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Introduction to Computer Vision

Lecture 3 Dr. Roger S. Gaborski. Introduction to Computer Vision. Quiz on Thursday Closed book, no notes Lectures 1-3 Textbook pp 1-64 pp80-86. Overview . Image displaying Image types Image adjustment Gamma t ransformation Logarithmic transformation

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Introduction to Computer Vision

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  1. Lecture 3 Dr. Roger S. Gaborski Introduction to Computer Vision Roger S. Gaborski

  2. Quiz on ThursdayClosed book, no notesLectures 1-3Textbook pp 1-64 pp80-86 Roger S. Gaborski

  3. Overview • Image displaying • Image types • Image adjustment • Gamma transformation • Logarithmic transformation • Component segmentation • Histogram distribution Roger S. Gaborski

  4. A Few Typical Operationswith Images >> ls *jpg OrangeFlower.jpgPatternOne.jpg >> I = imread('OrangeFlower.jpg'); >> whos I Name Size Bytes Class Attributes I 1880x2816x3 15882240 uint8 Roger S. Gaborski

  5. What are maximum and minimum pixel values of I? >> mx = max(I(:)) mx = 255 >> mn = min(I(:)) mn = 0 Roger S. Gaborski

  6. Displaying Images [0, 255] • Consider we would like to display a gray level image that has a possible range of values 0-255 • When we display the image we can arrange for each gray level value to be displayed as a different light level on the display • Black would map to the gray level 0, white would map to the gray level 255. • Gray level values between 0 and 255 would map to shades of gray. Roger S. Gaborski

  7. figure, imshow(I,'InitialMagnification' ,'fit') Roger S. Gaborski

  8. RECALL: Displaying Images [0,1] • The gray level of images can also be represented by real value numbers between 0 and 1. • 0 represents pixels that are black, 1 represents pixels that are white. • Values between 0 and 1 represent gray level values. Roger S. Gaborski

  9. im = uint8([0 50 100; 100 125 200; 200 250 275]) Im is of type uint8. What values are contained in im ? Roger S. Gaborski

  10. im = uint8([0 50 100; 100 125 200; 200 250 275]) Im is of type uint8. What values are contained in im ? >> im im = 0 50 100 100 125 200 200 250 255 Roger S. Gaborski

  11. Displaying Images >> figure, imshow(im, 'InitialMagnification' ,'fit') >> title('im') Roger S. Gaborski

  12. Range of Gray Level Values • The maximum range of values is [0,1] or [0,255] (for 8 bit images) • It is possible for images to use the maximum range of gray level values, or some subset • An image may only contain values between 0 and 0.6, or 0.3 and 0.9 Roger S. Gaborski

  13. Describe the displayed image A >> A = [.14 .15 ; .16 .17] A = 0.1400 0.1500 0.1600 0.1700 >> figure, imshow(A, 'InitialMagnification' ,'fit') Roger S. Gaborski

  14. WHY? Roger S. Gaborski

  15. figure, imshow(A, [],'InitialMagnification' ,'fit') The data in A didn’t change, only the display Roger S. Gaborski

  16. mat2gray Change Actual Data Values: mat2gray Convert matrix to intensity image. I = mat2gray(A,[AMIN AMAX]) converts the matrix A to the intensity image I. The returned matrix I contains values in the range 0.0 (black) to 1.0 (full intensity or white). AMIN and AMAX are the values in A that correspond to 0.0 and 1.0 in I. Values less than AMIN become 0.0, and values greater than AMAX become 1.0. I = mat2gray(A) sets the values of AMIN and AMAX to the minimum and maximum values in A. Roger S. Gaborski

  17. >> A A = 0.1400 0.1500 0.1600 0.1700 >> J = mat2gray(A) J = 0 0.3333 0.6667 1.0000 (Range is [0,1]) Roger S. Gaborski

  18. B = 0 0.5000 5.0000 10.0000 >> J = mat2gray(B) J = 0 0.0500 0.5000 1.0000 (Range is [0,1]) Roger S. Gaborski

  19. double and im2double >> Q=uint8([55, 100, 22]) Q = 55 100 22 >> whos Q Name Size Bytes Class Attributes Q 1x3 3 uint8 >> Qd = double(Q) What is the value of Qd? Roger S. Gaborski

  20. >>> Qd = double(Q) Qd = 55 100 22 >> whos Q Qd Name Size Bytes Class Attributes Q 1x3 3 uint8 Qd 1x3 24 double >> Qid = im2double(Q) What is the value of Qid? Roger S. Gaborski

  21. >> Qid = im2double(Q) Qid = 0.2157 0.3922 0.0863 >> whos Name Size Bytes Class Attributes Q 1x1 1 uint8 Qd 1x1 8 double Qid 1x1 8 double Roger S. Gaborski

  22. >>> Qd = double(Q) Qd = 55 100 22 >> im2double(Qd) = ?????? Roger S. Gaborski

  23. im2double(Qd) (Qd is already type double, no change) ans = 55 100 22 Roger S. Gaborski

  24. Image Types • Intensity images • When elements are class uint8 or uint16 they have integer values in the range [0 255] or [0 65535] • When elements are class double values are floating point numbers. Values are scaled in the range [0 1] by convention • Pixels with value 0.0 are displayed as black • Pixels with value 1.0 are displayed as white • Binary images • RGB images • Indexed images Roger S. Gaborski

  25. Intensity Image >> Im = imread('Flag1.jpg'); >> whos I Name Size Bytes Class Attributes Im 320x240 76800 uint8 % Image is of class uint8, >> >> max(Im(:)) ans = 255 >> min(Im(:)) ans = 0 Range 0 to 255 (uint8) >> Im1 = im2double(Im); % Convert to class double >> max(Im1(:)) ans = 1 >> min(Im1(:)) ans = 0 Range now 0 to 1 (im2double) which is default format of images read from disk Roger S. Gaborski

  26. Display images imshow(Im) imshow(Im) uint8 im2double(I) Roger S. Gaborski

  27. How is display affected if the range of pixel values is changed? >> Im2 = Im1*2 +1; >> min(Im2(:)) ans = 1 >> max(Im2(:)) ans = 3 >> figure, imshow(Im2) Roger S. Gaborski

  28. imshow(j) Reason: image Im2 is double class, which has the displaying range of [0, 1]. Range of image Im2: [1, 3] So all pixels are displayed as white. Roger S. Gaborski

  29. figure, imshow(Im2, [ ]) imshow(Im2, [min(Im2(:)), max(Im2(:))]) imshow(Im2, [ ]) Roger S. Gaborski

  30. Image Types • Intensity images • Binary images • A logical array of 0s and 1s • An array of 0s and 1s that are of type uint8 is NOT a binary image • If A is a numeric array of 0s and 1s can create a logical array B using statement: B = logical(A) (all non zero values converted to 1s, entries with value 0 converted to logical 0s • RGB images • Indexed images Roger S. Gaborski

  31. Binary Image >> BW = imread('circles.png'); >> whos BW Name Size Bytes Class Attributes BW 256x256 65536 logical >> imshow(BW) Roger S. Gaborski

  32. Image Types • Intensity images • Binary images • RGB images • RGB color image is an MxNx3 array of color pixels • Each pixel is a triplet corresponds to the red, green and blue components at a specific spatial location • Can be interpreted as 3 planes of gray scale images fed into red, green and blue inputs of a color monitor • Class double, range of values [0,1] • Class uint8 or uint16 ranges are [0 255], [0 65535] • Indexed images Roger S. Gaborski

  33. Chapter 2 – Fundamentals www.prenhall.com/gonzalezwoodseddins Roger S. Gaborski

  34. Image Types • Intensity images • Binary images • RGB images • Indexed images • Two components: data matrix of integers, X, and a color map matrix, map • Map matrix is an mx3 array of class double floating point numbers in the range [0,1] • m is the number of colors defined for the image • Each row of m specifies the r,g and b components of a single color • Example: imshow(X,map) Roger S. Gaborski

  35. Image Types • Indexed images • Indexed images use a direct mapping of pixel intensities to color map values • Color of each pixel is determined by using the corresponding values of integer matrix X as a pointer into map • If X is class uint8 or uint16 then all components with value 0 point to first row of map, value of 1 point to second row Roger S. Gaborski

  36. Chapter 2 – Fundamentals www.prenhall.com/gonzalezwoodseddins Roger S. Gaborski

  37. Image Enhancement • Brightness mapping • Contrast stretching/enhancement • Histogram modification • Noise Reduction • Mathematical Techniques • Convolution • Filtering • Edge and Line Detection and Extraction • Region Segmentation • Contour Extraction • Corner Detection • Higher Level Features Roger S. Gaborski

  38. Intensity Transformation and Spatial Transformation • Intensity – modify each pixel in the image independently of its neighbors • Spatial – modify a pixel as a function of its neighbors (spatial convolution) Roger S. Gaborski

  39. If you look at a pixel of an intensity (gray level image- Next Slide) in isolation what can you tell me about the image? Roger S. Gaborski

  40. Roger S. Gaborski

  41. If you look at a pixel of an intensity (gray level image- Next Slide) in isolation what can you tell me about the image? The brightness or intensity value at that spatial location Roger S. Gaborski

  42. What if you inspect a neighborhood of pixel values? Roger S. Gaborski

  43. Depends on the neighborhood Sky Region Flag Region (2 rows, 3 columns) The ‘flag region’ contains more information about the image – There is a horizontal line in this region Roger S. Gaborski

  44. Can we modify the intensity values to change the image (improve in some way) or extract information from the image (edges, shapes, etc.)? Roger S. Gaborski

  45. Spatial Transformation • The general spatial domain processing equation: g(x, y) = T [ f (x, y)] • f (x, y) is the input image • g(x, y) is the output image • T is an operator on f defined over a specific neighborhood Roger S. Gaborski

  46. Chapter 3 www.prenhall.com/gonzalezwoodseddins - Define spatial neighborhood about a point, (x, y) - Neighborhood is typically a square or rectangle, but could be other shapes - Center of neighborhood is moved from pixel to pixel starting at the upper left hand corner of the Image - Operator T is applied at each location (x, y) to yield g(x, y) at that location Roger S. Gaborski

  47. Intensity Transformations • Let the neighborhood be reduced to a size of 1 x 1 pixel • Now the transformation is only a function of the pixel itself. • This is commonly called an intensity transformation or gray level transformation function: s = T(r) where r is the intensity of f at (x, y) and s is the resulting intensity of g at (x, y) Roger S. Gaborski

  48. Intensity Transformations • Assume the range of pixel intensity values is [0,1] • What can be accomplished with transformation T ? Roger S. Gaborski

  49. Intensity Transformations >> R = rand([1 4]) R = 0.0272 0.7937 0.9992 0.1102 >> R2 = R .* R ( note .* and not simply * ) R2 = 0.0007 0.6299 0.9985 0.0122 (small numbers are much smaller) >> RSR = sqrt(R) RSR = 0.1649 0.8909 0.9996 0.3320 Roger S. Gaborski

  50. R = rand(1, 4) R2 = R .* R RSR = sqrt(R) In this case the data is actually changed Not the only display as in previous lecture Roger S. Gaborski

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