CS6825: Point
Processing
Contents – not complete

What is point processing?
• Altering/TRANSFORMING the image at a
pixel only as a function of that pixel
itself.






Negative images
Thresholding
Logarithmic transformation
Power law transforms
Grey level slicing
Bit plane slicing
Why Transform images?







Image has noise in it
Image is low contrast
Want to find things in an image
Want to emphasize things in an
image
Want to remove things in an image
Want to de-emphasize things in an
image
For fun?
What are we doing in this
lecture



Teaching you what image transformation
at a point is.
Showing you a number of common (but,
by no means alls) point-based transforms
Hopefully, you will understand, “You must
know why you want to transform and
image first. Then hopefully you can
remember these transforms to see if any
will work for you”.
2 basic kinds of Point
Processing

Spatial Processing



Pixel values are directly changed in the 2D
array of pixel values we use to represent an
image.
This 2D of array of pixel values is referred to
as the image SPATIAL DOMAIN.
The word SPATIAL comes from the fact as
we move through the image in x and y
directions it is moving through the space of
the image.
2 basic kinds of Point
Processing

Frequency Processing



We will discuss this later in class
For now, just like you have radio signals
that could be shown in the spatial domain,
you also can represent them in the
frequency domain.....Remember you tune
into radio stations by frequency!
Again we will discuss this later.
Spatial domain
Frequency Domain
General Spatial Processing

Spatial Processing Algorithms can be
reduced to the form
g (x, y) = T[ f (x, y)]

Origin
where f (x, y) is the
input image, g (x, y) is
the processed image
and T is some
operator defined over
some neighbourhood
of (x, y)
y
x
(x, y)
Image f (x, y)
Point Processing Spatial
Processing



The simplest spatial domain
operations occur when the
neighbourhood is simply the pixel
itself
In this case T is referred to as a
point processing operation
Point processing operations take the
form
 Pnew(r,c) = T ( P(r,c) )
Point Processing Spatial
Processing

We will discuss:
•
•
•
•
•
•
•
•
•
Negative Image Transformation
Thresholding
General Kinds of Transformations
Contrast Stretching
Piecewise Linear transformations
Grey Level Slicing
Logarithmic transformations
Power Law transformations
Gamma correction
Note: We will discuss histograms and more pointbased operations related to it in a future lecture
Point Processing Example:
Negative Images
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

Negative images enhancing white or
grey detail embedded in dark regions
of an image
• Note how much clearer tissue is in the
negative image below
Original
Image
Pnew = 255 - P
Negative
Image
Point Processing Example:
Thresholding
Images taken from Gonzalez & Woods, Digital Image Processing (2002)


Thresholding transformations are
useful for segmentation in which we
want to isolate/emphasize an object
of interest from a background
Result called “BINARY” image.
Pnew =
255.0 r > threshold
0.0
r <= threshold
Basic Grey Level
Transformations
Images taken from Gonzalez & Woods, Digital Image Processing (2002)


There are many different kinds of
grey level transformations
Three of the most
common are shown
here
• Linear

i.e. Negative/Identity
• Logarithmic

i.e. Log/Inverse log
• Power law

nth power/nth root
Contrast Stretching for LowContrast Images
Have an image of low contrast


Image has only a small number of grey levels (or
colors)
Stretch the over-concentrated grey levels
via a nonlinear mapping
• One technique - Piece-wise linear stretching function
• Assign slopes of the stretching region to be greater
than 1
Note: a to b in the input
grey levels get stretched to the
Larger range of  to 

.
v
output gray level

o


a
b
input gray level
u
Piecewise Linear Transformation
Images taken from Gonzalez & Woods, Digital Image Processing (2002)


We use user-defined transforms, defined by
a set of lines “pieced” together….piecewise
linear.
The images below show a contrast stretching
linear transform to add contrast to a poor
quality image
Gray Level Slicing
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

Highlights a specific range of grey
levels
• Similar to thresholding
• Other levels can be
suppressed or maintained
• Useful for highlighting features
in an image
Logarithmic Transformations



The general form of the log
transformation is
 Pnew = c * log(1 +P)
The log transformation maps a
narrow range of low input grey level
values into a wider range of output
values
The inverse log transformation
performs the opposite transformation
Logarithmic Transformations
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

In the following example the Fourier
transform of an image is put through
a log transform to reveal more detail
Pnew = log(1 + P)
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Power Law Transformations




Power law transformations have the
following form
Pnew = c * P γ
Map a narrow range
of dark input values
into a wider range of
output values or vice
versa
γ
Varying gives a whole
family of curves
Power Law Example
γ = 0.6
Transformed Intensities
Original
Transformed
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
Old Intensities
0.8
1
Power Law Example (cont…)
Transformed Intensities
γ = 0.4
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
Original Intensities
0.8
1
Power Law Example (cont…)
Transformed Intensities
γ = 0.3
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
Original Intensities
0.8
1
Power Law Example (cont…)

The images to the
right show a
magnetic resonance
(MR) image of a
fractured human
spine
Different curves
highlight different
detail
s = r 0.6
s = r 0.4
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

Power Law Example
Power Law Example (cont…)
Transformed Intensities
γ = 5.0
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
Original Intensities
0.8
1
Power Law Example


An aerial photo
of a runway is
shown
This time
power law
transforms are
used to darken
the image
Different curves
highlight
different detail
s = r 3.0
s = r 4.0
Images taken from Gonzalez & Woods, Digital Image Processing (2002)

Gamma Correction
Images taken from Gonzalez & Woods, Digital Image Processing (2002)



Many of you might be familiar
with gamma correction of
computer monitors
Problem is that
display devices do
not respond linearly
to different
intensities
Can be corrected
using a log
transform
Gamma Correction

One can form an approximate model for
displayed luminance Li due to the
excitation of gun i with voltage Vi for a
Monitor as:
Typically, 1< Gamma
2.2
Original image
γ
<= 2.5 , standard Gamma =
Gamma correction= 1.5
Gamma Correction

New Image pixel = (Original Image pixel )
Original image
-γ
New Image
Gamma correction= 1.5
New Image pixel = (Original Image pixel )^-1.5
Gamma Correction Examples

Here is an example at different gammas.
L0, gamma= 1
L0
2.2, gamma = 1/(2.2)
L01/2.2
, gamma = 2.2
This is the best gamma
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Bit Plane Slicing

Often by isolating particular bits of the
pixel values in an image we can highlight
interesting aspects of that image
• Higher-order bits usually contain most of the
significant visual information
• Lower-order bits contain
subtle details
Images taken from Gonzalez & Woods, Digital Image Processing (2002)
Bit Plane Slicing Example
[10000000]
[01000000]
[00010000]
[00100000]
[00001000]
[00000010]
[00000100]
[00000001]
Summary




There are many more
transformations. We will see some
later in class
We concentrated on some common
point-based transformations in the
spatial domain.
Know what your problem is and then
decide on or if there is
transformation that can help.
Your class website has some other
material that explores this.