The document discusses various intensity transformations that can be applied to digital images in the spatial domain. It describes transformations such as image negatives, log transformations, power law transformations, contrast stretching, intensity level slicing, bit plane slicing, and histogram equalization. These transformations are used for tasks like image enhancement, expanding the dynamic range of pixels, and emphasizing certain intensity levels. Formulas for calculating the transformed pixel intensities are provided for many of the methods.

1. Intensity transformations
Mithun kumar kar
Department of Electrical Engineering
BALASORE COLLEGE OF ENGINEERING AND TECHNOLOGY, BALASORE
August 23, 2020
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2. Intensity Transformations
All the intensity transformations are done in spatial domain.
The intensity transformations or spatial domain processes can be
denoted by the expression
g(x, y) = T[f (x, y)]
where f (x, y) is the input image and g(x, y) is the output image
T is an operator on f defined over a neighbor of point (x, y).
Intensity transformations are made for image enhancement and for
different applications. Let the value of pixels before transformation is
r and after transformation is s and the transformation is given by
s = T(r)
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3. Image Negatives
The negative of an image with intensity levels in the range [0, L − 1]
is obtained by using the negative transformation, given by the
expression s = (L − 1) − r.
Figure : image negetive
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4. Image Negatives
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5. Splitting colour image in to R,G,B channels
Figure : colour image, red channel,green channel,blue channel
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6. Image Negatives applications
Particularly suited for enhancing white or gray details embedded in
dark regions of an image when black images are dominant in size.
Used in digital mammogram to analyze cancer tissues.
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7. Log Transformations
The general form of log transformation is given by
s = c log(1 + r)
This transformation maps a narrow range of low intensity values in
the input in to a wider range of output levels and vice-verse.
This type of transformation is used to expand the value of dark pixels
in an image, while compressing the higher level values.
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8. Log Transformations
The log function has the important characteristics that it compress
the dynamic range of the image with large variation in pixel values.
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9. power law (gamma)transformation
The general form of power law (gamma)transformation is given by
s = crγ
Like log transformation, power-law transformation with fractional
value of γ maps a narrow range of dark input values into a wider
range of output values, with opposite being true for higher values of
input levels.
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10. power law (gamma)transformation
Simply varying γ a family of possible transformation curves can be
obtained.
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11. Contrast stretching
Contrast stretching is a process that expands the range of intensity
levels in an image so that it spans the full intensity range of the
recording medium or display device.
The result of contrast stretching is obtained by setting
(r1, s1) = (rmin, 0)
and
(r2, s2) = (rmax, L − 1)
where rmin and rmaxdenote the minimum and maximum intensity
levels in the image respectively.
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12. Contrast stretching
Figure : Original image, Contrast image
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13. Intensity level slicing
Intensity level slicing means highlighting a specific range of intensities
in an image.
one approach of implementing intensity slicing is to display in one
value to all the values in the range of interest and all other intensities
to another.
The second approach based on the transformation which brightens or
darkens the desired range of intensities while leaves all other intensity
levels unchanged.
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14. Intensity level slicing
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15. Bit plane slicing
Bit plane slicing is a method of representing an image with one or
more bits of the byte used for each pixel.
As in digital image the gray level of each pixel is stored as one or
more bytes, we could highlight the contribution made to the total
image appearance by specific bits.
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16. Bit plane slicing
It highlights the contribution made by each bits or specific bits
An 8 bit image may be considered as being composed of eight 1 bit
planes, with plane-0 containing the lowest order bit of all pixels in the
image and the plane-7 all the higher order bits
Decomposing an image in to its bit planes is useful for analyzing the
relative importance of each bit in the image.
This type of decomposition is useful for image compression in which
fewer planes are used in reconstruction of an image.
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17. Image rotation
Image rotation is a common image processing application where the
coordinates of the image is rotated with some angle θ.
The coordinates of a point (x1, y1) when rotated by an angle θ
around (x0, y0) become (x2, y2), as shown by the following equation
x2 = cos θ(x1 − x0) + sin θ(y1 − y0)
y2 = − sin θ(x1 − x0) + cos θ(y1 − y0)
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18. Histogram processing
The histogram of a digital image with intensity levels in the range
[0,L-1] is a disctete function h(rk) = nk, where rk is the kth intensity
value and nk is the number of pixels in the image with intensity rk
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19. Histogram processing
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20. Histogram processing
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21. Histogram Equalization
Histogram equalization is a process that attempts to spreadout the
gray levels in an image so that they are evenly distributed across their
range.
The transformation equation for histogram equalization is given by
Sk = T(rk) = (L − 1)
k
j=0
Pr (rj ) =
(L − 1)
MN
k
j=0
nj
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22. Histogram Equalization
Histogram equalization is a process that attempts to spreadout the
gray levels in an image so that they are evenly distributed across their
range.
The transformation equation for histogram equalization is given by
Sk = T(rk) = (L − 1)
k
j=0
Pr (rj ) =
(L − 1)
MN
k
j=0
nj
Figure : Original image, Histogram equalized imageMithun kumar kar (BCET) Intensity transformations August 23, 2020 22 / 21