dip image enhancement
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Image FundamentalsImage Fundamentals
What is an image?
An image is a 2D function I(x,y), where x and y
are spatial coordinates and the value of I at anypair of coordinates (x,y) is called the intensity orgray level.
When (x,y) and the amplitude values of I all arefinite and discrete then the image is a DigitalImage.
Digital Image is a 2D array of numbersrepresenting the sampled version of an image
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PixelPixel
- The images are defined over a grid. Eachgrid location is called as picture elements or
most popularly as Pixel.
What is Digital Image Processing (DIP)?
DIP is manipulation of an image to improve orchange some qualities of the image. DIPencompasses all the various operations done
through a digital processor which can beapplied to image data.
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Why image processing?Why image processing?
Two goals of Image Processing:
- Improvement of pictorial information for human
interpretation.
OR
- Processing of scene data for automatic machineperception
Image Processing may be considered as the
preprocessing for a Pattern Recognition System
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Related Areas of Image ProcessingRelated Areas of Image Processing
Image Processing:
Input: Image ---- Output: Image
Image Analysis/Understanding:
Input: Image ---- Output: Measurements
Computer Vision:
Input: Image ---- Output: High-level
description
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Aspects of image processingAspects of image processing
Processing of image
Low levelQuality improvement
Mid levelFeature/attribute extraction
High levelEmulation of HumanVision
Image
Processing
Image
Processing
Computer
Vision
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Black & White and Colour ImagesBlack & White and Colour Images
Black & white images are depicted by gray levels,they dont have any colour information.
A (digital) colour image is a digital image thatincludes colour information for each pixel.
- A colour image is typically represented by BITdepth. With a 24-BIT image, the BITs are oftendivided into three groupings: 8 for Red, 8 for Green,
and 8 for Blue. Combinations of those bits are usedto represent other composite colours. A 24-BITimage offers 16.7 million different colour values.
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Image EnhancementImage Enhancement
The purpose of image enhancement is toprocess an image so that the result is more
suitable than the original image for a specificapplication
Two approaches of image enhancement: Spatial domain methods
- direct manipulation of pixels Frequency domain methods
- based on modifying the Fourier transform
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Spatial Domain MethodsSpatial Domain Methods
In spatial domain image enhancement
methods, manipulations are done directlyon the pixels
Here,
f(x,y) is the input imageTis the operator
g(x,y) is the processed (enhanced) image
)],([),( yxfTyxg =
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Image enhancement in spatialImage enhancement in spatial
domaindomain Two methods of processing in spatial domain:
- Point processing
s=T(r)
Enhancement at any point depends only onthe gray level of that point
- Mask processingProcessing is done using gray levels of pixel
neighbourhood
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Image enhancement in spatialImage enhancement in spatial
domaindomain Point processing
- When the neighbourhood is of size 1 x 1 (that isa single pixel) then gdepends only on the value
of fat (x,y) and Tbecomes a gray-level (or
intensity or mapping) transformation function as:s=T(r)
r& s are the gray levels of f(x,y) and g(x,y) at (x,y)- Point processing methods are based only on the
intensity of single pixels
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Image enhancement in spatialImage enhancement in spatial
domaindomain Contrast stretching
- A simple method of image enhancementusing point processing
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A 3x3 Mask
Image enhancement in spatialImage enhancement in spatial
domaindomain Mask:
Mask is small 2-D array of pixels. It is alsocalled as kernel or template or window or
filter
Mask processing or filtering:
- Processing is done using mask co-efficients
p
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Image enhancement in spatialImage enhancement in spatial
domaindomain
A neighbourhood about (x,y) is defined by using a square (orrectangular) sub-image area centered at (x,y)
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Some Basic Gray LevelSome Basic Gray Level
TransformationsTransformations Image negatives
Log Transformations Power Law Transformations
Piecewise-Linear TransformationFunctions:
Contrast stretching Gray-level slicing
Bit-plane slicing
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Linear: Negative, Identity
Logarithmic: Log, Inverse Log
Power-Law: nth power, nth root
Some Basic Gray LevelSome Basic Gray Level
TransformationsTransformations
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Image NegativesImage Negatives
Function reverses the order from black to white
so that the intensity of the output image
decreases as the intensity of the input increases.
The negative of an image with gray levels in the
range [0,L-1] is obtained by using the negativetransformation given as:
s=(L-1)-r
- Image negatives are used mainly in medical
images and to produce slides of the screen
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Image NegativesImage Negatives
Image negative function:
s=(L-1)-rOutput gray
levels
0 L-1 input gray levels
L-1
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Image enhancement in spatialImage enhancement in spatial
domaindomain
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Log TransformationsLog Transformations
s = c log(1+r)
c is a constant& 0 r
Compresses the dynamic range of images
with large variations in pixel values
I h i i l
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Image enhancement in spatialImage enhancement in spatial
domaindomain
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PowerPower--Law TransformationsLaw Transformations
It is has the basic form as
c & are positive constants
To account an offset
is the offset
Gamma correction:
- It is a process used to correct power-law
response phenomena
( )s c r
= +
crs =
PP L T f tiL T f ti
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=c=1: identity
PowerPower--Law TransformationsLaw Transformations
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Gamma correction in CRTGamma correction in CRT
Application of PowerApplication of Power LawLaw
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Application of PowerApplication of Power--LawLaw
TransformationsTransformations
Pi iPi i Li T f tiLi T f ti
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PiecewisePiecewise--Linear TransformationLinear Transformation
Contrast Stretching- To increase the dynamic range of the gray levels
in the image being processed
C t t St t hiC t t St t hi
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Contrast StretchingContrast Stretching
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Contrast StretchingContrast Stretching
The locations of (r1,s1) and (r2,s2) guides
the characteristics of the transformation
function
If r1= s
1and r
2= s
2the transformation is a
linear function and produces no changes
If r1=r2, s1=0 and s2=L-1, the transformationbecomes a thresholding function that results a
binary image (that has two gray levels)
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Contrast StretchingContrast Stretching
-Intermediate values of (r1,s1) and (r2,s2)
produce various degrees of spread in the
gray levels of the output image, thus
affecting its contrast.
Generally, it is assumed that
r1r2
& s1s2
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GrayGray--Level SlicingLevel Slicing
Used to highlight a specific range of gray
levels in an image
One approach is to
display a high value for all
gray levels in the range of
interest and a low valuefor all other gray levels, so
it produces binary image
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GrayGray--Level SlicingLevel Slicing
The second approach is to brighten the desired
range of gray levels but to preserve the
background and gray-level tonalities in the
image
Image enhancement in spatialImage enhancement in spatial
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g pg p
domaindomain
BITBIT Plane SlicingPlane Slicing
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BITBIT--Plane SlicingPlane Slicing
To highlight the contribution made to the total imageappearance by specific BIT in the image
In a gray level image of 8-BIT, each pixel isrepresented by 8 BITs. So, it can be consideredthat the image is composed of eight 1-BIT plan
(BIT plan 0 to BIT plan 7)
BIT plane 0 contains the least significant BIT(LSB) and plane 7 contains the most significantBIT (MSB)
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BITBIT--Plane SlicingPlane Slicing
The higher order BITs (top four) contain the
majority of visually significant data. The other BIT
planes contribute the more subtle details in theimage
Binary image can be obtained from BIT planslicing. Plane 7 corresponds exactly with an image
thresholded at gray level 128
That is- Pixel values between 0 to 127 0
- Pixel values between 128 to 255 1
BIT Plan Representation of anBIT Plan Representation of an
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BIT Plan Representation of anBIT Plan Representation of an
ImageImage
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BIT Plan Slicing of an ImageBIT Plan Slicing of an Image
BIT Pl Sli i f IBIT Plan Slicing of an Image
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BIT Plan Slicing of an ImageBIT Plan Slicing of an Image
Image enhancement in spatialImage enhancement in spatial
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Image enhancement in spatialImage enhancement in spatial
domaindomainHistogram: The plot of gray level (X-axis) versus number ofpixels with that gray level (Y-axis) is called a histogram
It is a discrete function h(l)=nlWhere l [0, L-1]is a gray value
nl= no. of pixels in the image having gray levell
Normalized Histogram:
It gives an estimate of the probability of occurrence of gray
level lNormalized histogramp(l)=nl/n
Where n=total number of pixels in an image
Image enhancement in spatialImage enhancement in spatial
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Image enhancement in spatialImage enhancement in spatial
domaindomain Histogram transformation
Dark image Bright image
Low-contrast image High contrast image
Hi t P iHi t P i
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Histogram ProcessingHistogram Processing
The shape of the histogram of an image doesprovide useful information about the possibility
for contrast enhancement
Types of processing:- Histogram equalization
- Histogram matching (specification)
- Local enhancement- Use of Histogram statistics for image
enhancement
Histogram Equalization
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Histogram Equalization
For gray levels that take on discrete values, wedeal with probabilities:p(rk)=nk/n
The technique used for obtaining a uniformhistogram is known as histogram equalization (or
histogram linearization)
Histogram equalization results are similar to
contrast stretching but offer the advantage of fullautomation
Histogram equalizationHistogram equalization
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Histogram equalizationHistogram equalization
Expand pixels in peaks over a wider range of
gray-levels
Squeeze low plans pixels into a narrower
range of gray levels
Flat histogram.
Histogram equalizationHistogram equalization
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Histogram equalizationHistogram equalization
To equalize the histogram, probabilities of
occurrences of the gray levels in the image are
taken into account.- That is the normalized histogram is used to
spread the histogram throughout the range of
the gray level of the image.
The transformation is
( )0 0
( )k k
j
k k r j
j j
ns T r P r
n= == = =
Hi t li tiHistogram equalization
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Histogram equalizationHistogram equalization
Histogram matching/specificationHistogram matching/specification
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g g pg g p
Histogram equalization does not allow interactiveimage enhancement and generates only one result
that is an approximation to a uniform histogram
Sometimes though, particular histogram shapes are
specified to highlight certain gray-level ranges
- The method used to generate a processed image
that has a specified histogram is called
histogram matching orhistogram specification
Histogram matching/specificationHistogram matching/specification
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Histogram matching/specificationHistogram matching/specification
The procedure for histogram-specification basedenhancement is:
1. Obtain the histogram of the given image
2. Use the following equation to pre-compute a
mapped levelsk for each level of rk
( )0 0( )
k kj
k k r j
j j
ns T r P r
n= == = =
Histogram matching/specificationHistogram matching/specification
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Histogram matching/specificationg g p
3. Obtain the transformation function G from the givenpz(z)using
4. Pre-compute zkfor each value of skusing iterative process
5. For each pixel in the original image, if the value of that pixel isrk, map this value to its corresponding level sk, then map levels
k
into final level zk
- In these mappings the pre-computed values from step (2) andstep (4) are used
( ) ( )1 1
z G s z G T r
= =
( ) ( )0 0
k k
k k z i k
i j
nv G z p z s
n= == = =
Histogram matching/specificationHistogram matching/specification
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g g pg g p
The principal difficulty in applying the histogramspecification method to image enhancement lies in
being able to construct a meaningful histogram
So,
- Either a particular probability density function (such
as a Gaussian density) is specified and then ahistogram is formed by digitizing the given function
- Or a histogram shape is specified on a graphicdevice and then is fed into the processor executing
the histogram specification algorithm.
Histogram matching/specificationHistogram matching/specification
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Histogram matching/specificationHistogram matching/specification
Histogram equalizationHistogram equalization
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g qg q
Histogram equalizationHistogram equalization
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Histogram equalizationHistogram equalization
Histogram equalizationHistogram equalization
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Histogram equalizationHistogram equalization
Local enhancementLocal enhancement
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Local enhancement using histogram is done
basically for two purposes:
- When it is necessary to enhance details
over small areas in an image
- To devise transformation functions based
on the gray-level distribution in theneighbourhood of every pixel in the image
Local enhancementLocal enhancement
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The procedure is:
- Define a square (or rectangular)
neighbourhood and move the center of thisarea from pixel to pixel
- At each location, the histogram of the pointsin the neighbourhood is computed and
either a histogram equalization or histogramspecification transformation function isobtained
Local enhancementLocal enhancement
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- This function is finally used to map the
gray level of the pixel centered in the
neighbourhood
- The centre of the neighbourhood region isthen moved to an adjacent pixel location
and the procedure is repeated
Local enhancementLocal enhancement
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Local enhancementLocal enhancement
Local enhancementLocal enhancement
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Local enhancementLocal enhancement
Local enhancementLocal enhancement
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Local enhancementLocal enhancement
Image enhancement usingImage enhancement using
Arithmetic/Logic operationsArithmetic/Logic operations
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Arithmetic/Logic operationsArithmetic/Logic operations
Logical
- AND, OR, NOT functionally complete
- In conjunction with morphological operations
Arithmetic
- Subtraction/Addition
- Multiplication / Division (as multiplication of
reciprocal)- May use multiplication to implement gray-levelmasks
Logical operationsLogical operations
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Logical operationsLogical operations
Image SubtractionImage Subtraction
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Image subtraction of a mask from an image
is given as:
Where,f(x,y) is the imageh(x,y) is the image mask
Image subtraction is used in medical
imaging, eg. Mask mode radiography
),(),(),( yxhyxfyxg =
Image subtractionImage subtraction
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Mask mode radiography-h(x,y) is the mask,f(x,y) is image taken after
injecting the contrast medium
Image subtractionImage subtraction
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Image subtraction isg(x, y) = f (x, y)
h(x, y)
Image averagingImage averaging
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g g gg g g
A noisy image can be modeled as:
g(x,y)=f(x,y)+(x,y)
Where,f(x,y) is the original image
(x,y) is the noise
Averaging k different noisy images:
==M
i
i yxgM
yxg1
),(1),(
Image AveragingImage Averaging
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AsKincreases, the variability of the pixel
values at each location decreases
- This means thatg(x,y) approachesf(x,y) as
the number of noisy images used in theaveraging process increases.
Registering of the images is necessary toavoid blurring in the output image.
Image AveragingImage Averaging
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g g gg g g
Image AveragingImage Averaging
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g g gg g g
Spatial FilteringSpatial Filtering
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Use of spatial masks for image processing
(spatial filters)
Linear and nonlinear filters(a 3x3 mask)
Low-pass filters eliminate or attenuate
high frequency components in the
frequency domain (sharp image details),and result in image blurring
p
Spatial FilteringSpatial Filtering
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High-pass filters attenuate or eliminate
low-frequency components (resulting insharpening edges and other sharp details)
Band-pass filters remove selectedfrequency regions between low and high
frequencies (for image restoration, notenhancement)
Spatial filteringSpatial filtering
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Different filters can be designed to do thefollowing:
- Blurring / Smoothing
- Sharpening
- Edge Detection
- All these effects can be achieved usingdifferent coefficients in the mask
Spatial filteringSpatial filtering
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Blurring / Smoothing- (Sometimes also referred to as averaging or
lowpass-filtering)
~Average the values of the centre pixel and itsneighbours
Purposes:
- Reduction of irrelevant details
- Noise reduction- Reduction of false contours (e.g. produced by
zooming)
Spatial filteringSpatial filtering
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Sharpening
- Used to highlight fine detail in an image
- Or to enhance detail that has been blurred
Edge Detection
Purposes:
- Pre-processing- Sharpening
Spatial filteringSpatial filtering
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A mask of a fixed size and having constant
weight in its every location is used to do
the filtering
The mask is moved from point to point on
the image
At each point (x,y), the response of the
filter at that point is calculated using apredefined relationship
Spatial filteringSpatial filtering
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For a linear spatial filtering, the response isgiven by a sum of products of the filtercoefficients and the corresponding image
pixels in the area spanned by the filter mask
For a 33 mask, the result (response) R, of
linear filtering with the filter mask at a point(x,y) in the image is
R=w(-1,-1)f(x-1,y-1)+w(-1,0)f(x-1,y)+ .... +w(0,0)f(x,y)+.. +w(1,0)f(x+1,y)+w(1,1)f(x+1,y+1)
Spatial filteringSpatial filtering
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Spatial FilteringSpatial Filtering
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The basic approach is to sum products betweenthe mask coefficients and the intensities of the
pixels under the mask at a specific location in the
image
For a 3 x 3 filter
992211 ... zwzwzwR +++=
1
mn
i i
i
R w z=
=
Spatial FilteringSpatial Filtering
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Spatial filteringSpatial filtering
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z3z2z1
z6z5z4
z9z8z7
Image pixels (N8)
Spatial filteringSpatial filtering
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Linear filtering of an image of size MN withfilter mask of size mn is given as
a=(m-1)/2 and b=(n-1)/2,
Forx=0,1,,M-1 andy=0,1,,N-1
Linear spatial filtering is also called convolvinga mask with an image
g(x ,y )= w (s, t)f(x+ s,y+ t)t= b
b
s= a
a
Smoothing FiltersSmoothing Filters
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Used for blurring (removal of small details
prior to large object extraction, bridging
small gaps in lines) and noise reduction.
Low-pass (smoothing) spatial filtering Neighborhood averaging
- Results image blurring
Smoothing FilteringSmoothing Filtering
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(Used in box filter) Weighted average
(used to reduce blurring)
Averaging filterAveraging filter
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In averaging filter
( , ) ( , )( , )
( , )
a b
s a t b
a b
s a s b
w s t f x s y t g x y
w s t
= =
= =
+ +=
Smoothing FilteringSmoothing Filtering
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Averaging using
different mask sizes
- Note the blurring at
greater mask size
Smoothing FilteringSmoothing Filtering
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Smoothing FilteringSmoothing Filtering
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1 1 1
1 1 1
1 1 1
* 1/9
Apply this scheme
to every single pixel !
Some more examples:
Blurring / Smoothing
Smoothing FilteringSmoothing Filtering
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1 2 1
2 4 2
1 2 1
* 1/16
Example 2:
Weighted average
Spatial FilteringSpatial Filtering
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Non-linear filters also use pixel
neighbourhoods but do not explicitly use
coefficients
e.g. noise reduction by median gray-levelvalue computation in the neighbourhood
of the filter
OrderOrder--statistics filtersstatistics filters
M di filt ( li )
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Median filter(nonlinear)
- Used primarily for noise reduction, eliminates
isolated spikes
Most important properties of the median:- Less sensible to noise than mean
- An element of the original set of values- Needs sorting
Median filterMedian filter
Th l l f h i l i l d b
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- The gray level of each pixel is replaced bythe median of the gray levels in the
neighborhood of that pixel (instead of by
the average as before)
To calculate the median of a set of gray
values, arrange the values in the set in
ascending order. Then the middle most
value in the string is the median (in case of
odd number of values)
1 2 3 3 4 4 5 6 6
4 1 2
6 5 3
3 4 6
4 1 2
6 4 3
3 4 6
Median filterMedian filter
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Sharpening filterSharpening filter
U d t hi hli ht fi d t il i i t h
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Used to highlight fine detail in an image or to enhanceimage that has been blurred
Accomplished by spatial differentiation, as it enhances the
sharp transition in gray levels First derivative of a 1-D functionf(x) is given as
And Second derivative
( 1) ( )f f x f xx
= +
2
2 ( 1) ( 1) 2 ( )
ff x f x f x
x
= + +
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First derivative enhances any sharp
transition
Second derivative enhances even a fine
transition
- Usually the second derivative is preferredwhen fine details are to be enhanced
Sharpening filterSharpening filter
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Sharpening filterSharpening filter First order derivatives produce thick edges and second
order derivatives much finer ones
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order derivatives much finer ones
A second order derivative is much more aggressive than
a first order derivative in enhancing sharp changes
Sharpening filterSharpening filterThe first and second order derivatives:
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1. First order derivative produces thicker edges
2. Second order derivative has a stronger response tofine detail such as thin lines and isolated points
3. First order derivative has a stringer response to agray level step
4. Second order derivative produces a doubleresponse at step changes in gray levels
Sharpening filterSharpening filter
Laplacian operator
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Laplacian operator- It is a linear operator; used for image
sharpening
For an image functionf(x,y), Laplacian isdefined as
2 2
22 2
f ff x y
= +
Sharpening filterSharpening filter
Partial second order derivative in X direction:
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Partial second order derivative in X-direction:
Partial second order derivative in Y-direction:
So,2 [ ( 1, ) ( 1, ) ( , 1) ( , 1)] 4 ( , )f f x y f x y f x y f x y f x y = + + + + +
2
2 ( 1, ) ( 1, ) 2 ( , )
fx y f x y f x y
x
= + +
2
2 ( , 1) ( , 1) 2 ( , )f
f x y f x y f x yy
= + +
Sharpening filterSharpening filter
If the centre coefficient of the Laplacian mask is
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If the centre coefficient of the Laplacian mask isnegative
If the centre coefficient of the Laplacian mask ispositive
2( , ) ( , ) ( , )g x y f x y f x y=
2
( , ) ( , ) ( , )g x y f x y f x y= +
Sharpening filterSharpening filter
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