,y) is obtained by computing the difference
between all pairs of corresponding pixels from
f1( x,y) and f2(x,y)  g(x,y) f1(x,y) -
f2(x,y)
Subtracting two 8-bit greyscale images can
produce values between -255 and 255. This
necessitates the use of 16-bit signed integers in
the output image - unless sign is unimportant, in
which case we can simply take the modulus of the
result and store it using 8-bit integer
g(x,y) ? f1(x,y) - f2(x,y) ?
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The main application for image subtraction is in
change detection
In the simples form, a binary difference image
DP1,2(x,y) between frames f1(x,y) and f2(x,y) is
obtained by
In a difference picture, pixels, which have
value 1 may be considered to be the result of
object motion or illumination changes.
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The main application for image subtraction is in
change detection
Mask Image
Live Image
Digital Subtraction Angiography (DSA) Image
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Binary operations
Operations based on binary (Boolean) arithmetic
form the basis for a powerful set of tools that
will be described here and extended in
mathematical morphology. The operations described
below are point operations and thus admit a
variety of efficient implementations including
simple look-up tables. The standard notation for
the basic set of binary operations is
The implication is that each operation is applied
on a pixel-by-pixel basis.
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Binary operations
For example, .
The definition of each operation is
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Binary operations
These operations are illustrated in Figure where
the binary value "1" is shown in black and the
value "0" in white.
a) Image a b) Image b
c) NOT(b) d) OR(a,b) a b e) AND(a,b) a b
f) XOR(a,b) a b g) SUB(a,b) a \ b
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Find more applications of point to point image
operation