PREPROCESSING

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• PREPROCESSING
• Preprocessing is basically used to improve the
  quality of an image. This is essential, because
  image acquisition device may be badly calibrated
  or there may be noise in the system.
• Some of the other reasons could include poor
  lighting conditions, lossy transmission,
  existence of unfriendly operating environment,
  erroneous information introduced during data
  transmission or other variety of reasons.
• If you apply image processing techniques to such
  noisy images, the results may not be acceptable
  and the decisions could even be wrong.
• Interpretation of image may even become
  impossible.

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• PREPROCESSING
• In order to improve the quality of original
  image, it is essential to transform the raw image
  data by some appropriate means.
• A prime objective of image transformation is to
  improve the visual quality of the raw image to
  human observance or for machine interpretation.
• Such processing algorithm may be said to be
  concerned in a general sense with image
  enhancement.
• A simplest way to transform the visual image
  f(x,y) is to map directly to the new transformed
  version g(x,y).
• The transformation may be carried out using an
  algorithm which should be easy to implement on a
  pixel-by-pixel basis, on the entire image.

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• PREPROCESSING
• Some such operations are defined as histogram
  modification techniques.
• Binarization technique is one such technique. We
  examine each pixel, compare its value against a
  threshold, and map its value to one of two
  possible transformed values ( 0 and 1) according
  to a simple rule.
• Accuracy of the method depends upon the value of
  the threshold chosen. If proper care is not
  taken, you may lose a lot of image information
  during binarization,.
• Some kind of preprocessing is essential before
  starting this process.
• The approaches could be spatial-domain or
  frequency- domain. Together, these approaches
  encompass most of the preprocessing algorithms
  used in image processing systems.

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• PREPROCESSING
• Spatial-Domain Method
• Refers to aggregate of pixels composing an image.
• Preprocessing methods are procedures that
  operate directly on these pixels.
• Preprocessing function in spatial domain is
  expressed as
• where f(x,y) is input image and g(x,y) is output
  image. h is an operator on f(.), defined over
  some neighborhood of f(x,y).
• It is possible to let h( ) operate on a set of
  input image(s), such as performing a pixel by
  pixel sum of k images for noise reduction.
• The principal approach used in defining a
  neighborhood around (x,y) is to use a square or
  rectangular sub-image area centered at (x,y).

g(x,y) h(f(x,y))
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• PREPROCESSING
• Spatial-Domain Method
• The center of sub-image or the mask is moved
  from pixel-to-pixel, starting, say at the top
  left corner, applying the operator at each pixel
  location p(x,y) to yield new pixel g(x,y).

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• PREPROCESSING
• Spatial-Domain Method
• A simplest form of h(.) operation is when the
  neighborhood is 1 x 1 and g(x,y) depends on the
  value of f(x,y) only. In this case h becomes an
  intensity transformation.
• S T. y
• where y is current intensity of an image point.

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• PREPROCESSING
• Spatial-Domain Method
• One of the spatial domain technique used most
  frequently is based on the use of convolution
  mask (also known as template, window or filter).
  Basically the mask is a small (3X3) two
  dimensional array.

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• PREPROCESSING
• Spatial-Domain Method
• Masks coefficients are chosen to detect a
  desired property in an image.
• Suppose we have an image of constant intensity
  which contains isolated pixels whose intensities
  differ from background. These points can be
  detected by the mask.
• If all the pixels within the mask area have the
  same value, the sum will be zero. If on the other
  hand, the center of the mask is located at one
  isolated intensity value, the sum will be
  different from zero.

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• PREPROCESSING
• Spatial-Domain Method
• These different values can be eliminated by
  comparing against the threshold.

w2
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(x,y1)
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(
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(x
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(x, y-1)
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q w1x1w2x2w3x3w4x4w5x5w6x6w7x7w8x8w9x9 C
ompare this value against pre-assigned threshold
for the center pixel.
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• PREPROCESSING
• Frequency Domain Methods
• This refers to an aggregate of complex pixels
  resulting from the Fourier transform of an image.
• The concept of frequency is often used in
  interpreting the Fourier transform coefficients
  of the image.
• This represents a very mathematical technique and
  requires very large amount of computer processing
  time.
• However, these techniques are very powerful and
  give very good results.
• Due to complex nature of algorithms, the details
  will not be covered here. Normally FFT or DFT
  coefficients are obtained and used for image
  processing and transformations. However, you
  will be required to use the MATLAB commands in
  frequency domain.

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Image Normalization The simplest way to
normalize an object in an image with respect to
its position within the image boundaries is - to
implement re-labeling of axes. In such case the
coordinates are translated so as to align the
extremities of the object of interest
cg
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Image Normalization Some basic mathematical
operations required to perform such
normalization. One of the important feature
which is often needed is to align an object to
the center of the window is CG. In such cases, we
have to calculate the center of gravity of an
image and align this CG to the center of the
window. The center of gravity of an object is
defined by the following relation ( apply after
binarization ).
This operation is performed on binarized image
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Where x and y represent the coordinates of CG
of the object. f(x,y) represents the intensity
of image points of the binarized image. Some of
the operations required for the normalization
are Translation of An Image Suppose we wish to
translate a point with coordinates (x,y) to a new
location ( x1, y1) by using a displacement vector
(x0,y0). x1 x x0 y1 y y0 In
mathematical form, it can be written
as Apply this transformation to all the
coordinate points of the image. You would get
the original image translated by by (x0, y0)
values.
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Scaling of an Image Scaling by a factor Sx and Sy
in x and y directions can be performed by using
the following transformation This
transformation is applied to all the coordinate
points points of the image. The factors Sx and Sy
are constants. A value greater than one implies
larger image and smaller value implies a
reduction in the size of the image.
Scaling of 1.8 implies Sx and Sy are 1.8 each
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Rotation of an Image The transformation matrix
for two dimensional images( which will rotate an
object image by an angle ? degrees in clockwise
direction is defined as The transformation
requires a recalculation of coordinates of all
pixels defining the image. There is no change in
the intensity values of the image. If necessary,
all these operations can be applied
simultaneously on a given image.
x x cos ? y sin ? y - x sin ? y cos ?
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There are other operations which can be performed
on an image for obtaining required results. Some
of the important ones will be explained later.
(x, y)
y
y
x
?
?
?
x
Rotation is defined by an angle theta, clockwise
direction. However the coordinates x and y are
in opposite direction. (x,y) are original
coordinates and (x,y )are target coordinates of
the object and rotated images respectively
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• IMAGE TRANSFORMATION
• Monadic or One Point Transformation
• Monadic point-by-point operators are the
  simplest types for image processing operations.
  The process involves a single input image, f(x,y)
  and results in a single output image, g(x,y).
• Following operators are very useful for image
  processing.
• Identity Operator
• This operator results in the creation of an
  output image which is identical to the input
  image. The value of each pixel in the second
  image q is identical to the value of
  corresponding pixel p in the first image.
• p q f(x,y), for x 1,2, . N, and y
  1,2,M.
• Inverse Operator
• This operator involves creation of an output
  image which is inverse of the input image. The
  process is similar to an identity-

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• operator, except that the new values of
  intensities are different at every point .
• If g(x,y) is new intensity value of the original
  image f(x,y) at point (x,y), then g(x,y) (L-1)
  - f(x,y), for all (x,y).
• If, L 16, and image matrix is
• Threshold Operator
• This class of operator results in a binary
  output image from a gray scale input image where
  the level of transition is given by the input
  parameter p1 - which is the threshold..

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q
q 0 for p lt p1 and q 1 for p gt p1 Let p1
5, and the input image be
1
p
p1
0
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• All values below or equal to p1intensities are
  converted to 0 and rest to 1. This operator can
  be used to obtain spatial information or to
  extract some simple image features

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• from the histogram by repeating the procedure
  using different threshold values.
• Binary Threshold Interval Operator
• This class of operator results in a binary output
  image where all the input gray values in the
  interval p1 to p2 are converted to 1 and all the
  values outside the interval are converted to 0.
  This operator can be used to obtain required
  features from an image based on intensity values.
  
• Gray Threshold Interval Operator.
• This class of operator results in a gray scale
  output image for
• pixel intensity values between p1 and p2, and
  converts all other input values outside the
  interval to 0. This operator can be used to
  identify image features having specific gray
  intensity values.
• Inverted Gray Threshold Operator
• It is similar to Gray threshold operator, except
  that output image is inverted after applying
  the threshold function in the

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• gray image. Every pixel in the original image
  which was light will become dark and pixels
  which were dark will become light information
  from histogram based on intensity.
• Stretch Operator
• This class of operators results in a
• full gray scale output image
• corresponding to input interval p1
• and p2 and suppresses all the values
• outside this range.

q
p
p1
p2
q
15
0
p
p1
p2
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• There can be many such monadic operators to
  change the appearance of the input image.
• Dyadic or Two-Point Transformations
• These operators utilize the information contained
  at the same location in two images. In the
  two-point transformation, pixels from images A
  and B ( from the same coordinates (x,y) )are used
  to create a new image, C. The size of the matrix
  does not change and the dyadic function fD can
  be either linear or non-linear.
• The transformation function is applied to all
  pixel location pairs in the input image.
• The information from a pixel location in one
  image is combined with the information of the
  corresponding pixel location of a second image to
  produce the value of a corresponding pixel in the
  output image.

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• Image Addition
• Image addition can be used to reduce the effects
  of noise in the data. The value of the output,
  Ci,j is given by
• ci,j ( ai,j bi,j . ) / k
• over the entire( i, j) coordinate range of
  values, where k equals to number of samples
  added. The image addition process averages the
  data in the two input image matrices.
• In general, there is an accuracy improvement and
  reduction of noise when the procedure is used
  with a large number of samples.
• Image Subtraction
• Image subtraction can be used to detect changes
  that have occurred during the time interval when
  the two images were taken - if the two images are
  of the same object.

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• The data may also represent some abnormal changes
  in the tissues or textures over a period of time.
  You have to make a note that the images have to
  be registered exactly if any meaningful
  information has to be achieved.
• ci,j k ( ai,j - bi,j ),
• where k is a nonlinear function such that the
  minimum value of ci,j is always positive. This
  process is used in dental treatments. It is also
  used in angiography.
• Image Multiplication
• Multiplication of two image matrices is used to
  correct for the non-linearity of sensors where
  there is a spatial non-uniform sensitivity over
  the viewing area. This can be corrected by
  multiplying the image matrix by a correction
  matrix. The relationship is given by the
  equation
• ci,j k (ai,j bi,j ) a i,j,
• where all the values are rounded up to the next
  integer, the maximum value is 255. ai,j
  represent image points, and

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• and bi,j represents correction factors at point
  (i, j).
• Another use for the multiplication operator would
  be to create a small size window to reduce the
  computations and concentrate in the specific
  area of interest. The corresponding matrix bi,j
  would be given by the equation
• ci,j ai,j x bi,j ,
• where bi,j is 1 for all points inside the
  desired window area and 0 for all points outside
  the window area.
• During the dyadic operations, the size of the
  output image matrix is identical to the size of
  the input matrix. No rows or columns are lost in
  the process as happens with convolutions. A
  normalizing constant may always be required for
  all the dyadic operations.
• Convolution Spatial Transformation
• Using this transformation a new image matrix is
  generated, where the new pixel value assigned to
  each location is a function.

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Image multiplication
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• of the pixel values of the adjacent locations (
  neighbors) as indicated by the 3 x 3 or other
  size convolution masks. In a 3x3 convolution, a
  new intensity value for the pixel at the center
  location is computed - based on the values of the
  nine or more neighbor ( depending upon the mask
  size). Subsequently, the mask is then shifted by
  1 position and the process is repeated until the
  entire image matrix is regenerated.
• It should be noted that the size of the
  resultant matrix is reduced in each direction due
  to edge effect. The size of reduction depends
  upon the mask size.
• If it is undesirable to reduce the matrix size,
  this can be modified using a rule which assumes
  that the data is constant in the row and columns
  adjacent to the outside edge of the image matrix.

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Convolution ( neighborhood) Transformation