MATLAB

2Image Processing

Filtering

Linear Filtering(using Convolution and Correlation)

Image Noise

Edge detection

Is a technique for modifying or enhancing an image;

Is a neighbourhood operation;

Linear filtering is filtering in which the value of an output pixel, is a linear combination of the values of the pixels in the input pixels neighbourhood.

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Linear filtering of an Image is achieved through an operation called convolution.

In convolution the value of an output pixel is computed as a weighted sum of neighbouring pixels.

The matrix of weights is called the convolution kernel(filter).

The convolution kernel is rotated 180 about its centre element.

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Similar to convolution;

The value of the output pixel is computed as a weighted sum of neighbouring pixels;

The correlation Kernel is not rotated during the computation.

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In Matlab filtering of images either by correlation or convolution can be performed using imfilter toolbox function.

It uses correlation by default imfilter(A,h)

For using convolution imfilter(A,h,conv)

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Example 1 :

imfilter, does not convert input images to the output.

>>h=ones(5,5)/25; I1=imfilter(I,h);

(I is original image andh is an averaging filter)

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Example 2 :

imfilter, does not convert input images to the output.

>>h=ones(5,5)/25; >>I1=imfilter(I,h,conv); >> imshow(I),figure,

imshow(I1);

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Zero padding imfilter function(notice the black border in the filtered image)

To avoid this, pass the optional argument replicate

>>imfilter(I,h,replicate);

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o fspecial,createspredefined2Dlinearspatialfilters:

>>h=fspecial(type,parameters)(typeisthefiltertypeandparametersdefinethespecifiedfilter)

o After creating a filter with fspecial we can apply directly to your image using imfilter

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Example 2 :

>>I=imread(elarco.jpg); >> h=fspecial('unsharp'); >> I1=imfilter(I,h); >>imshow(I),figure, imshow(I1);

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filter2, performs two dimensional correlation; converts the input to double:

conv2, performs two dimensional convolution;

Convn, performs multidimensional convolution

(see help menu in matlab)

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Devise a 3x3 mask which causes no change in the image.

Apply larger and larger averaging filters to this image. What happens?

Read through the help page of the fspecialfunction, and apply some of the other filters to an image.

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Degradation in the image signal

Matlab function for adding noise

J =imnoise (I,type)

Where I represents the image and type one of the following:

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>>J=imnoise(B,'gaussian');

>>imshow(B),title('Originalimage'),

>>figure,imshow(J),title('gaussiannoise');

Examples:

>> K=imnoise(G,'salt & pepper');

>> imshow(G),title('Original image'),

>> figure, imshow(K),title('salt&pepper noise')

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Examples:

The aim of image smoothing is to diminish the effects of camera noise, spurious pixel values, missing pixel values etc.

In the frequency domain, this process refers to the suppression of high frequencies.

Techniques for image smoothing: neighbourhood averaging, edge-preserving smoothing.

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Example:

>>h= fspecial('average');

>> Y=imfilter(G,h);

>> imshow(G)

>> figure,imshow(Y)

Mean filtero replaces each pixel value in an image with the mean

(`average') value of its neighbours, including itself.

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>>h=fspecial(average)>>B=imfilter(I,h)

(filtered image I using h filter)

Median filter(medfilt2), is a nonlinear operation, replaces the pixel value with the median of neighbouring pixel values.

>>B = medfilt2(A, [m n]),(Where A is the image and [m n] the neighbourhood)

Example:

>>YY=medfilt2(G,[33]);>>imshow(G)>>figure,imshow(YY)

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Gaussian smoothing operator the Gaussian smoothing operator is a 2-Dconvolution

operator that is used to `blur' images and remove detail

and noise

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Use imnoise function to add salt&pepper noise to an image.

Now apply median and mean filter to the obtained image.

Which one is better? Why?

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We can only do edge tracing for gray images

Edges contain some of the most useful information in an image.

We may use edges to measure the size of objects in an image; to isolate particular objects from their background; to recognize or classify objects.

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Matlab function (edge ) syntax edge(image,'method',parameters. . . )

Finds edges in greyscale image.

edge supports the following detectors: sobel prewitt Roberts Laplacian of Gaussian Canny zerocross

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Example : Sobel operator - Canny Operator

>>Im=imread(BomJesus.jpeg);

>> figure, imshow(Im)

>> BW1 = edge(Im,'sobel'); >>BW2 = edge(Im,'canny');

>> figure, imshow(BW1)

>> figure, imshow(BW2)

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Original image Sobel operator Canny operator

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Look in help Matlab for edge function and experiment all the operators

Try the effect of LoG filters using different width Gaussians

What is the general effect of increasing the Gaussian width? Notice particularly the effect on features of different sizes and thicknesses.

Compare the result of applying the Roberts Cross operator with the one of using the Sobel operator

Under what situations might you choose to use the Roberts Cross rather than the Sobel? And under what conditions would you avoid it?

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