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LINEAR FILTERING INIMAGE PROCESSING

APPLICATIONS

ByPrateek Joshi

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INTRODUCTION

Filtering is a technique for modifying or enhancing an image. An image is filtereed to emphasize certain features or remove

other features. Image processing operations implemented with filtering

includes Smoothing, Sharpening, and Edge enhancement.


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DEFINITION

Linear filteringis filtering in which the value of anoutput pixel is a linear combination of the values of

the pixels in the input pixel's neighborhood.

A pixel is the smallest single component of a digital image.

The more pixels used to represent an image, the closer the result canresemble the original.


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NOISE IN DIGITAL IMAGES

Digital images are prone to a variety of types of noise.Noise is the result of errors in the image acquisition processthat result in pixel values that do not reflect the true intensitiesof the real scene.There are several ways that noise can be introduced into animage, depending on how the image is created.Eg: If the image is scanned from a photograph made on film, the

film gain is a source of noise. Noise can also be the result of

damage to the film, or be introduced by the scanner itself. If the image is acquired directly in a digital format, themechanism for gathering the data (such as a CCD detector)can introduce noise.

Electronic transmission of image data can introduce noise.


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REMOVING THE NOISE

We can use linear filtering to remove certain types of noise.Certain filters, such as averaging or Gaussian filters, areappropriate for this purpose. For example, an averaging filteris useful for removing noise from a photograph.

Linear image processing is based on the same twotechniques as conventional DSP:o convolution ando Fourier analysis.

The process is carried out by convolving the original imagewith an appropriate filter kernel, producing the filtered image.


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LINEAR CONVOLUTION

Convolution is a neighborhood operation in which eachoutput pixel is the weighted sum of neighboring input pixels.

The matrix of weights is called the convolution kernel, also

known as the filter.

A convolution kernel is a correlation kernel that has beenrotated 180 degrees.


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For example, suppose the image is

A = [17 24 1 8 15

23 5 7 14 16

4 6 13 20 2210 12 19 21 3

11 18 25 2 9]and the convolution kernel is

h = [8 1 6

3 5 74 9 2]

STEPS

Rotate the convolution kernel 180deg about its center element. Slide the center element of the convolution kernel so that it lies on top of the (2,4) element of A. Multiply each weight in the rotated convolution kernel by the pixel of A underneath.

Sum the individual products from step 3.


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ence the (2,4) output pixel is


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LINEAR FILTERS

Uniform filter- The output image is based on a local averagingof the input filter where all of the values within the filter supporthave the same weight.

Gaussian filter- The use of the Gaussian kernel for smoothinghas become extremely popular. This has to do with certainproperties of the Gaussian (e.g. the central limit theorem,minimum space-bandwidth product) as well as several

application areas such as edge finding and scale spaceanalysis. .


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Performing Linear Filtering of ImagesUsing imfilter

Filtering of images, either by correlation or convolution, can beperformed using the toolbox function imfilter.

This example filters an image with a 5-by-5 filter containingequal weights. Such a filter is often called an averaging filter.

>>>>>>MATLAB


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A serious problem with image convolution is the enormousnumber of calculations that need to be performed, oftenresulting in unacceptably long execution times.Thus we use FFT convolution for faster execution.


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