noise filtering

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`Noise Addition and Filtering

Presented By : Sara El-Masri Alaa

Sababbah Amna El-Sheikh

Ali

Supervised By : Dr. Samy Salamah

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Outline

1. Introduction .2. Image .3. Image noise .4. Source of image noise .5. Types of image noise .6. Filtering7. Filtering Techniques .8. Filters types .9. Conclusion .

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1. Introduction

• It is generally desirable for image brightness to be uniform except where it changes to form an image.

• There are factors, however, that tend to produce variation in the brightness of a displayed image even when no image detail is present.

• This variation is usually random and has no particular pattern.

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1. Introduction (cont.)

In many cases, it reduces image quality and is especially significant when the objects being imaged are small and have relatively low contrast.

This random variation in image brightness is designated noise.

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1. Introduction (cont.)

Image on the right has more noise than the image on the left

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Images

• There are two types of images :

Vector images

Digital images

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Vector Images

• Vector images made up of vectors which lead through locations called control points.

• Each of these control points has define on the x and y axes of the work plain .

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Digital Images

• A digital image is 2-dim array of real numbers

• 2-D image is divided into N rows and M columns

• the intersection of these rows and columns is known as pixels

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Types of Digital Images

• Binary images (black and white images)

• Gray scale images

• Color images

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Binary Images

• Each pixel is just black or white

• There is only two possible values for each pixel i.e. 0 or 1

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Gray Scale Images

• Each pixel value of gray scale images normally from 0 (black) to 255 (white)

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Color images • In color images each pixel has a particular color ; that

color being described by the amount of red , blue and green in it .

• Each of these components has a rang 0-255

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2. Image noise Noise in image , is any degradation in an image signal , caused by external disturbance while an image is being sent from one place to another place via satellite , wireless and network cable . We can model a noisy image as follows:

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Source of Image Noise

• Error occurs in image signal while an image is being sent electronically from one place to another .

• Sensor heat while clicking an image

• ISO factor ISO number indicates how quickly a camera’s sensor absorbs , light , higher ISO used mare chance of noticeable noise

• By memory cell failure.

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Types of Image Noise

1) Salt and pepper noise

2) Gaussian noise

3) Speckle noise

4) Uniform noise

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Salt and pepper noise

• It known as shot noise, impulse noise or Spike noise .

• Its appearance is randomly scattered white or black or both pixel over the image .

• there are only two possible values exists that is a and b and the probability of each is less than 0.2 .

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Salt and pepper noise (cont.)

Reasons for Salt and Pepper Noise:

1) By memory cell failure. 2) By malfunctioning of camera’s sensor cells. 3) By synchronization errors in image digitizing or transmission.

Where: pa, pb are the Probabilities Density Function (PDF), p(z) is distribution salt and pepper noise in image and A, B are the arrays size image.

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Salt and pepper noise (cont.)

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Original Image

Image with Salt and Pepper

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• filtering techniques :

Salt and pepper noise (cont.)

mean filtering .

Median filtering

Gaussian filtering

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Gaussian Noise

Gaussian noise is caused by random fluctuations in the signal , its modeled by random values add to an image

This noise has a probability density function [pdf] of the normal distribution. It is also known as Gaussian distribution.

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Gaussian Noise (cont.)

Without Noise With Gaussian Noise

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Image with Gaussian Noise

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Sources of Gaussian Noise

• In digital images arise during acquisition .

e.g. Sensor noise caused by poor illumination and/or high temperature

• Transmission

e.g. Electronic circuit noise .

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• filtering techniques :mean (convolution) filtering

Median filtering

Gaussian filtering

Gaussian Noise (cont.)

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Speckle Noise

• Speckle noise can be modeled by random values multiplied by pixel values of an image

• results from random fluctuations in the return signal from an object that is no bigger than a single image-processing element.

It increases the mean grey level of a local area.

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The distribution noise can be expressed by:

Where g(n,m), is the observed image , u(n,m) is the multiplicative component . and &(n,m) is the additive component of the speckle noise.

Speckle Noise

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Image with Noise

Original Image

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• filtering techniques :mean (convolution) filtering

Median filtering

Speckle Noise (cont.)

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Uniform Noise

• The uniform noise cause by quantizing the pixels of image to a number of distinct levels is known as quantization noise.

• Uniform noise can be analytically described by :

• The gray level values of the noise are evenly distributed across a specific range

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Uniform Noise (cont.)• Quantization noise has an approximately uniform

distribution

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Uniform Noise (cont.)

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3. Filtering

• Filtering image data is a standard process used in almost all image processing systems.

• Filters are used to remove noise from digital image while keeping the details of image preserved.

• The choice of filter is determined by the nature of the task performed by filter . Filter behavior . type of the data .

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Filtering Techniques

Linear Filtering

Non-Linear Filtering

Linear Filter

• Linear filters are used to remove certain type of noise.

• The linear filters work best with salt and pepper noise, and Gaussian noise.

• Gaussian and mean filters.

• Simple to design .

• These filters also tend to blur the sharp edges . destroy the lines and other fine details of image .

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Linear Filters – Example

Filtered Gaussian noise.

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Non-Linear Filters• Can preserve edges .

• Very effective at removing impulsive noise .

• They are more powerful than linear filters because they are able to reduce noise levels without blurring edges.

• Can be difficult to design.

• Median Filter.

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Non-linear Filter vs. linear Filter

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Filters Types

1) Median filter .

2) Wiener Filter .

3) Mean filter .

4) Gaussian filter

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Median Filter

• Median Filter is a simple and powerful non-linear filter .

• It is used for reducing the amount of intensity variation between one pixel and the other pixel.

• In this filter, we replaces pixel value with the median value .

• The median is calculated by first sorting all the pixel values into ascending order and then replace the pixel being calculated with the middle pixel value

• Salt and pepper noise.

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Median Filter

• Advantage: It is easy to implement. Used for de-noising different types of noises.

• Disadvantage: Median Filter tends to remove image details when the impulse

noise percentage is more than 0.4 %.

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Example : 3x3 Median

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Original

Salt & pepper%20

De-noising by Median filter

Original

Salt & pepper%60

De-noising by Median filter

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Wiener Filter

• The purpose of the Wiener filter is to filter out the noise that has corrupted a signal.

• This filter is based on a statistical approach.

• The goal of wiener filter is reduced the mean square error (MSE) as much as possible.

• Poisson noise , speckle noise .

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• One method that we assume we have knowledge of the spectral property of the noise and original signal.

• The Fourier domain of the Wiener filter is Where :• H*(u, v) = Complex conjugate of degradation function • Pn (u, v) = Power Spectral Density of Noise • Ps (u, v) = Power Spectral Density of non-degraded image • H (u, v) = Degradation function

Wiener Filter

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Wiener filter Example

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Mean Filter• Mean Filter (average filter) is a simple linear filter .

• Replace each pixel value in an image with the mean value of its neighbors, including itself.

• Gaussian noise .

• Advantage: Easy to implement Used to remove the impulse noise.

• Disadvantage: It does not preserve details of image. Some details are removes of image

with using the mean filter.

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Mean Filtering Example

Average filtering example using a 3 x 3 sampling window:Keeping border values unchanged

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Mean Filtering - Boundaries• Average filtering example using a 3 x 3 sampling

window:Extending border values outside with values at boundary

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Mean Filter Example

• (a) Original Image

• (b) Image corrupted by %12 Gaussian noise .

• (c)De –noising by mean filter

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Gaussian noise

• Gaussian is smoothing filter in the 2D convolution operation that is used to remove noise and blur from image.

• Probably the most useful filter (although not the fastest).

• Gaussian filtering is done by convolution each point in the input array with a Gaussian kernel and then summing them all to produce the output array.

Gaussian filter

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Gaussian filter Example

(a ) ) ( ) ( Original b Noisy c Gaussian filter

Image corrupted by %60 salt & Pepper Noise

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• For comparing original image and filtered image, we calculate following parameters: 1) Mean Square Error (MSE): The MSE is the cumulative square error

between the encoded and the original image defined by:

Where, f is the original image and g is the filtered image. The dimension of the images is m x n. Thus MSE should be as low as possible for effective filtering .

Performance Parameters

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2) Signal to Noise Ratio is defined by the power ratio between a signal and the background noise.

Where P is average power. Both noise and power must be measured at the same points in a system, and within system with same bandwidth.

Performance Parameters

𝑆𝑁𝑅=𝑃 𝒔𝒊𝒈𝒏𝒂𝒍 /𝑃𝒏𝒐𝒊𝒔𝒆

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3) Peak signal to Noise ratio (PSNR): – It is defined by:

PSNR = 10 log (255^2/mse)

Performance Parameters

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Implementation in Matlab

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Conclusion

• Enhancement of an noisy image is necessary task in image processing.

• Filters are used best for removing noise from the images.

• The decision to apply a which particular filter is based on the different noise level at the different test pixel location or performance of the filter scheme on a filtering mask.

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QUESTIONS ?Be nice ...

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