Digital Image Processing. Today Outline. Matlab Desktop. Matlab Basics

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1 Today Outline Matlab Basics Intensity transform and Histogram Equalization Exercise one Basic Image Processing Digital Image Processing Teacher Assistance: Yael Pritch course impr@cshujiacil personal yaelpri@cshujiacil Reception hour: Thursday 4:00-5:00 Newsgroup: localcourseimpr Web site: wwwcshujiacil/~impr Getting Help >> help help explain how to get help >> helpbrowser open the online Matlab help browser with browser interface >> help images list of all commands in the Image Processing Toolbox >> demo Matlab Desktop to operate Matlab : type matlab or matlab7 from linux xterm >> lookfor read (display list of function with read in the name or help first line text) >> type imread >> help imread (function name + % block) >> doc imread (function documentation in help browser) >> mathworks website: Vector indexing row vector (xn) >> v = [ 3 5 7]; (elements separated by space or comma (,)) >> v(2) = 3; column vector (MX) >> w = [;3;5;7]; (elements separated semi-comma (;)) >> w = v (transpose operation) w = To Access blocks of elements we use colon notation >> v(2:4) ans = >> v(:end) end is the last element in the vector >> v(:) produce a column vector >> v(:2:end) enables steps (jumps) >> v(end:-2:) steps can be negative as well Vector can be used as an index into another vector >> v([ 3 4]) ans = 5 7 Matlab Basics Digital image representation : 2D function f(x,y) -> finite discrete quantities Coordinate Conventions img(r,c) r rows (height) c cols (width) The first pixel: img(,) Color/Gray

2 Matrix Addressing Matrix indexing A very useful approach is to use logical matrix as an index to the matrix >> D = logical([ 0 0; 0 0 ; 0 0 0]) D = >> A(D) ans = 6 The use of column operation on a matrix produce a single column vector from the matrix (on a column by column basis) It is very useful for image operations like sum or max >> s = sum(f(:)) (equivalent to: sum(sum(f))) Image 2D array, matrix Matrix can be represented as a sequence of row vectors >>A = [ 2 3; 4 5 6; 7 8 9] A = To access element 2 indexes are used row index and column index >> A(2,3) 6 >> A(:,3) >> A(2,:) >> a(:2,:3) >> B = A; >> B(:,3) = 0 B = Using vectors to index into a matrix provide a powerful tool for element selection A([ 3], [2 3]) >> s = i(end:-:,:); >> s = i(end:-:,:); 2

3 >> s = i(end:-:,:); >> s = i(end:-:,:); >> s = i(end:-:,:); >> t = i(:2:end, :2:end); >> s = i(end:-:,:); >> t = i(:2:end, :2:end); >> s = i(end:-:,:); >> t = i(:2:end, :2:end); ; >> s = i(end:-:,:); >> t = i(:2:end, :2:end); ; 3

4 >> s = i(end:-:,:); >> t = i(:2:end, :2:end); ; >> imshow(i/2); >> s = i(end:-:,:); >> t = i(:2:end, :2:end); ; >> imshow(i/2); >> s = i(end:-:,:); >> t = i(:2:end, :2:end); ; >> imshow(i/2); >> imshow((i>08)*i); >> s = i(end:-:,:); >> t = i(:2:end, :2:end); ; >> imshow(i/2); >> imshow((i>08)*i); Standard Arrays Generating simple array enables trying out simple ideas and test the syntax of a function during development >> zeros(m,n) >> ones(m,n) >> true(m,n) >> false(m,n) >> magic(m) >> rand(n) >> randn(n) Array dimensions Matlab arrays can be of any dimensions It is useful to operate on specific dimension of the array, for example: >> height = size(i,); Usually we deal with 2D array but there are cases (such as color images) we need to address higher dimensions >> i(200:300, 200:400,3) To get the number of dimensions of an array >> d = ndims(f) 4

5 >> edit testm M-Function Programming function [p, pmax, pmin, pn] = improd(f,g) % improd computes the product of two images % [p, pmax, pmin, pn] = improd(f,g) output the element by element product % of two input images, f ang g, the product maximum and minimum values % and a normalized product array with values in the range [0,] % The input images must be of the same size They can be of the class % uint8, unit6 or double The outputs are of class double fd = double(f); gd = double(g) p = fd*gd; pmax = max(p(:)); pmin = min(p(:)); % comments starts with % pn = mat2gray(p); M-Function Programming M-files can be scripts of functions that accept input argument and produce one or more outputs Components of m files: Function definition line function [out out2] = name(in, in2, in3) H line - a single comment line that follows the function definition line % SQUARESUM compute the sum of the square of the matrix elements it is the first text appears when user write >> help function_name >> lookfor keyword display all functions where the keyword appeared in H line Help Text - text block following the H line without any blank line in between the two Function body the Matlab code Comments lines starting with % (note add short and clear comments to your code) Flow control Operators if, else, elseif, end switch, case, otherwise, end return try,catch for i=start:increment:end, end while, end break (used with for or while) continue (used with for or while) Try not to use Arithmetic operators (numeric computations) matrix arithmetic (linear algebra A*B) array arithmetic (element by element A*B) +, -, /, ^,: Relational operators (compare) Compare corresponding elements of arrays of equal dimensions (<, >,<=, >=, ==, ~=) or an array to scalar Logical operators can operate both on logical and numeric data (and: &, or:, not: ~) true: logical or non-zero numeric quantity false: logical or numerical 0 logical functions : xor, any, all Code optimization vectorizing loops 2D indexing meshgrid convert rows vectors to arrays C and R that can be used for evaluating function with two variables >> for r = :0 >> for c = :0 >> b(r,c) = r^2+ c^2 >> end >> end >> [C, R] = meshgrid(:c, :r) >> h = R^2 + C^2; Vectorzing code accelerates the computation significantly For Example: compute 2D sin using meshgrid runs on the order of 30 times faster the same computation based on loops on Image of 52x52 pixels Code optimization vectorizing loops Convert for / while loops to equivalent vector or matrix operations D indexing >> for x = :k ff(x) = 5*sin((x-)/(2*pi)); end 2D indexing Try to avoid 2D loops >> x = 0:k- >> ff = 5*sin(x/(2*pi)); 5

6 Cell arrays and Structures Cell array is multidimensional array whose elements are copies of other arrays >> c = { gauss,[ 0;0 ], 3} >> c{} ans = gauss Structures are similar to cell arrays (allow grouping of a collection of dissimilar data) but they addressed by fields rather than by numbers >> paramsnimgs = 00; >> paramsjump = 2; >> paramsbasestr = testimg Code Optimization Preallocating arrays Simple way to improve code execution is to pre-allocate the size of the arrays in the program The preallocation also help reduce memory fragmentation when working with large matrixes >> f = zeros(024); Reading Images >> f = imread( filename ); filename is a string include the file type (jpg, tiff, bmp, gif, ) ; is used for suppressing output >>[height, width] = size(f); >> whos f display additional information about an array Name Size Bytes Class f 52x52x uint8 array Grand total is elements using byte Arguments Matlab arguments are always passed by value Checking whether an argument exist >> exist(a, var ) Checking number of arguments to the functions >> nargin, nargout, nargchk Getting variable number of arguments >>varargin, varargout Writing Images >> imwrite(f, filename ) f is an image array filename must include the file format (tif, jpg, bmp,) >> k = imfinfo( testjpg ) Filename: 'testjpg' FileModDate: '22-Oct :07:36' FileSize: 3464 Format: 'jpg' FormatVersion: '' Width: 256 Height: 256 BitDepth: 24 ColorType: 'truecolor' FormatSignature: '' Comment: {} The answer is a structure variable with different fields: kwidth Displaying Images >> imshow(f, G) f is an image array G is the number of intensity level used to display it (default 256) >> imshow(f, [low high]) display as black all values less than low and as white all values greater or equal to high (in grayscale images) >> imshow(f, []) set low and high as the minimal and maximal values of array f useful for low dynamic range images or that have negative values >> pixval display intensity value of individual pixel interactively >> figure(2), imshow(g) Open a new figure before displaying the image (the default using the same figure) 6

7 Image Types Data Classes - representing pixel values Intensity images scaled to represent intensities (uint8 [0,255], double [0,]) Reading 8 bit images Binary images logical array of 0s and s Indexed images Look up table [x, map] RGB images truecolor, array of (m*n*3) Checking the image type : isind, isbw, isgray, isrgb Converting image types: rgb2ind, rgb2gray, gray2ind, ind2gray, logical operations Converting between types : B = data_class_name(a) for example: B = double(a) Gui >> guide (Graphic User Interface Development Environment) Start the GUI Layout Editor Guide create fig file: complete description of the gui elements and their arrangements Conversions When converting between data classes and types it is important to keep the value range for each data class >> img = double(img)/255; >> img = im2double(img); gui m-file: the code that controls the gui operations, initializations functions, callback functions Intensity Transformation Intensity Transformation Spatial Domain image plane itself direct manipulation of pixels in the image g(x,y) = T(f(x,y) T is an operator of f, defined over specific neighborhood about a pixel Principle approach use a square around the pixel In the simplest case the square size is one pixel 7

8 Simple Examples for Intensity Transformations Image negative Intensity Transformation function In the case of single pixel transformation we can use a lookup table 0 s 0 s = T(r) r gray level of the input image s gray level of the output image 2 3 s s 2 s 3 s Dark light Dark light r 255 s 255 Simple Examples for Intensity Transformations Image negative s = L--r L number of gray levels s Dark light Simple Examples for Intensity Transformations Image negative s = L--r L number of gray levels s Dark light Dark light r Dark light r Examples for Intensity Transformations Power Law Transform s = c*r γ γ =2 γ Examples for Intensity Transformations Log Transform s = c*log(+r) s Dark light Dark light r What does the slope of the function Indicating? 8

9 k k k i= i Example - Gamma Correction Example - Gamma Correction γ=3, 4, 5 What kind of correction can we try here? Sample of Image Histogram Histogram Processing h(r k ) = n k Normalized: p(r k ) = n k /N h ( r k ) = n k in Matlab: imhist(img) Histogram Equalization Histogram Equalization Equalize :For every original gray level k Calculate the image histogram 2 Find the accumulative sum of the histogram values - y k (in Matlab cumsum(vec)) 3 Normalize the values of the histogram accumulative sum by dividing in the total number of pixels 4 Multiple the normalized vector in the maximal gray level value (K-) and round (shift back to the original gray level range) 5 Map the gray levels values to the result of step (3) 6 Stretch the values back to the range,k (improve contrast in the end of this process) s k Normalized Accumulative histogram We are interested in equal use of all gray level N pixels, range 0,K- n k number of pixels in level k histogram Accumulative histogram Normalized Accumulative s k histogram k sk = ni *( L ) N i= #p < level #p in level #p < level #p < level 0 r k s k k N sk = n i i= r k=k/k 0 graylevels graylevels k y k = n i i= graylevels s = y N = n N r k=k/k 9

10 When will this fail? In General : on images with gray level distribution that is not standard we may get unwanted results from the histogram equalization process Histogram Equalization Can we get uniform histogram? In discrete images it is in most cases impossible to obtain uniform histogram, we want to get as close as possible to uniform So what do we get? The distribution of gray level in area along the histogram will result in approximately same number of pixels Note that no bins are split What happen to the number of bins? The number of bins can only decrease: bins are not split and small bins in the histogram may be united (but the effect is not visibly disturbing since it involves very small number of pixels) What features are kept after the equalization? The histogram equalization process is monotonic (as the process involves accumulative sum) and therefore the relative brightness of a pixel is preserved Exercise Equalization results Targets: Getting familiar with the Matlab environment Learning image formats and conversions between them Argument error checking Working with image histogram Write an efficient code A few more important commands for image operations (look in the help) find repmat reshape clear save plot, subplot disp 0