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Image Processing

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Image processing Once we have an image in a digital form we can process it in the computer. We apply a “filter” and recalculate the pixel values of the processed image. We will look at the application of filters to sharpen and soften (make less sharp) the image.

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Filters or Kernals Our filters take the form of a small matrix or vector which we place (in turn ) over the image at each pixel position. Typically our filters are symmetrical 3 x 3 matrices. We use a process called convolution to apply the filter to the image.

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Convolution Convolution is the process of multiplying each element of our filter by the pixel values of the image that the filter covers and adding the products. We can describe the result as “the original image convolved with the filter”. conv2 is a Matlab function which can do this. Strictly what is described above is not a convolution but a correlation, however if our filters are symmetric the result is the same.

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Convolution and filters Filter Image sample set

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Convolution and filters Image sample set

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Convolution and filters So the value of 3 in the centre of the original image is replaced with –5 on the convolved image.

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Image softening If we make all the elements of the filter equal to one ninth, then the convolution value will be the average of all the elements “covered” by the filter. It is the same as adding all the 9 values together and dividing by nine.

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Image softening The following block of image samples represents a sharp vertical edge as pixel values suddenly change from 0 (black) to 255 (white). We will attempt to smooth it (make it less sharp) Sample Block

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Image softening Consider the operation of the averaging filter on the block of image samples /9 Filter Sample Block

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Image softening As we “run” the filter over the centre of the sample block. The following changes will take place. See next slide Sample Block Filter

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Image softening The zeros in the 4 th column are replaced with 85, since:

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Image softening Similarly as we perform the convolution of the filter with the rest of the centre of the sample block we get:

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Image softening The resultant convolution (image) no longer has a sharp edge, but a more gradual one

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Image softening That’s the theory; lets try it. for i=1:256 grey(i, 1:3)=(i-1)/255 end colormap(grey) myedge=zeros(5, 8) myedge(:, 5:8)=255 filt=ones(3,3)/9 image(myedge) myconv=conv2(myedge,filt, 'valid') image(myconv)

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Softening an image im=imread(‘urban.bmp'); smooth=[ 1 1 1; 1 1 1; 1 1 1]/9 % convolve all colours sharpim(:,:,1)=conv2(im(:,:,1),smooth); sharpim(:,:,2)=conv2(im(:,:,2),smooth); sharpim(:,:,3)=conv2(im(:,:,3),smooth); image(im) figure image(uint8(smoothim))

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Image sharpening It is easier to see this in one dimension initially. Consider some neighbouring pixels that are not sharp. If they are not sharp there will be no abrupt change in value between them. If we can cause an a more abrupt change in value between neighbouring pixels, we will sharpen the image.

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Image sharpening It is easier to see this in one dimension initially. Consider some neighbouring pixels that are not sharp. If they are not sharp there will be no abrupt change in value between them. If we can cause an a more abrupt change in value between neighbouring pixels, we will sharpen the image.

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Image sharpening The idea is to generate artificial sharp edges at the points of differing neighbouring pixels and then add these edges to the original image. The following diagram shows the variation in brightness values for: –(a) A perfect (sharp) edge. –(b) A blurred edge. –(c) The artificial correction to be added. –(d) The corrected (enhaced) edge.

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Image sharpening (a) (b) (c) (d)

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Image sharpening What kernal (filter) will (when convolved with the image) generate the correction waveform (c) ? In one dimension Check it. –It produces zero for flat fields, but a negative and positive edge at edges In two dimensions

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Image sharpening We need to produce a kernal which will add the artificial edges and the original together. The original will be produced if we only have a one (1) in the centre of the a convolution kernal. Check it. Add this to the edge generator + =

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Sharpening an Image im=imread(‘urban.bmp'); sharp=[ 0 –1 0; -1 5 –1; 0 –1 0] % convolve all colours sharpim(:,:,1)=conv2(im(:,:,1),sharp); sharpim(:,:,2)=conv2(im(:,:,2),sharp); sharpim(:,:,3)=conv2(im(:,:,3),sharp); image(sharpim) figure image(uint8(sharpim))

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