Noise Removal in Digital Image by Using Six

8/3/2019 Noise Removal in Digital Image by Using Six

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Noise Removal In Digital Image By UsingNoise Removal In Digital Image By Using

Six Types Of FiltersSix Types Of Filters

Under guidance ofMr. K. Kiran Kumar ,M.Tech

Asst. Professor,

Dept.of E.C.E, B.I.T.I.T

Presented By

K. N. Dinesh Reddy(08F31A0431)

E. Hareesh (08F31A0434)

B. Gowtham Reddy(08F31A0445)

G. Govardhan (08F31A0449)

Department Of Electronics and Communication Engineering

B.I.T.Institute of Technology,

Hindupur-515212.


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OBJECTIVE

The purpose of these algorithms is to remove noise from a

signal that might occur through the transmission of an image.

Comparing the different algorithm results.


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Introduction

Modules Smoothing Algorithm

Mean Filter

Median Filter

Component Median Filter

Vector Median Filter Spatial Median Filter

Modified Spatial Median Filter

Block diagram

Advantages & ApplicationsConclusion

Reference

Outlinesutlines


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In image processing it is usually necessary to perform high

degree of noise reduction in a digital image.

In each snap of a digital photograph, a signal is transmitted

from a photon sensor to a memory chip embedded inside a

camera.

Transmission technology is prone to a degree of error, and noise

is added to each photograph.

Significant work has been done in both hardware and software

to improve the signal-to-noise ratio in digital photography.

Introductionntroduction


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In software, a smoothing filter is used to remove noise

from an image.

Each pixel is represented by three scalar values

representing the red, green, and blue chromatic

intensities.

At each pixel studied, a smoothing filter takes into

account the surrounding pixels to derive a more

accurate version of this pixel.

By taking neighboring pixels into consideration, extremenoisy pixels can be replaced.

However, outlier pixels may represent uncorrupted fine

details, which may be lost due to the smoothing

process.

moo ngoo ngAlgorithmslgorithms


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The Mean Filter is a linear filter which uses a maskover each pixel in the signal.

Each of the components of the pixels which fall underthe mask are averaged together to form a single

pixel.

This new pixel is then used to replace the pixel in thesignal studied.

Mean Filterean Filter


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Example:

8+5+3+2+7+1+4+6+98+5+3+2+7+1+4+6+9

99

Mean=5Mean=5

996644

117722

335588

Formula:


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Drawback in the Mean Filter is poor at maintaining edges

within the image.

The Median Filter is performed by taking the magnitude of all

of the vectors within a mask and sorting the magnitudes.

The pixel with the median magnitude is then used to replacethe pixel studied.

The Simple Median Filter has an advantage over the Mean

filter in that it relies on median of the data instead of the

mean.

The median of a set is more robust with respect to the presence

of noise.

Medianedian FilterFilter


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First of all you have to sort the values of vectors and then you

have to find out center value that is median value.Here in median filter we are taking the magnitude value.

If it will be matrix data means you have to sort the column values

first and row values.

Formula:

A=[4 2 3;7 9 6;2 5 6];

4 2 3 2 2 3

Median=5 A= 7 9 6 = 4 55 6

2 5 6 6 7 9

Example:Example:

5


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In the Component Median Filter each scalar

component is treated independently.

A filter mask is placed over a point in the signal. For

each component of each point under the mask, a

single median component is determined.

These components are then combined to form a new

point, which is then used to represent the point in

the signal studied.

Component Medianomponent MedianFilterilter


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When noise affects a point in a grayscale image, the result is

called salt and pepper noise.

In color images, this property of salt and pepper noise is typical

of noise models where only one scalar value of a point is

affected.

For this noise model, the Component Median Filter is more

accurate than the Simple Median Filter.


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Formula:

Component Median Filter 4 3 8 2 1 3

A= 2 7 3 = 4 3 5 = 3 5 1 5 5 7 8

Examplexample :


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Formula:

Vector Median Filter Result=min[31.3 29.4 53.8 33.2 45.7 29.4 31.6 35.9

31.6]

Second value is minimum so 3 is the vmf value.

Examplexample :


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The Spatial Median Filter (SMF) is a new noise removal filter.

The SMF and the VMF follow a similar algorithm and it will be shown

that they produce comparable results.

Here we are going to find out the depth of the set.

Using Spatial depth we are going to find out the Spatial Median of set.

First of all we have to find out the depth and we have to order that in

descending order.

According to that order we are going to replace pixel which one has firstrank in order (highest depth).

Spatial Median Filterpatial Median Filter


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Examplexample :Formula:

Here r1, r2, r3rN represent the x1, x2,.xN in rank order.Spatial Median Filter depth=[0.9573, 0.6542, 0.6787, 0.8936, 0.3937, 0.2808, 0.3647 ,

0.8543, 0.6537] Rank order=8 2 6 3 5 9 7 4 1First pixel has first rank so we are going to replace first pixel asSMF 8


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The SMF is similar to the VMF in that in both filters, the vectorsare ranked by some criteria and the top ranking point is used to

replace the center point.

No consideration is made to determine if that center point is

original data or not.

The unfortunate drawback to using these filters is the smoothing

that occurs uniformly across the image.

By this the areas where there is no noise, uncorrupted data isremoved unnecessarily.

Modified Spatial Medianodified Spatial MedianFilterilter


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But in the Modified Spatial Median Filter (MSMF), after

the spatial depth of each point within the mask is

computed, an attempt is made to use this information to

first decide if the masks center point is an uncorrupted

point.

If the determination is made that a point is not corrupted,

then the point will not be changed.


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Examplexample :Formula:

Here we are going to find the center pixel rank that is 5

th

pixelrank.5thpixel rank=7 so we replace this pixel value only to the

corrupted pixel value

From the SMF values we can get theMSMF i.e., T= 7


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Input Image

Different types ofAlgorithms

Noisy Image Impulse Detection

Output ImageRandom Noise

Generation

Block Diagram


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Simple to implementLow cost and highly reliable

portability

Advantagesdvantages

ApplicationsPhotoshop Applications

Installation in digital cameras


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We have successfully found out the corrupted pixel

and uncorrupted pixel in a noisy image by using

different filter techniques and we compared the

results.

Conclusiononclusion


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[1] J. W. Tukey, (1974). Nonlinear (Nonsuperposable) Methods forSmoothing Data. Conference Record EASCON, p. 673.

[2] N. C. Gallagher, Jr. and G. L. Wise, (1981). A The-oreticalAnalysis of the Properties of Median Filters.IEEE Transactions on

Acoustics, Speech, and Signal Processing, Vol. 29, pp. 1136-1141.[3] Jaakko Astola, Petri Haavisto, and Yrjo Neuvo, (1990). Vector

Median Filters. Proceedings of the IEEE, Vol. 78, No. 4, pp. 678-689.

[4] Probal Chaudhuri, (1996). On a Geometric Notion of Quantilesfor Multivariate Data. Journal of the American Statistical

Association, Vol. 91, No. 434, pp. 862-872.[5] Robert Serfling, (2002). A Depth Function and a Scale Curve

Based on Spatial Quantiles. In Y. Dodge (Ed.): Statistical DataAnalysis Based on the L1-Norm and Related Methods (pp. 25-38).Published by Birkhauser Basel.

[6] Yehuda Vardi and Cun-Hui Zhang, (2000). The Multivariate L1-median and Associated Data Depth. Proceedings of the National

Academy of Sciences, Vol. 97, No. 4, pp. 1423-1426.

References


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Noise Removal in Digital Image by Using Six

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