Chapter 3 image enhancement (spatial domain)

Intensity Transformation and Spatial
Filtering
Subject: FIP (181102)
Prof. Asodariya Bhavesh
ECD,SSASIT, Surat

Digital Image Processing, 3rd edition by
Gonzalez and Woods

Spatial Operations
– Single-pixel operation (Intensity Transformation)
• Negative Image, contrast stretching etc.
– Neighborhood operations
• Averaging filter, median filtering etc.
– Geometric spatial transformations
• Scaling, Rotation, Translations etc

Geometric Spatial Operations
Digital Communication Abdullah Al-
Meshal

Image Enhancement
 The objective of image enhancement is to process
an image so that the result is more suitable than
the original image for a specific application.
 There are two main approaches:
 Image enhancement in spatial domain: Direct
manipulation of pixels in an image
 Point processing: Change pixel intensities
 Spatial filtering
 Image enhancement in frequency domain:
Modifying the Fourier transform of an image

Some Basic Intensity
Transformation Functions
• Image Negatives
s = L – 1 – r
• S is the output intensity value
• L is the highest intensity levels
• r is the input intensity value
• Particularly suited for enhancing white or gray
detail embedded in dark regions of an image,
especially when the black areas are dominant in
size

• Image Negatives

• Log Transformations
• s = c log(1 + r)
• c is constant
• It maps a narrow range of low intensity values in the
input into a wide range of output levels
• The opposite is true of higher values of input levels
• It expands the values of dark pixels in an image while
compressing the higher level values
• It compresses the dynamic range of images with large
variations in pixel values

• Log Transformations

Log Transform
( ) log(1 )T r c r 

• Power Law (Gamma) Transformations
• s = c rγ
• c and γ are both positive constants
• With fractional values(0<γ<1) of gamma map a narrow
range of dark input values into a wider range of
output values, with the opposite being true for higher
values (γ >1)of input levels.
• C=gamma=1 means it is an identity transformations.
• Variety of devices used for image capture , printing,
and display respond according to a power law.
• Process used to correct these power law response
phenomena is called gamma correction.

• Images that are not corrected properly look either
bleached out or too dark.
• Varying gamma changes not only intensity, but also
the ratio of red to green to blue in a color images.
• Gamma correction has become increasingly
important, as the use of the digital images over
internet.
• Useful for general purpose contrast manipulation.
• Apply gamma correction on CRT (Television, monitor),
printers, scanners etc.
• Gamma value depends on device.

Piecewise-Linear Transformation
Functions
• Contrast Stretching
• Low contrast images can result from poor
illuminations.
• Lack of dynamic range in the imaging sensor, or even
the wrong setting of a lens aperture during image
acquisition.
• It expands the range of intensity levels in an image so
that it spans the full intensity range of display devices.
• Contrast stretching is obtained by setting
(r1,s1) = (rmin , 0) and (r2,s2) = (rmax , L-1)

Functions

Functions
• Intensity Level Slicing
• Highlighting specific range of intensities in an image.
• Enhances features such as masses of water in satellite
imagery and enhancing flaws in X-ray images.
• It can be Implemented two ways:
• 1) To display only one value (say, white) in the range of
interest and rests are black which produces binary
image.
• 2) brightens (or darkens) the desired range of
intensities but leaves all other intensity levels in the
image unchanged.

Functions
• Intensity Level Slicing

Functions
• Bit Plane Slicing
• Pixels are digital numbers composed of bits.
• 256 gray scale image is composed of 8 bits.
• Instead of highlighting intensity level ranges, we could
highlight the contribution made to total image
appearance by specific bits.
• 8-bit image may be considered as being composed of
eight 1-bit planes, with plane 1 containing the lowest-
order bit of all pixels in the image and plane 8 all the
highest-order bits.

Functions
• Bit Plane Slicing

Histogram Processing
• Histogram of a digital image with intensity levels in
the range [0,L-1] is a discrete function h(rk) = nk,
where rk is the kth intensity value and nk is the
number of pixels in the image with intensity rk
• Normalized histogram p(rk)=nk/MN, for k = 0,1,2..…..
L-1.
• Histogram manipulation can be used for image
enhancement.
• Information inherent in histogram also is quite useful
in other image processing applications, such as
image compression and segmentation.

Histogram Equalization
• Intensity mapping form
Conditions:
a) T(r) is a monotonically increasing function in the
interval [0, L-1] and
b)
In some formulations, we use the inverse in which case
(a) change to
a’) T(r) is a strictly monotonically increasing function in the
interval [0, L-1]
10),(  LrrTs
10),(1
 
ssTr
101)(0  LrforLrT

• Intensity levels in an image may be viewed as
random variables in the interval [0,L-1]
• Fundamental descriptor of a random variable is its
probability density function (PDF)
• Let pr(r) and ps(s) denote the PDFs of r and s
respectively
ds
dr
rpsp rs )()( 

r
r dwwpLrTs
0
)()1()(
)()1()()1(
)(
0
rpLdwwp
dr
d
L
dr
rdT
dr
ds
r
r
r 



 

1
1
)(


L
sps
1,...,2,1,0,)1()()1()(
00
  
Lk
MN
n
LrpLrTs
k
j
j
k
j
jrkk

• Transformation functions

Histogram Matching (Specification)
• Histogram equalization automatically determines a
transformation function produce uniform histogram
• When automatic enhancement is desired, equalization is a
good approach
• There are some applications in which attempting to base
enhancement on a uniform histogram is not the best
approach
• In particular, it is useful sometimes to be able to specify the
shape of the histogram that we wish the processed image
to have.
• The method used to generate a processed image that has a
specified histogram is called histogram matching or
specification

• Histogram Specification Procedure:
1) Compute the histogram pr (r) of the given image, and use
it to find the histogram equalization transformation in
equation
and round the resulting values to the integer range [0, L-1]
2) Compute all values of the transformation function G using
same equation
and round values of G
3) For every value of sk, k = 0,1,…,L-1, use the stored values
of G to find the corresponding value of zq so that G(zq) is
closet to sk and store these mappings from s to z.
1,...,2,1,0,)1()(
0
 
Lk
MN
n
LrTs
k
j
j
kk
1,...,2,1,0,)()1()(
0
 
LqrpLzG
q
i
izq

• Histogram Specification Procedure:
4) Form the histogram-specified image by first histogram-
equalizing the input image and then mapping every
equalized pixel value, sk , of this image to the corresponding
value zq in the histogram-specified image using the
mappings found in step 3.

Histogram Matching
rk Sk G(Zq)
0 1 0
1 3 0
2 5 0
3 6 1
4 6 2
5 7 5
6 7 6
7 7 7

Local Histogram Processing
• Histogram Processing methods discussed in the previous two
sections are Global, in the sense that pixels are modified by a
transformation function based on the intensity distribution of
an entire image.
• There are some cases in which it is necessary to enhance detail
over small areas in an image.
• This procedure is to define a neighborhood and move its center
pixel to pixel.
• At each location, the histogram of the points in the
neighborhood is computed and either a histogram equalization
or histogram specification transformation function is obtained.
• Map the intensity of the pixel centered in the neighborhood.
• Center of the neighborhood region is then moved to an
adjacent pixel location and the procedure is repeated.

Local Histogram Processing
• This approach has obvious advantages over repeatedly
computing the histogram of all pixels in the neighborhood
region each time the region is moved one pixel location.
• Another approach used sometimes to reduce computation
is to utilize non overlapping regions, but this method
usually produces an undesirable “blocky” effect.

Spatial Filtering
• Also called spatial masks, kernels, templates, and windows.
• It consists of (1) a neighborhood (typically a small window),
and (2) a predefined operation that is performed on the
image pixels encompassed by the neighborhood.
• Filtering creates a new pixel with coordinates equal to the
center of the neighborhood.
• If operation is linear, then filter is called a linear spatial
filter otherwise nonlinear.

Mechanics of Spatial Filtering

Spatial Correlation & Convolution
• Correlation is the process of moving a filter mask over the
image and computing the sum of the products at each
location.
• Convolution process is same except that the filter is first
rotated by 180 degree.

Chapter 3 image enhancement (spatial domain)

Smoothing Spatial Linear Filters
• Also called averaging filters or Lowpass filter.
• By replacing the value of every pixel in an image by
the average of the intensity levels in the
neighborhood defined by the filter mask.
• Reduced “sharp” transition in intensities.
• Random noise typically consists of sharp transition.
• Edges also characterized by sharp intensity
transitions, so averaging filters have the undesirable
side effect that they blur edges.
• If all coefficients are equal in filter than it is also
called a box filter.

Smoothing Spatial Linear Filters
• The other mask is called weighted average,
terminology used to indicate that pixels are
multiplied by different coefficient.
• Center point is more weighted than any other
points.
• Strategy behind weighing the center point the
highest and then reducing value of the coefficients
as a function of increasing distance from the origin
is simply an attempt to reduce blurring in the
smoothing process.
• Intensity of smaller object blends with background.

Order-Statistic (Nonlinear) Filters
• Response is based on ordering (ranking) the pixels
contained in the image area encompassed by the filter, and
then replacing the value of the center pixel with the value
determined by the ranking result.
• Best-known filter is median filter.
• Replaces the value of a center pixel by the median of the
intensity values in the neighborhood of that pixel.
• Used to remove impulse or salt-pepper noise.
• Larger clusters are affected considerably less. ?
• Median represents the 50th percentile of a ranked set of
numbers while 100th or 0th percentile results in the so-
called max filter or min filter respectively.

Sharpening Spatial Filters
• Objective of sharpening is to highlight transitions in
intensity.
• Uses in printing and medical imaging to industrial
inspection and autonomous guidance in military systems.
• Averaging is analogous to integration, so sharpening is
analogous to spatial differentiation.
• Thus, image differentiation enhances edges and other
discontinuities (such as noise) and deemphasizes areas
with slowly varying intensities.

Foundation
• Definition for a first order derivative (1) must be zero in
areas of constant intensity (2) must be nonzero at the onset
of an intensity step or ramp and (3) must be nonzero along
ramps.
• For a second order derivatives (1) must be zero in constant
areas (2) must be nonzero at the onset and (3) must be
zero along ramps of constant slope.
• First order derivative of a one dimensional function f(x) is
the difference of f(x+1) – f(x).
• Second order = f(x+1) + f(x-1) -2f(x)

Second Derivatives-The Laplacian

Second Derivatives - The Laplacian

Unsharp Masking and High boost
Filtering

Unsharp Masking and High boost
Filtering
• Unsharp Masking
– Read Original Image f(x,y)
– Blurred original image f’(x,y)
– Mask = f(x,y) – f’(x,y)
– g(x,y) = f(x,y) + Mask
• High Boost Filtering
– Read Original Image f(x,y)
– Blurred original image f’(x,y)
– Mask = f(x,y) – f’(x,y)
– g(x,y) = f(x,y) + k*Mask, where k>1

First Derivative – The Gradient

Combining Spatial Enhancement
Methods

Chapter 3 image enhancement (spatial domain)

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