Intensive Course on Image Processing Matlab project

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1 Intensive Course on Image Processing Matlab project All the project will be done using Matlab software. First run the following command : then source /tsi/tp/bin/tp-athens.sh matlab and in the matlab command window : init matlab To do the project, you can use either the functions that exist in the Image Toolbox of Matlab, or use some functions that have already been put on your account. In this text, you have some information ondifferent functions that can be useful for the projects. They are grouped on different subjects that you have seen in the courses. 1 Histogram, Fourier domain, linear filtering 1.1 Image visualization To load the image as a matrix for Matlab, use the function imread with the synthax : name=imread( nameimage.tif ); For instance here, ima=imread( images/zebras.jpg );. To visualize the image, you may use the following image command : image(ima); To obtain a grey image with 256 levels, you have to use the proper colormap : colormap(gray(256)); If you want to know the grey-level of a pixel, select the data cursor icon (the 10th icon in the second line under Figure 1 ) and then click with the left button in the image : the spatial coordinates and the grey-level are indicated. Be careful with function image and the colormap. To be sure to exploit the full dynamic of the image you can also use the plotim(ima) command which streches the dynamic between the minimum and maximum values. We suggest you to use plotim(name) in the following. You can use also the mesh command to obtain a 3D visualization of the image (the image is seen as a surface). For instance, try this command for the pyramide image. pyramide=imread( images/pyramide ); plotim(pyramide);

2 mesh(pyramide); 1.2 Histogram visualization The histogram visualization can be done using the command hist. To consider the whole image and to have 256 bins for the histogram, you have to use the following command : figure(2) hist(ima(:),256); 1.3 Fourier domain To compute the 2D Fourier transform of an image you can use fft2. To have a display between [-0.5,0.5] [-0.5,0.5], we recommend to use the fftshift command (the (0,0) component is then in the center of the image). Do not forget that the Fourier transform is a set of complex numbers and use abs to obtain the modulus and use plotim to have a good display. modfft=(abs(fftshift(fft2(name)))); plotim(modfft) If you want to have a look to the phase of an image, you can use the following commands. phifft=(angle(fftshift(fft2(name)))); plotim(phifft) 1.4 Subsampling To apply a direct sub-sampling on an image keeping one pixel of each 2x2 square in the original image, you can use the following commands : nlines=size(ima) ncolumns=size(ima) imasubsampled=ima(1:2:nlines,1:2:ncolumns); 1.5 Linear filtering Low-pass filtering Let us build a mean filter on a 5 5 window. h=[ ] hh=h *h/25 plotim(log(abs(fftshift(fft2(hh,512,512))))) You can use conv2 to do the filtering and apply this kernel on an image. 2

3 You can also build a gaussian filter in the Fourier domain. The kerngauss(σ,n) function generates a 2 n 2n gaussian image with a standard deviation σ. kg=kerngauss(2,11); 2 Radiometry and colorimetry 2.1 Image display and histogram manipulation This part is dedicated to visualization and histogram manipulation. First, use the image spot.tif. Display it with image command and colormap(gray(256)) to have a grey level image. Have a look to the histogram of the image to explain the dark appearance. Compare the image display with plotim command which applies an histogram stretching. We have seen during the course how it is possible to give to an image u the histogram of an image v : [x,index]= sort(u(:)); u(index)=sort(v(:)); Take images vue1.tif and vue2.tif and apply this histogram transfert. Have a look to the absolute value of the difference between the two images. We would like to use this transfert fonction to do an histogram egalization. This means that we would like to apply a uniform histogram to the spot image. How can you create an image with a uniform histogram? Apply the previous commands to do the transfert of the histogram. Compare histogram egalization to histogram stretching. 2.2 Color spaces You can use fleur.tif image. The conversion in the HSV (Hue Saturation Value) space is given by the command rgb2hsv (inverse operation being hsv2rgb). It is then possible to display each channel separately : imahsv(:,:,1) selects the first channel of the HSV image imahsv, which corresponds to the hue value. Yan can compare histogram stretching in the different spaces for color image visualization. 3 Classification, segmentation, edge detection This part is dedicated to segmentation algorithms. 3

4 3.1 Bayesian classification You have a draft program pw2.m where some commands are written It is not a finished program and you have to do modifications to do the processing. The following commands can help you to do some supervised learning on an image. This command can select an area on the image; launch the following command on the image bin=my_get_roi(ima) and then click with the right button to define an area of interest; to close the defined contour click with the left button; the output is a binary image (matrix called bin ) with ones in the region of interest. Then, you can compute the mean and standard deviation of the selected area : [m,st]=para_roi(bin,ima) this command gives you the mean (m) and the standard deviation (st) of the selected area. Then you can modify the program pw2.m to do the classification (the program is written to classify an image with 3 classes, by computing the distance maps between the image and a defined gray value). You can visualize the result with a colormap adapted to very few values (for instance colormap(hot)). 3.2 K-means classification By modifying again the program, you can program a k-means algorithm with the same number of classes. This time, the class centers have to be computed after each iteration by taking the pixels classified in each class. You can compare the k-means algorithm to the supervised bayesian classification. 3.3 Region growing The following set of commands (see also pw2.m) allows you to select a point and start a region growing processing. my_imshow(im) disp( acquire 1 manual point ); P = my_getpts; P = round([p(2) P(1)]); Thresh_tolerance=1.1; Seg = region_growing(im,p,thresh_tolerance); 4

5 3.4 Edge filters You can simply implement the 4 edge filters described during the lecture: Gradient, Roberts, Prewitt, Sobel by using the Matlab function convn.m to perform the 2D convolutions and choosing the adapted kernel. Youi can combine horizontal and vertical edge maps via maximum value selection (use the max.m function applied on matrices). Apply a segmentation procedure by thresholding the edge maps to half maximum values. What phenomenons do you observe and which filter performs best? 4 Mathematical morphology The aim of this part is to get acquainted with mathematical morphology transformations. Applying different operations with several structuring elements on simple images will allow you understanding the actions, effects and properties of the operations, the role of the structuring element, as well as the need for appropriate preprocessing depending on the application at hand. 4.1 Structuring element The structuring element is defined by the function makese. You can choose the shape: diamond, square, disk, and the radius. For instance se = makese( square,1); creates a 3 3 square structuring element. 4.2 Binary morphology Forthispart,youhavetouseabinaryimage(youcanusecafe.imaorcell256.ima). The image can be opened and visualized using : cell=uint8(ima2mat( cell256 )); image(cell); Apply the four basic operations : ero=erosion(cell,se); dil=dilation(cell,se); open=opening(cell,se); close=closing(cell,se); with structuring elements of various shape and size. You can test the influence of the shape and size of the structuring element. 4.3 Grey-level morphology In this part, the following images can be used : 5

6 bat200.ima aneurism.ima To open the image and visualize it, use : im=uint8(ima2mat( bat200 )); or im=uint8(ima2mat( aneurism )); image(im); colormap(gray(256)); You can apply the four basic operations on a grey level image and study the influence of the size and shape of the structuring element. Here are some questions that can help you understand the course : How can you illustrate the iterativity property of the dilation? What is the result of a dilation by a structuring element of size 2 followed by a dilation by a structuring element of size 3 (and same shape)? What is the result of an opening by a structuring element of size 2 followed by an opening by a structuring element of size 3 (and same shape)? How can you illustrate the idempotence of closing? Perform a top-hat transform (difference between the image and its opening). Comment the result depending on the choice of the structuring element. 4.4 Alternate sequential filters You can perform alternate sequential filters, for instance by using : se1=makese( disk,1); se2=makese( disk,2); se3=makese( disk,3); se4=makese( disk,4); se5=makese( disk,5); fas1=closing(opening(im,se1),se1); fas2=closing(opening(fas1,se2),se2); fas3=closing(opening(fas2,se3),se3); fas4=closing(opening(fas3,se4),se4); fas5=closing(opening(fas4,se5),se5); You can analyze the results according to the shape of the structuring element and the maximal size used in the filter. What kind of filtering can be expected from such operations? 4.5 Reconstruction You can perform an opening by reconstruction on the image aneurism.ima, using : open=opening(im,se); rec=recons(im,open, dilation ); with different choice of structuring element. 6

7 4.6 Segmentation You can apply a morphological gradient to the image bat200.ima (difference between dilation and erosion with a structuring element of radius1). What do you observe? You can try to threshold the gradient, for instance : temp = grad; temp(temp<100)=0; Why is it difficult to find an appropriate threshold value? You can apply the watershed algorithm to the gradient image : wat=watershed(grad,8); What do you observe? You can select the watershed lines as the points with grey value 0 in the result and superimpose them to the original image for visualization purpose. You can also apply first a closing on the gradient image and then the watershed. Is the result better? 5 Useful Matlab commands All the documentation of Matlab commands can be found in the Product Help tab of the Help menu. For image processing commands see the Image Processing Toolbox section. To view a summary of the usage of command command name type help command name 5.1 Matrix generation Vector handling To enter a row vector v type v = [ ]; To enter a column vector v type v = [ 7; 2; 5; 6 ]; A row vector can be converted to a column vector (and viceversa) using the transpose operator denoted by a single quote ( ). For example, w = v ; creates the column (row) vector w from the row (column) vector v. v(1) is the first element of vector v, v(2) is the second element and so forth. To access groups of elements use colon notation. For example, to access the three first elemenst of v type >> v(1:3) ans =

8 5.1.2 Matrix handling To enter a matrix M such as type M = M = [2 5 8; ; ]; Use for example M(3,2) to access the element of the third row and second column, it s value is 8. >> M(3,2) ans = 8 Use for example M(:,3) to access all rows of the third column or M(2,:) to access all columns of the second row. >> M(:,3) ans = >> M(2,:) ans = To access the size of a matrix or vector use the command size(m) Matrix arithmetic M + N Matrix addition M.*N Elementwise multiplication M - N Matrix subtraction M. n Elementwise exponentiation M * N Matrix multiplication M./N Elementwise division inv(m) Matrix inversion 5.2 Control flow commands Matlab supports the following control flow statements : if, for, while and switch. Type : >> help if 8

9 to check the syntax of the if command. Idem for the other commands. 5.3 Open and visualize an image I = imread( filename ); Reads a grayscale or color image from the file specified by the string filename. If the file is not in the current directory specify the full pathname. figure; image(i); Displays matrix I as an image. imagesc(i);isthesameasimageexceptthedataisscaledtousethefullcolormap. 5.4 Save an image imwrite(i, filename, format ); Writes the image I to the file specified by filename in the format specified by format, e.g. imwrite(i, test.png, png );. The image I can be an M-by-N (grayscale image) or M-by-N-by-3 (color image) array. 5.5 Open data vector FID = fopen( filename, r ); A = fread(fid); Reads binary data from the specified file and writes it into matrix A. FID = fopen( filename, r ); A = fread(fid,size,precision); Reads the file according to the data format specified by the string PRECISION. The PRECISION input commonly contains a datatype specifier like int or float, followed by an integer giving the size in bits. The SIZE argument is optional when using this syntax. 5.6 Save data vector FID = fopen( filename, w ); COUNT = fwrite(fid,a); Writes the elements of matrix A to the specified file. The data are written in column order. COUNT is the number of elements successfully written. FID = fopen( filename, w ); COUNT = fwrite(fid,a,precision); Writesthe elements of matrix A to the specified file, translating Matlab values to the specified precision. 5.7 Labelling of connected components L = bwlabel(bw,n); Label connected components in 2-D binary image. Returns a matrix L, of the same size as BW, containing labels for the connected components in BW. STATS = regionprops(bw,properties); Measure properties of image regions. Measures a set of properties for each connected component in the binary image BW. Properties examples are : area, bounding box, centroid. 9

10 5.8 Color space conversion YCBCRMAP = rgb2ycbcr(map); Converts the RGB values in MAP to the YCBCR color space. 10

Fundamentals of Digital Image Processing

\L\.6 Gw.i Fundamentals of Digital Image Processing A Practical Approach with Examples in Matlab Chris Solomon School of Physical Sciences, University of Kent, Canterbury, UK Toby Breckon School of Engineering,