image enhancement in the spacial domain

8/2/2019 Image Enhancement in the Spacial Domain

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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:



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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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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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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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 enhancement




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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ii. Gray level slicing:

Highlight specific ranges of gray-levels only.

Same as double

thresholding!


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33


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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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 enhancement


pixel point processing

Intensity transformation with unknown image 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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for PGM images, L=256, k=0,1,2, , 255, rk=k/(L-1)=k/255


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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 enhancement


pixel point processing

Intensity transformation with unknown image 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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Chapter 3I E h t i th


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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.



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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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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.



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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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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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Spatial Domain

Chapter 3


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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.



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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.



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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.



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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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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



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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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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


S ti l D i


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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.


S ti l D i


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Spatial Domain


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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-
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