1 / 53

Fundamentals of Computer Vision

Lecture 5 Dr. Roger S. Gaborski. Fundamentals of Computer Vision. Quiz 1. In Class Exercise. Intensity image is simply a matrix of numbers. We can summary this information by only retaining the distribution if gray level values:. PARTIAL IMAGE INFO:.

ulric
Download Presentation

Fundamentals of Computer Vision

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 5 Dr. Roger S. Gaborski Fundamentals of Computer Vision Roger S. Gaborski

  2. Quiz 1 Roger S. Gaborski

  3. In Class Exercise Roger S. Gaborski

  4. Intensity image is simply a matrix of numbers We can summary this information by only retaining the distribution if gray level values: PARTIAL IMAGE INFO: 117 83 59 59 68 77 84 94 82 67 62 70 83 86 85 81 71 65 77 89 86 82 76 67 72 90 97 86 66 54 68 104 121 107 85 46 58 89 138 165 137 91 38 80 147 200 211 187 138 40 80 149 197 202 187 146 56 76 114 159 181 160 113 An image shows the spatial distribution of gray level values Roger S. Gaborski

  5. Image Histogram Plot of Pixel Count as a Function of Gray Level Value Pixel Count Gray Level Value Roger S. Gaborski

  6. Histogram • Histogram consists of • Peaks: high concentration of gray level values • Valleys: low concentration • Flat regions Roger S. Gaborski

  7. Formally, Image Histograms Histogram: • Digital image • L possible intensity levels in range [0,G] • Defined: h(rk) = nk • Where rk is the kth intensity level in the interval [0,G] and nk is the number of pixels in the image whose level is rk . • G: uint8 255 uint16 65535 double 1.0 Roger S. Gaborski

  8. Notation • L levels in range [0, G] • For example: • 0, 1, 2, 3, 4, in this case G = 4, L = 5 • Since we cannot have an index of zero, • In this example, index of: Index 1 maps to gray level 0 2 maps to 1 3 maps to 2 4 maps to 3 5 maps to 4 Roger S. Gaborski

  9. Normalized Histogram • Normalized histogram is obtained by dividing elements of h(rk) by the total number of pixels in the image (n): fork = 1, 2,…, L p(rk) is an estimate of the probability of occurrence of intensity level rk Roger S. Gaborski

  10. MATLAB Histogram • h = imhist( f, b ) • h is the histogram, h(rk) • f is the input image • b is the number of bins (default is 256) • Normalized histogram Roger S. Gaborski

  11. Color and Gray Scale Images Roger S. Gaborski

  12. Background: Gray Image >> I = imread('Flags.jpg'); >> figure, imshow(I) % uint8 >> Im= im2double(I); % convert to double >> Igray = (Im(:,:,1)+Im(:,:,2)+Im(:,:,3))/3; >> figure, imshow(Igray) There is also the rgb2gray function that results in a slightly different image Roger S. Gaborski

  13. Gray Scale Histogram Roger S. Gaborski

  14. Plots • bar(horz, v, width) • v is row vector • points to be plotted • horz is a vector same dimension as v • increments of horizontal scale • omitted  axis divided in units 0 to length(v) • width number in [0 1] • 1 bars touch • 0 vertical lines • 0.8 default Roger S. Gaborski

  15. p= imhist(Igray)/numel(Igray); >> h1 = p(1:10:256); >> horz = (1:10:256); >> figure, bar(horz,h1) Review other examples in text and in MATLAB documentation Roger S. Gaborski

  16. Chapter 3 www.prenhall.com/gonzalezwoodseddins Roger S. Gaborski

  17. Color and Gray Scale ImagesRecall from Previous Slide Roger S. Gaborski

  18. Gray Scale Histogram Roger S. Gaborski

  19. Normalized Gray Scale Histogram >> p= imhist(Igray)/numel(Igray); >> figure, plot(p) Roger S. Gaborski

  20. Normalized Gray Scale Histogram 256 bins 32 bins imhist(Igray)/numel(Igray); imhist(Igray,32)/numel(Igray) Roger S. Gaborski

  21. Normalized Gray Scale Histogram >> p= imhist(Igray)/numel(Igray); >> figure, plot(p) probability Gray level values Roger S. Gaborski

  22. Original Dark Light Roger S. Gaborski

  23. Contrast enhancement • How could we transform the pixel values of an image so that they occupy the whole range of values between 0 and 255? Roger S. Gaborski

  24. Gray Scale Transformation • How could we transform the pixel values of an image so that they occupy the whole range of values between 0 and 255? • If they were uniformly distributed between 0 and x we could multiply all the gray level values by 255/x • BUT – what if they are not uniformly distributed?? Roger S. Gaborski

  25. Cumulative Distribution Function Histogram CDF Roger S. Gaborski

  26. Histogram Equalization(HE) • HE generates an image with equally likely intensity values • Transformation function: Cumulative Distribution Function (CDF) • The intensity values in the output image cover the full range, [0 1] • The resulting image has higher dynamic range • The values in the normalized histogram are approximately the probability of occurrence of those values Roger S. Gaborski

  27. Histogram Equalization • Let pr(rj), j = 1, 2, … , L denote the histogram associated with intensity levels of a given image • Values in normalized histogram are approximately equal to the probability of occurrence of each intensity level in image • Equalization transformation is: k = 1,2,…,L sk is intensity value of output rk is input value Sum of probability up to k value Roger S. Gaborski

  28. Histogram Equalization Example • g = histeq(f, nlev) where f is the original image and nlev number of intensity levels in output image Roger S. Gaborski

  29. Original Image INPUT Roger S. Gaborski

  30. Transformation x255 Output Gray Level Value Input Gray Level Value Roger S. Gaborski

  31. Equalization of Original Image OUTPUT Roger S. Gaborski

  32. Roger S. Gaborski

  33. Roger S. Gaborski

  34. Simple Histogram Equalization Example Roger S. Gaborski

  35. Histogram Equalization Input Image Output Image Roger S. Gaborski

  36. Adaptive Equalization • g = adapthisteq(f, parameters..) • Contrast-limited adaptive histogram equalization • Process small regions of the image (tiles) individually • Can limit contrast in uniform areas to avoid noise amplification Roger S. Gaborski

  37. >> help adapthisteq adapthisteq Contrast-limited Adaptive Histogram Equalization (CLAHE). adapthisteq enhances the contrast of images by transforming the values in the intensity image I. Unlike HISTEQ, it operates on small data regions (tiles), rather than the entire image. Each tile's contrast is enhanced, so that the histogram of the output region approximately matches the specified histogram. The neighboring tiles are then combined using bilinear interpolation in order to eliminate artificially induced boundaries. The contrast, especially in homogeneous areas, can be limited in order to avoid amplifying the noise which might be present in the image. J = adapthisteq(I) Performs CLAHE on the intensity image I. J = adapthisteq(I,PARAM1,VAL1,PARAM2,VAL2...) sets various parameters. Parameter names can be abbreviated, and case does not matter. Each string parameter is followed by a value as indicated below: 'NumTiles' Two-element vector of positive integers: [M N]. [M N] specifies the number of tile rows and columns. Both M and N must be at least 2. The total number of image tiles is equal to M*N. Default: [8 8]. Roger S. Gaborski

  38. Adaptive Histogram Equalization Default, 8x8 tiles Roger S. Gaborski

  39. Adaptive Equalization Roger S. Gaborski

  40. Chapter 3 www.prenhall.com/gonzalezwoodseddins Roger S. Gaborski

  41. Chapter 3 www.prenhall.com/gonzalezwoodseddins Roger S. Gaborski

  42. Histograms • Histogram is nothing more than mapping the pixels in a 2 dimensional matrix into a vector • Each component in the vector is a bin (range of gray level values) and the corresponding value is the number of pixels with that gray level value

  43. Similarity between Histograms • Similarity between histogram bins: • Assuming both histograms have ∑nj j=1…B pixels M. Swain and D. Ballard. “Color indexing,”International Journal of Computer Vision, 7(1):11–32, 1991.

  44. Histogram Intersection • A simple example: • g = [ 17, 23, 45, 61, 15]; (histogram bins) • h = [ 15, 21, 42, 51, 17]; • in=sum(min(h,g))/min( sum(h),sum(g)) • in = 0.9863

  45. >> g = [17,23,45,61,15]; >> h = [15,21,42,51,17]; >> min(g,h) ans= 15 21 42 51 15 >> N = sum(min(g,h)) N = 144 >> D=min(sum(h),sum(g)) D = 146 >> intersection = N/D intersection = 0.9863 Roger S. Gaborski

  46. If Histograms Identical • g = 15 21 42 51 17 • h = 15 21 42 51 17 • >> in=sum(min(h,g))/min( sum(h),sum(g)) • in = 1

  47. Different Histograms • h = 15 21 42 51 17 • g = 57 83 15 11 1 • >> in=sum(min(h,g))/min( sum(h),sum(g)) • in = 0.4315

  48. Use Gray Scale for Example

  49. Region and Histogram Similarity with itself: >>h = hist(q(:),256); >> g=h; >> in=sum(min(h,g))/min( sum(h),sum(g)) in = 1

  50. >> r=236;c=236; >> g=im(1:r,1:c); >> g= hist(g(:),256); >> in=sum(min(h,g))/min( sum(h),sum(g)) in = 0.5474

More Related