Post on 06-Apr-2018
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Image Enhancement in the Spatial Domain
(Chapter 3)
Prepared by:
Mohammed Ali AbbakerFakher Aldin Yahia Omer
Waleed Ahmed Hussein
Diploma/M. Sc. On Computer Architecture and Networking
Third Term, 2011/12
Digital Image Processing (DIP) SC614Seminar
Supervised by:
Dr. Abdelrahim Elobeid Ahmed
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outline
Image enhancement
Image transformation
pixel point processing Intensity transformation with unknown image information
Intensity transformation with histogram information.
spatial filtering
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Image enhancement
The principal objective is to process an image so that the
result is more suitable than the original image for a specific
application
specific is important, because it establishes at the outset
that the techniques discussed in this seminar are very much
problem oriented
The best approach for enhancing X-ray images may not
necessarily be the best for enhancing pictures of Mars
transmitted by a space probe too
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Evaluation of image enhancement method There is no general theory of image enhancement. When an image is
processed:
for visual interpretation:
The algorithm performance evaluation depends ultimately on theviewers judgment.
subjective process, different form person to person & from situationto another.
for machine perception:
The evaluation task is somewhat easier.
objective process with specific object to achieve. For example, at
the recognition application: the object could as specific computationalrequirements. The best image processing method would be the oneyielding the best machine recognition results.
However, even in situations when a clear-cut criterion of performance canbe imposed on the problem, a certain amount of trial and error usually is
required before a particular image enhancement approach is selected.
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Image enhancement approaches
two broad categories:-
1. spatial domain methods:
based on direct manipulation of pixels in an imageimage plane.
2. frequency domain methods:
based on modifying the Fourier transform of an image.
Enhancement techniques like most of the other image
processing applications based on various combinations of
methods from these categories.
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Background
value f(x,y) at each x, y is called intensity
levelor gray level
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Digital image representation
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Image Transformation - Definition
Is a process of changing the color or grayscale
values of an image pixel by operations like
adjusting the contrast or brightness, sharpening
lines, modifying colors, or smoothing edges, etc
This discussion divides image transforms into two
types:
pixel point processing Intensity transformation with unknown image information
Intensity transformation with histogram information.
spatial filtering
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Intensity Transformations and Filters spatial domain :the aggregate of
pixels composing an image.
Spatial process expression:
g(x,y)=T[f(x,y)]
f(x,y) input image,
g(x,y) output image
T is an operator on f
defined over a neighborhood of
point (x,y)
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Spatial Domain Methods
f(x,y)
g(x,y)
g(x,y)
f(x,y)
Point pixel
Processing
Area/Mask
Processing
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Intensity Transformation 1 x 1 is the smallest possible neighborhood.
In this case g depends only on value of f at a single point
(x,y)
and we call T an intensity (gray-level or mapping)
transformation and write
s = T(r)
where r and s denotes respectively the intensity of g and f at
any point (x, y).
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Transform Functions and Curves (2)
Transforms can be applied to pixel values in a variety of
color modes
If the pixels are grayscale, thenp1
andp2
are values
between 0 and 255
If the color mode is RGB or some other three-component
model
f(p) implies three components, and the transform may be
applied either to each of the components separately or to the
three as a composite
For simplicity, we look at transforms as they apply to
grayscale images first
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Transform Functions and Curves (3)
An easy way to understand a transform function is to look
at its graph
A graph of transform function Tfor a grayscale image has
p1 on the horizontal axis andp2 on the vertical axis, with
the values on both axes going from 0 to 255, i.e., from
black to white (see figure 1)
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Transform Functions and Curves (4)
The transform in Figure 1.adoesnt change the
pixel values. The output equals the input.
The transform in Figure 1.b lightens all the
pixels in the image by a constant amount.
The transform in Figure 1.c darkens all the
pixels in the image by a constant amount.
The transform in Figure 1.d inverts the image,
reversing dark pixels for light ones.
The transform in Figure 1.e is a threshold
function, which makes all the pixels either black
or white. A pixel with a value below 128
becomes black, and all the rest become white.
The transform in Figure 1.fincreases contrast.
Darks become darker and lights become lighter. Figure 1 Curves for adjusting
contrast
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Transform Functions and Curves (5)
In Figure 2, weve applied the functions shown in Figure 1
so you can see for yourself what effect they have
Figure 2 Adjusting
contrast and brightness
with curves function
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Point Processing Transformations
Convert a given pixel value to a new pixel value based on some
predefined function.
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Image transformation
Image enhancement
Image transformation
pixel point processing Intensity transformation with unknown image information
Intensity transformation with histogram information.
spatial filtering
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1- Identity Transformation
Some Basic Intensity Transformation Functions
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2- Negative Image Negative of an image with intensity levels in the range [0,
L-1] is obtained using the expression
s = L1r
Suited for enhancing white or gray detail embedded in dark
regions of an image specially when the black areas are
dominant in size
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3- Contrast Stretching or Compression
Stretch gray-level ranges where
we desire more information
(slope > 1).
Compress gray-level ranges that
are of little interest
(0 < slope < 1).
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Thresholding
Special case of contrast compression
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3- Contrast-Stretching Transformations
ErmrTs
)(1
1)(
where rrepresents the intensities of the input image, s
the corresponding intensity values in the output image,
andEcontrols the slope of the function.
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Fig. 3.2(a): Produce an image of higher contrast than the original in themiddle by:
by darkening the levels below m & compressing values of r into a narrowrange of s toward black
By brightening the levels above m in the original image through &compressing values of r into a narrow range of s toward white.
Fig. 3.2(b): special compressing techniques T(r) produces a two-level
(binary) image. A mapping of this form is called a thresholding function.
Thresholding:
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i. Contrast Stretching: expands the range of intensity levels in an
image so that it spans the full intensity range
Points: (r1, s1) , (r2, s2)
if: r1 = s1 and r2 = s2linear transformation that produces nochanges in the intensity levels
if: r1 = r2 and s1 = 0 and s2 =L -1the transformation becomes athresholding function that creates a binary image
intermediate values of (r1, s1) , (r2, s2) produces various degrees of
spread in the intensity levels of the output image, thus affecting its
contrast
Use: (r1, s1) = (rmin, 0) and (r2, s2) = (rmax,L - 1)
Piecewise-Linear Transformation Functions
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Contrast stretching
Low-contrast images can result from:
poor illumination.
lack of dynamic range in the imaging sensor.
or even wrong setting of a lens aperture during image
acquisition.
The idea behind contrast stretching is to increase the
dynamic range of the gray levels in the image being
processed.
The implementation through wisely slices the linear
transformation line into different slopes
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Piecewise-Linear Transformation Functions
ii. Gray level slicing:
Highlight specific ranges of gray-levels only.
Same as double
thresholding!
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33
Piecewise-Linear Transformation Functions
iii. Bit-Plane Slicing :pixels are digital numbers composed of bits
In the 256-level gray-scale image is composed of 8 bits
each pixel is represented by 8 bits
each 8bit would distributed to 8-planes
Highlighting the contribution made by a specific bit.
Each bit-plane is a binary image
Useful for image compression
Storing planes: 5, 6, 7, and 8 requires 50% less storage
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4- Logarithmic transformation
Enhance expand details in the darker regions of an image at
the expense of detail in brighter regions.
( ) ( rcrTs +== 1log
The dynamic range of the Fourier coefficients (i.e. the intensity values in the Fourier image)
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Exponential transformation
Log inverse transformation
Reverse effect of that obtained using logarithmic mapping.
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Log transformation
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41
5- Power-Law (Gamma) Transformations
Basic form is s = c r
wherec and : positive constants Transformation maps a narrow range of dark input values into a
wider ranger of output values, with the opposite being true for
higher value of input levels Family of possible transformation curves obtained simply by
varying Identity transformation when: c = = 1
Gamma correction: for displaying an image accurately on acomputer screen
Too dark
Washed out
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Image transformation
Image enhancement
Image transformation
pixel point processing
Intensity transformation with unknown image information
Intensity transformation with histogram information.
spatial filtering
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Histogram Equalization
A fully automatic gray-level stretching technique.
Need to talk about image histograms first ...
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Image Histograms
An image histogram is a plot of the gray-level frequencies (i.e.,
the number of pixels in the image that have that gray level).
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Image Histograms (contd)
Divide frequencies by total number of pixels to represent
as probabilities.
Nnp kk /=
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Image Histograms (contd)
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Properties of Image Histograms
Histograms clustered at the low end correspond to dark images.
Histograms clustered at the high end correspond to bright
images.
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Properties of Image Histograms (contd)
Histograms with small spread correspond to low contrast
images (i.e., mostly dark, mostly bright, or mostly gray).
Histograms with wide spread correspond to high contrast
images.
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Properties of Image Histograms (contd)
Low contrast High contrast
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Histogram Equalization
The main idea is to redistribute the gray-level values uniformly.
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Histogram Equalization (contd)
In practice, the equalized histogram might not be completely
flat.
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Probability - Definitions
Random experiment: an experiment whose result is not
certain in advance (e.g., throwing a die)
Outcome: the result of a random experiment
Sample space: the set of all possible outcomes (e.g.,
{1,2,3,4,5,6})
Event: a subset of the sample space (e.g., obtain an odd
number in the experiment of throwing a die = {1,3,5})
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Random Variables - Review
A function that assigns a real number to random experiment
outcomes (i.e., helps to reduce space of possible outcomes)
X(j)
X: # of heads
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Random Variables - Example
Consider the experiment of throwing a pair of dice
Define the r.v. X=sum of dice
X=x corresponds to the event
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Probability density function
Theprobability density function(pdf) is a real-valued function
fX(x) describing the density of probability at each point in the
sample space.
In the discrete case, this is just a histogram!
Gaussian
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Probability distribution function
The integral offX(x) defines theprobability distribution function
FX(x) (i.e., cumulative probability)
In the discrete case, simply take the sum:
fX(x) FX(x)
GaussianfX(a)da
non-decreasing
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Probability distribution function (contd)
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Uniform Distribution
fX(x) FX(x)
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Random Variable Transformations
Suppose Y=T(X)
e.g., Y=X+1
If we know fX(x), can we find fY(y)?
Yes; it can be shown that:
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Transformations of r.v. - Example
=0, =1
=1, =1
0
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Special transformation!
1 1( ) ( )
1( ) [ ( ) ] [ ( ) ] 1
( )Y X X x T y x T yX
dX f y f x f x
dY f x
Proof:
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Histogram Equalization (contd)
for PGM images, L=256, k=0,1,2, , 255, rk=k/(L-1)=k/255
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Histogram Equalization (contd)
then, de-normalize:
skx (L-1)
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Histogram Equalization Example
3 bit
64 x 64 image
input histogram equalized histogram
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Histogram Equalization Examples
equalized images and histogramsoriginal images and histograms
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Histogram matching
The desired shape of histogram is specified (not
necessarily uniform)
Derivation of histogram matching function:
s
uniform
r
inputz
desireds=T(r)
histogram
equalization
s=G(z)
z=G
-1
(s)
z=G-1(T(r))
histogram
equalization
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Histogram Matching
To generate a processed image that has a specified
histogram. (pz(z) is the specified probability density
function)
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Implementation
Inversefunction
of G
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Histogram Specification Example
3 bit
64 x 64 image
specified histogram
actual histogram
input histogram
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Histogram Statistics
1
0
( ) ( ) ( )L
n
n i i
i
r r m p r
1
0
( )L
i i
i
m r p r
1 1
0 0
1( , )
M N
x y
f x yMN
12 2
2
0
( ) ( ) ( )L
i i
i
r r m p r
1 1 2
0 0
1 ( , )M N
x y
f x y mMN
n-th momentaround mean
Variance(2nd moment)
Useful for estimating image contrast!
Mean(average intensity)
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Local Histogram Statistics
12 2
0
Local variance
( ) ( ) xy xy xy
L
s i s s i
i
r m p r
1
0
Local average intensity
( )
denotes a neighborhood
xy xy
L
s i s ii
xy
m r p r
s
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Using Histogram Statistics
for Image Enhancement
Useful when parts of the image might contain hidden
features.
Task: enhance darkareas without changing
bright areas.
Idea: Find dark, low contrastareas using local statistics.
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Using Histogram Statistics
for Image Enhancement: Example
0 1 2
0 1 2
( , ), if and( , )
( , ), otherwise
: global mean; : global standard deviation
0.4; 0.02; 0.4; 4
xy xys G G s G
G G
E f x y m k m k k g x y
f x y
m
k k k E
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Image transformation
Image enhancement
Image transformation
pixel point processing
Intensity transformation with unknown image information
Intensity transformation with histogram information.
spatial filtering
Chapter 3Image Enhancement in the
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Image Enhancement in theSpatial Domain
Enhancement Using
Arithmetic/Logic Operations1. Arithmetic/logic operations involving images
are performed on a pixel-by-pixel basisbetween two or more images (this excludes thelogic operation NOT, which is performed on asingle image).
2. The AND and OR operations are used formasking: that is for selecting subimages in animage.
3. Image multiplication finds use in enhancementprimarily as a masking operation that is moregeneral than the logical masks, since it canimplement gray-level rather than binary masks.
Chapter 3h h
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Image Enhancement in theSpatial Domain
Chapter 3I E h t i th
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Image Enhancement in theSpatial Domain
Image Subtraction1. The difference between two images f(x, y) and h(x,y) is expressed as
g(x. y) = f(x. y) - h(x,y) .
2. The key usefulness of subtraction is the enhancement ofdifferences
between images.
3. higher-order bit planes of an image carry a significant amount of visually relevant detail,
while the lower planes contribute more to fine (often imperceptible) details. If these lowerplanes are extracted out , by subtracting the higher-order bit planes image form the original
image . Then we can enhance these fine details of the image.
4. we note also that change detection via image subtraction
finds another major application in the area of segmentation. Basically, segmentation
techniques attempt to subdivide an image into regions based on a specified criterion. Image
subtraction for segmentation is used when the criterion is "changes." For instance, in tracking(segmenting) moving vehicles in a sequence of images, subtraction is used to remove
all stationary components in an image. What is left should be the moving elements
in the image, plus noise.
Chapter 3I E h t i th
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Image Enhancement in theSpatial Domain
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Chapter 3Image Enhancement in the
Spatial Domain
Image Averaging1- Consider a noisy image g(x, y ) formed by the addition of noise (x, y) to an
original imagef(x, y); that is,
g(x,y) = f(x,y) + (x,y)
2- The assumption is that at every pair of coordinates (x, y) the noise is uncorrelated,and
has zero average value.
E((x,y,t)* (x,y,t+))=0 ; for 0; = for =0.
E((x,y,t))=0.
3- The objective of the Averaging procedure is to reduce the noise content by adding a set
of noisy images, {gi( x, y)}. If the noise satisfies the constraints just stated, if an image
(x, y) is formed by averaging K different noisy images,then
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Chapter 3Image Enhancement in the
Spatial Domain Then it follows that
E{ (x, y)} = f(x, y) And
As K increases, indicates that the variability (noise) ofthe
pixel values at each location (x, y) decreases, and hence E{g(x,
y)} f(x, y). This means that (x, y) approaches f(x, y) as the
number of noisy images usedin the averaging process
increases.
Chapter 3Image Enhancement in the
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Image Enhancement in theSpatial Domain
Chapter 3I E h t i th
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Image Enhancement in theSpatial Domain
Spatial Filtering1- Filtering is neighborhood operations work with the values of the image pixels in the neighborhood
and the corresponding values of a subimage that has the same dimensions as the neighborhood.
2- The subimage is called afilter, mask,kernel, template, or window, the first three terms being the
most prevalent terminology. The values in a filter subimage are referred to as coefficients, rather
than pixels.
3- The process consists simply of moving the filter mask from point to point in an image.
4- Spatial filters categorized in to two groups linear spatial filtering and non linear spatial filtering .
5- For linear spatial the response is given by a sum of products of the filter coefficients and the
corresponding image pixels in the area spanned by the filter mask.
6- In general, linear filtering of an imagef of size M X N with a filter wmaskofsize m X n is given by
the expression:
a = (m - 1)/2 and b = (n -1 )/2.
To generate a complete filtered image this equation must be applied forx = 0,1,2,.. , M - 1 andy = 0, 1,2,
.... N - 1.From the above equation m &n are odd numbers.
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Chapter 3Image Enhancement in the
Spatial Domain
With the previous approach, there will be bands of pixelsnear the border that will have been processed with a partialfilter mask.
Other approaches include "padding" the image by addingrows and columns of O's (or other constant gray level), orpadding by replicating rows and columns,or Mirroring .The padding is then stripped off at the end of the process.This keeps the size of the filtered image the same as the
original. but the values of the padding will have an effectnear the edges that becomes more prevalentas the size ofthe mask increases.
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Chapter 3Image Enhancement in the
Spatial Domain
Chapter 3
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Chapter 3Image Enhancement in the
Spatial DomainSmoothing Spatial Filters
1- Smoothing filters are used for blurring and for noise reduction. Blurring isused in preprocessing steps, such as removal of small details from an imageprior to (large) object extraction.And bridging of small gaps in lines or curves.
Noise reduction can be accomplished by blurring with a linear filter and alsoby nonlinear filtering.
2- The output (response) of a smoothing. linear spatial filter is simply the average of thepixels contained in the neighborhood of the filter mask. These filters sometimes arecalled averaging filters.
3- This process results in an image with reduced "sharp" transitions in gray levels. Because
random noise typically consists of sharp transitions in gray levels. the most obviousapplication of smoothing is noise reduction. However edges (which almost always aredesirable features of an image) also are characterized by sharp transitions in gray levels.So averaging filters have the undesirable side effect that they blur edges.
Chapter 3Image Enhancement in the
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Image Enhancement in theSpatial Domain
1- Another application of this type of process includes the smoothing of false contours that
result from using an insufficient number of gray levels
2- A major use of averaging filters is in the reduction of "irrelevant" detail in an image. By
"irrelevant" we mean pixel regions that are small with respect to the size of the filter mask.
3- The averaging scheme deployed here can be the conventional one (summing and divide by
the number of entities) or using a weight to each individual pixel targeted by the MASK .
4- The general implementation for filtering an MxN image with a weighted averaging filter of
size mX n (m and nodd) is given by the expression:
5- From the expression smoothing filters are linear spatial filters.
Chapter 3Image Enhancement in the
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Spatial Domain
As mentioned earlier, an important application of spatial averaging is to blure the imagefor
the purpose getting a gross representation of objects of interest, such that the intensity of
smaller objects blends with the background and larger objects become "bloblike" and easy to
detect. The size of the mask establishes the relative size of the objects that will be blended
with the
Background.
Chapter 3Image Enhancement in the
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gSpatial Domain
Non Linear Spatial Filter1- Nonlinear spatial filters also operate on neighborhoods, and the mechanics of sliding a mask
past an image are the same as was just outlined. In general, however, the filtering operation is
based conditionally on the values of the pixels in the neighborhood under consideration, and
they do not explicitly use coefficients in the sum-of-products manner described.
2- Order-statistics filters are nonlinear spatial filters whose response is based on ordering
(ranking)the pixels contained in the image area encompassed by the filter. Then replacing
the value of the center pixel with the value determined by the ranking result.
3- Median filters are Order-statistics filters replaces the value of the centre pixel value with
the Median of the gray levels in the neighborhood of that pixel and the pixel. Median filters
are quite popular because for certain types of random noise. They proivde excellent
noise-reduction capabilities, with considerably less blurring than linear smoothing filters of
similar size. Median filters arce particularlv effective in the presence ofimpulse noise also
called salt-And-pepper Noise because of its appearance as white and black dots superimposed
on an image.4- In fact, isolated clusters of pixels that are light or dark with respect to their neighbors, and
whose area is less than n^2/2 (one-half the filter area), are eliminated by an n X n median
filter.
Chapter 3
Image Enhancement in the
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Image Enhancement in theSpatial Domain
Chapter 3Image Enhancement in the
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gSpatial Domain
Sharpening Spatial Filters1- Principal objective of sharpening is to highlight fine detail in animage or to enhance detail that has been blurred, either in error or as
a natural effect of a particular method of image acquisition.
2- Sharpening could be accomplished by spatial differentiation.Fundamentally, the strength of the response of a derivative operator
is proportional to the degree of discontinuity of the image at the
point at which the operator is applied. Thus, image differentiation
enhances edges and other discontinuities (such as noise) and
deemphasizes areas with slowly varying gray-level values
Chapter 3Image Enhancement in the
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Image Enhancement in theSpatial Domain
The derivatives of a digital function are defined in terms of
differences. There are various ways to define these differences.
However, we require that and definition we use for a first derivative
(1) must be zero in flat segments (areas of constant gray-level
values); (2) must be nonzero at the onset of a gray-level step or
ramp; and (3) must be nonzero along ramps. Similarly, anydefinition ofa second derivative (1) must be zero in flat areas; (2)
must be nonzero at the
onset and end of a gray-level step or ramp; and (3) must be zero
along ramps of constant slope. Since we are dealing with digital
quantities whose values are finite, the maximum possible gray-levelchange also is finite, and the shortest distance over which that
change can occur is between adjacent pixels.
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age a ce e eSpatial Domain
1- A basic definition of the first-order derivative of a one-dimensional function
f(x) is the difference:
Similarly, we define a second-order derivative as the difference:
2- It is easily verified that these two definitions satisfy the conditions stated previously
regarding derivatives of the first and second order.
3- In summary. comparing the response between first- and second-order derivatives. we arriveat the following conclusions. (l) First -order derivatives generally produce thicker edges in animage. (2) Second-order derivatives have a stronger response to fine detail , such as thin lines
and isolated points. (3) First-order derivatives generally have a stronger response to a gray-level step. (4) Second-order derivatives produce a double response at step changes in graylevel. We also note of second-order derivatives that for similar changes in gray-level values inan image. Their response is stronger to a line than to a step. and to a point than to a line.
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Image Enhancement in theSpatial Domain
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gSpatial Domain
The Laplacian
1- The simplest isotropic derivative operator is theLaplacian, which, for a function(image)f(x,y)of two variables, is defined as:
2- The digital implementation of the two-dimensional Laplacian with recalling the previous
definition of the second derivatitor, and obtained by summing these two components:
Which gives an isotropic result for rotations in increments of 90 deg.
3- The diagonal directions can be incorporated in the definition of the digital Laplacian by adding
two more terms , one for each of the two diagonal directions . The total subtracted from the
difference terms now would be -8f(x, y).
4- Because the Laplacian is a derivative operator. Its use highlights gray-level discontinuities in
an image and deemphasizes regions with slowly varying gray levels. This will tend to produceimages that have grayish edge lines and other discontinuities all superimposed on a dark.
featureless background.
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Spatial Domain
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Spatial Domain
The basic way in which we use the Laplacian for image enhancement is as follows:
g(x,y)= if the center coefficient of the Laplacian mask is negative.
g(x,y)= if the center coefficient of the Laplacian mask is positive.
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gSpatial Domain
1- Other way of generating a sharpened Immage as laplacian is
to subtract a blurred image version from the original .)
2- A slight further generalization of sharpping is called high-boost filtering. A high-boost filtered image is defined at any
point (x, y) as:g(x,y)=A if the center coefficient of the Laplacian
mask is negative.
g(x,y)= A if the center coefficient of the Laplacianmask is positive.
If A is large enough, the high-boost image will beapproximately equal to the original image multiplied by aconstant.
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Questions???!
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References
R.C.Gonzalez, R.E.Woods. 2002.Digital Image Processing. 2ndEdition. s.l. : Prentice Hall, 2002.
http://www.imageprocessingplace.com/downloads_V3/dip3e_downl
oads/dip3e_classroom_presentations/DIP3E_CH03_Art_PowerPoint
.zip
http://www.cse.unr.edu/~bebis/CS474/Lectures/IntensityTransforma
tions.ppt
www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppt
ebookbrowse.com/3-digital-image-processing-ppt-d178445572
moodle.ncnu.edu.tw/mod/resource/view.php?id=88282
http://www.cs.bgu.ac.il/~klara/ATCS111/Intensity%20Transformati
on%20and%20Spatial%20Filtering%20-
http://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/dip3e_classroom_presentations/DIP3E_CH03_Art_PowerPoint.ziphttp://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/dip3e_classroom_presentations/DIP3E_CH03_Art_PowerPoint.ziphttp://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/dip3e_classroom_presentations/DIP3E_CH03_Art_PowerPoint.ziphttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.moodle.ncnu.edu.tw/mod/resource/view.php?id=88282http://www.cs.bgu.ac.il/~klara/ATCS111/Intensity%20Transformation%20and%20Spatial%20Filtering%20-Gonzales%20Chapter%203.1-3.3.ppthttp://www.cs.bgu.ac.il/~klara/ATCS111/Intensity%20Transformation%20and%20Spatial%20Filtering%20-Gonzales%20Chapter%203.1-3.3.ppthttp://www.cs.bgu.ac.il/~klara/ATCS111/Intensity%20Transformation%20and%20Spatial%20Filtering%20-Gonzales%20Chapter%203.1-3.3.ppthttp://www.cs.bgu.ac.il/~klara/ATCS111/Intensity%20Transformation%20and%20Spatial%20Filtering%20-Gonzales%20Chapter%203.1-3.3.ppthttp://www.cs.bgu.ac.il/~klara/ATCS111/Intensity%20Transformation%20and%20Spatial%20Filtering%20-Gonzales%20Chapter%203.1-3.3.ppthttp://www.moodle.ncnu.edu.tw/mod/resource/view.php?id=88282http://www.moodle.ncnu.edu.tw/mod/resource/view.php?id=88282http://www.moodle.ncnu.edu.tw/mod/resource/view.php?id=88282http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.ebookbrowse.com/3-digital-image-processing-ppt-d178445572http://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.kau.edu.sa/GetFile.aspx?id=94771&fn=CS482_3.ppthttp://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/dip3e_classroom_presentations/DIP3E_CH03_Art_PowerPoint.ziphttp://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/dip3e_classroom_presentations/DIP3E_CH03_Art_PowerPoint.ziphttp://www.imageprocessingplace.com/downloads_V3/dip3e_downloads/dip3e_classroom_presentations/DIP3E_CH03_Art_PowerPoint.zip