Image processing using matlab

Image processing using matlab

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  G.KARTHIGAM.SC INFO TECH DEPARTMENTOF CS &IT NADAR SARASWATHI COLLEGE OF ARTS AND SCIENCE,THENI
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   Matlab isoptimised for operating on matrices  Images are matrices!  Many useful built-in functions in the Matlab Image Processing Toolbox  Very easy to write your own image processing functions Image Processing using Matlab Sumitha Balasuriya 2
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  >> I=imread('mandrill.bmp','bmp'); %load image >> image(I) % display image >> whos I Name Size Bytes Class I 512x512x3 786432 uint8 array Grand total is 786432 elements using 786432 bytes Image Processing using Matlab Sumitha Balasuriya 3 image filename as a string image format as a stringMatrix with image data Dimensions of I (red, green and blue intensity information) Matlab can only perform arithmetic operations on data with class double! Display the left half of the mandrill image
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   Images arejust an array of numbers >> I % ctrl+c to halt output!  Intensity of each pixel is represented by the pixel element’s value in the red, green and blue matrices >> I(1,1,:) % RGB values of element (1,1) ans(:,:,1) = 135 ans(:,:,2) = 97 ans(:,:,3) = 33 Image Processing using Matlab Sumitha Balasuriya 4 Images where the pixel value in the image represents the intensity of the pixel are called intensity images. Red Green Blue
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   An indexedimage is where the pixel values are indices to elements in a colour map or colour lookup table.  The colour map will contain entries corresponding to red, green and blue intensities for each index in the image. >> jet(20) % Generate a jet colourmap for 20 indices ans = 0 0 0.6000 0 0 0.8000 0 0 1.0000 0 0.2000 1.0000 0 0.4000 1.0000 0 0.6000 1.0000 0 0.8000 1.0000 0 1.0000 1.0000 0.2000 1.0000 0.8000 0.4000 1.0000 0.6000 0.6000 1.0000 0.4000 0.8000 1.0000 0.2000 1.0000 1.0000 0 1.0000 0.8000 0 1.0000 0.6000 0 1.0000 0.4000 0 1.0000 0.2000 0 1.0000 0 0 0.8000 0 0 0.6000 0 0 Image Processing using Matlab Sumitha Balasuriya 5 RGB Entry for index value 3 3 4 7 3 6 1 9 8 9 1 2 5 6 14 4 2 5 6 1 4 5 2 8 9 4 2 13 7 8 4 5 5 1 11 5 6 4 1 7 4 4 1 9 5 6 5 5 1 4 4 6 5 5 9 2 1 11 1 3 6 1 9 7 6 8 18 1 8 1 9 1 3 3 9 2 3 7 2 9 8 1 6 6 4 7 8 6 7 4 15 8 2 1 3 7 5 10 8 4 10 4 3 6 4 Values can range from 0.0 to 1.0 Red, green and blue intensities of the nearest index in the colourmap are used to display the image.
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  >> I2=I(:,:,2); %green values of I >> image(I2) >> colorbar % display colourmap Image Processing using Matlab Sumitha Balasuriya 6 Matlab considers I2 as an indexed image as it doesn’t contain entries for red, green and blue entries Index Associated color Colour Lookup Table
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   change colourmap >>colormap(gray)  scale colourmap >> imagesc(I2) Image Processing using Matlab Sumitha Balasuriya 7 Type >>help graph3d to get a list of built-in colourmaps. Experiment with different built-in colourmaps. Define your own colourmap mymap by creating a matrix (size m x 3 ) with red, green, blue entries. Display an image using your colourmap. Red =1.0, Green = 1.0, Blue =1.0, corresponds to index 64 Red =1.0, Green = 1.0, Blue =1.0, corresponds to index 255 Red =0.0, Green = 0.0, Blue = 0.0, corresponds to index 1 Red =0.0, Green = 0.0, Blue = 0.0, corresponds to index 0
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  >> axis image% plot fits to data >> h=axes('position', [0 0 0.5 0.5]); >> axes(h); >> imagesc(I2) Image Processing using Matlab Sumitha Balasuriya 8 Investigate axis and axes functions using Matlab’s help
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   Frequency ofthe intensity values of the image  Quantise frequency into intervals (called bins)  (Un-normalised) probability density function of image intensities Image Processing using Matlab Sumitha Balasuriya 9
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  >>hist(reshape(double(Lena(:,:,2)),[512*512 1]),50) Image Processing usingMatlab Sumitha Balasuriya 10 Convert image into a 262144 by 1 distribution of values Histogram function Number of bins Histogram equalisation works by equitably distributing the pixels among the histogram bins. Histogram equalise the green channel of the Lena image using Matlab’s histeq function. Compare the equalised image with the original. Display the histogram of the equalised image. The number of pixels in each bin should be approximately equal. Generate the histograms of the green channel of the Lena image using the following number of bins : 10, 20, 50, 100, 200, 500, 1000
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  >>surf(double(imresize(Lena(:,:,2),[50 50]))) Image Processingusing Matlab Sumitha Balasuriya 11 Remember to reduce size of image! Use Matlab’s built-in mesh and shading surface visualisation functions Change type to double precision
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   Convert imageto grayscale >>Igray=rgb2gray(I);  Resize image >>Ismall=imresize(I,[100 100], 'bilinear');  Rotate image >>I90=imrotate(I,90); Image Processing using Matlab Sumitha Balasuriya 12
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  Image Processing usingMatlab Sumitha Balasuriya 13 Convert polar coordinates to cartesian coordinates >>pol2cart(rho,theta) Check if a variable is null >>isempty(I) Trigonometric functions sin, cos, tan Convert polar coordinates to cartesian coordinates >>cart2pol(x,y) Find indices and elements in a matrix >>[X,Y]=find(I>100) Fast Fourier Transform Get size of matrix >>size(I) Change the dimensions of a matrix >>reshape(rand(10,10),[100 1]) Discrete Cosine Transform Add elements of a Matrix (columnwise addition in matrices) >>sum(I) Exponentials and Logarithms exp log log10 fft2(I) dct(I)
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  Bit of theory!Convolution of two functions f(x) and g(x) Discrete image processing 2D form Image Processing using Matlab Sumitha Balasuriya 14 ( ) ( ) ( ) ( ) ( )h x f x g x f r g x r dr       convolution operator Image Filter (mask/kernel) Support region of filter where g(x-r) is nonzero Output filtered image 1 1 ( , ) ( , ) ( , ) height width j i H x y I i j M x i y j       Compute the convolution where there are valid indices in the kernel
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  Image Processing usingMatlab Sumitha Balasuriya 15 Write your own convolution function myconv.m to perform a convolution. It should accept two parameters – the input matrix (image) and convolution kernel, and output the filtered matrix.  1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 i j Filter (M) Image (I) 197 199 195 194 189 190 132 90 112 101 194 194 198 201 189 196 150 85 87 97 194 194 198 195 186 191 109 90 90 124 197 187 195 198 185 186 115 78 81 96 194 190 198 193 187 177 88 86 94 69 194 194 190 190 179 177 93 99 95 100 201 194 191 186 186 181 74 110 82 76 196 194 195 191 183 164 77 119 84 88 192 194 199 192 191 174 89 164 103 129 201 190 187 189 178 168 90 82 88 84 0 0 0 0 0 0 0 0 0 0 0 196 196 194 192 170 137 105 97 0 0 195 196 194 192 167 133 98 92 0 0 194 194 193 189 158 124 92 90 0 0 193 193 191 186 154 122 92 89 0 0 194 192 189 184 149 121 91 90 0 0 194 192 188 182 146 122 93 95 0 0 195 193 190 183 147 128 100 106 0 0 194 192 189 181 146 125 100 105 0 0 0 0 0 0 0 0 0 0 0 = 1 1 ( , ) ( , ) ( , ) height width j i H x y I i j M x i y j       http://www.s2.chalmers.se/undergraduate/courses0203/ess060/PDFdocuments/ForScreen/Notes/Convolution.pdf
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  Image Processing usingMatlab Sumitha Balasuriya 16 Horizontal slice from Mandrill image 0.01 0.08 0.24 0.34 0.24 0.08 0.01 1D Gaussian filter  = Filtered Signal
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  Image Processing usingMatlab Sumitha Balasuriya 17 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 Arithmetic mean filter (smoothing) >>fspecial('average') -0.17 -0.67 -0.17 -0.67 3.33 -0.67 -0.17 -0.67 -0.17 Laplacian (enhance edges) >>fspecial('laplacian') -0.17 -0.67 -0.17 -0.67 4.33 -0.67 -0.17 -0.67 -0.17 Sharpening filter >>fspecial('unsharp') 0.01 0.08 0.01 0.08 0.62 0.08 0.01 0.08 0.01 Gaussian filter (smoothing) >>fspecial('gaussian') Investigate the listed kernels in Matlab by performing convolutions on the Mandrill and Lena images. Study the effects of different kernel sizes (3x3, 9x9, 25x25) on the output. 1 2 1 0 0 0 -1 -2 -1 1 0 -1 2 0 -2 1 0 -1 Sobel operators (edge detection in x and y directions) >>fspecial('sobel') >>fspecial('sobel')’ The median filter is used for noise reduction. It works by replacing a pixel value with the median of its neighbourhood pixel values (vs the mean filter which uses the mean of the neighbourhood pixel values). Apply Matlab’s median filter function medfilt2 on the Mandrill and Lena images. Remember to use different filter sizes (3x3, 9x9, 16x16).
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   Generate usefulfilters for convolution >>fspecial('gaussian',[kernel_height kernel_width],sigma)  1D convolution >>conv(signal,filter)  2D convolution >>conv2(double(I(:,:,2)),fspecial('gaussian‘,[kernel_height kernel_width] ,sigma),'valid') Image Processing using Matlab Sumitha Balasuriya 18 Perform the convolution of an image using Gaussian kernels with different sizes and standard deviations and display the output images. Border padding optionskernelimage
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  1) Type thecode in this handout in Matlab and investigate the results. 2) Do the exercises in the notes. 3) Create a grating2d.m function that generates a 2D steerable spatial frequency. Compute spatial frequencies with an amplitude =1 and the following parameters frequency = 1/50, 1/25, 1/10, 1/5 cycles per pixel, phase= 0, pi/5, pi/4, pi/3, pi/2, pi theta = 0, pi/5, pi/4, pi/3, pi/2, pi The value for pi is returned by the in-built matlab function pi. Display your gratings using the in-built gray colourmap. (figure 1) 3) Create a superposition of two or more gratings with different frequencies and thetas and display the result. You can do this by simply adding the images you generated with grating2d (figure 2) frequency = (1/10 and 1/20), (1/20 and 1/30) theta = (pi/2 and pi/5), (pi/10 and pi/2), (pi/2 and pi) Make sure you examine combinations of different frequencies and theta values. (figure 3). Visualise the intensity surface of the outputs that you have generated. (figure 4) 4) Write a matlab function that segments a greyscale image based on a given threshold (i.e. display pixels values greater than the threshold value, zero otherwise). The function should accept two inputs, the image matrix and the threshold value, and output the thresholded image matrix. (figure 5) Image Processing using Matlab Sumitha Balasuriya 19 function H=grating2d(f,phi,theta,A) % function to generate a 2D grating image % f = frequency % phi = phase % theta = angle % A = amplitude % H=grating2d(f,phi,theta,A) % size of grating height=100; width=100; wr=2*pi*f; % angular frequency wx=wr*cos(theta); wy=wr*sin(theta); for y=1:height for x=1:width H(x,y)=A*cos(wx*(x)+phi+wy*(y)); end end Figure 1 Figure 3Figure 2 Figure 4 Figure 5