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Point Processing

Point Processing. Basic Image Processing Operations Arithmetic Operations Histograms. Basic Image Processing Operations. Image-Processing operations may be divided into 3 classes based on information required to perform the transformation. Transforms

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Point Processing

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  1. Point Processing Basic Image Processing Operations Arithmetic Operations Histograms SCCS 476

  2. Basic Image Processing Operations Image-Processing operations may be divided into 3 classes based on information required to perform the transformation. • Transforms • process entire image as one large block • Neighborhood processing • process the pixel in a small neighborhood of pixels around the given pixel. • Point operations • process according to the pixel’s value alone (single pixel). SCCS 476

  3. Transformed Image Transform Image-processing operation Output Image Processed Transformed Image Inverse Transform Schema of Image Processing Image SCCS 476

  4. Arithmetic Operations • Addition • Subtraction • Multiplication • Division • Complement SCCS 476

  5. Arithmetic Operations (cont) Let x is the old gray value, yis the new gray value, c is a positive constant. • Addition: y = x + c • Subtraction: y = x - c • Multiplication: y = cx • Division: y = x/c • Complement: y= 255 - x SCCS 476

  6. Arithmetic Operations (cont) • Addition: y = x + c • Subtraction: y = x - c • Multiplication: y = cx • Division: y = x/c • Complement: y= 255 - x • To ensure that the results are integers in the range [0, 255], • the following operations should be performed • Rounding the result to obtain an integer • Clippingthe result by setting • y = 255 if y > 255 • y = 0 if y < 0 SCCS 476

  7. Arithmetic Operations (cont) • MATLAB functions • Addition: imadd(x,y) • Add two images or add constant to image • Subtraction: imsubstract(x,y) • Subtract two images or subtract constant to image • Multiplication: immultiply(x,y) • Multiply two images or multiply image by constant • Division: imdivide(x,y) • Divide two images or divide image by constant • Complement: imcomplement(x) SCCS 476

  8. Addition & Subtraction • Lighten/darken the image • Some details may be lost • MATLAB: • commands: • x = imread(‘filename.ext’); • y = uint8(double(x) + c); or • y = uint8(double(x) - c); • function: • x = imread(‘filename.ext’); • y = imadd(x, c); or • y = imsubtract(x, c); SCCS 476

  9. Ex: Addition & Subtraction Added by 128 Subtracted by 128 Draw graphs of the transformation functions !!! SCCS 476

  10. Multiplication & Division • Lighten/darken the image • Some details may be lost (but less than addition/subtraction) • MATLAB: • commands: • x = imread(‘filename.ext’); • y = uint8(double(x)*c); or • y = uint8(double(x)/c); • functions: • x = imread(‘filename.ext’); • y = immultiply(x, c); or • y = imdivide(x, c); SCCS 476

  11. Ex: Multiplication & Division Multiplied by 2 Divided by 2 Draw graphs of the transformation functions !!! SCCS 476

  12. Comparison: Addition VS Multiplication SCCS 476

  13. Comparison: Subtraction VS Division SCCS 476

  14. Complement • Create the negative image • MATLAB: • commands: • x = imread(‘filename.ext’); • y = uint8(255 - double(x)); • function: • x = imread(‘filename.ext’); • y = imcomplement(x); SCCS 476

  15. Ex: Complement Draw a graph of the transformation function !!! SCCS 476

  16. Histogram • Graph showing the number of pixels for each intensity • Normalized histogram: histogram where the number of pixel is divided by the total number of pixel so the range is [0,1] • Cumulative histogram: histogram which shows the number of pixels whose intensity is less or equal to each intensity. SCCS 476

  17. Histogram Example >> p = imread(‘pout.tif’) >> inshow(p) >> figure;imhist(p) SCCS 476

  18. What Histogram Describes? • Brightness • dark image has gray levels (histogram) clutered at the lower end. • bright image has gray levels (histogram) clutered at the higher end. • Contrast • well contrasted image has gray levels (histogram) spread out over much of the range. • low contrasted image has gray levels (histogram) clutered in the center. SCCS 476

  19. Contrast Enhancement by Spreading Out Histogram • Histogram Stretching (Contrast Stretching) • Histogram Equalization SCCS 476

  20. 1. Histogram Stretching #pixel #pixel I I Imin Imax max 0 SCCS 476

  21. Steps of Histogram/Contrast Stretching • Create the histogram of the image Gray level ( i ) No. of gray value ( ni ) 0……………………………………………. 15 1……………………………………………. . 0 2……………………………………………. . 0 3……………………………………………. .0 4……………………………………………. . 0 5……………………………………………. 70 6……………………………………………110 7……………………………………………. 45 8…………………………………………… 70 9……………………………………………. 35 10………………………………………..... . 0 11………………………………………….. 0 12…………………………………………... 0 13…………………………………………… 0 14…………………………………………… 0 15………………………………………….. 15 Draw the histogram. SCCS 476

  22. Steps of Histogram/Contrast Stretching (cont) • From the histogram, stretch out the gray levels in the center of the range by applying the piecewise linear function • Ex: [5,9]  [2,14] • y= [(14 – 2)/(9 – 5)](x– 5) + 2, Draw a graph of transformation • Gray levels outside this range are either left as original values or transforming according to the linear function at the ends of the graph. • x y • 2 • 5 • 8 • 11 • 14 SCCS 476

  23. Steps of Histogram/Contrast Stretching (cont) • Change the old gray values to the new gray values by using the piecewise linear function from the previous step as a mapping function. • Create the histogram from the new image SCCS 476

  24. Histogram Stretching: Example original output SCCS 476

  25. Histogram before/after Adjustment After Before SCCS 476

  26. Imin Imax Iy2 Iy1 Mapping function: Histogram Mapping: Piecewise Linear #pixel #pixel I I Imin Imax Ix1 Ix2 SCCS 476

  27. MATLAB: Histogram/Contrast Stretching • Command: imadjust • Syntax: imadjust(x, [a,b], [c,d]); imadjust(x, [a,b], [c,d], ); • convert intensity x ato c • convert intensity x  bto d • values of a,b,c,d must be between 0 and 1 •  : positive constant (describe the shape of the function, < 1 concave downward, > 1 concave upward) SCCS 476

  28. Transformation Function with Gamma (Power –Law Transformation) Brighten image Linear mapping Darken image SCCS 476

  29. Example of Adjusting by the Power-Law Transformation Adjust by using Gamma = 0.5 Original SCCS 476

  30. MATLAB: Piecewise Linear • A MATLAB function for applying a piecewise linear-stretching function (see Figure 4.15) • Command: find • Syntax: find(condition) • Ex pix = find(im >= a(i) & im < a(i+1)); pix holds the index for members in im having intensity between a(i) and a(i+1) include a(i). SCCS 476

  31. 2. Histogram Equalization • The trouble with the methods of histogram stretching is that they require user input. • Histogram equalization is an entirely automatic procedure. • Idea: Each gray level in the image occurs with the same frequency. • Give the output image with uniform intensity distribution. SCCS 476

  32. Histogram Equalization (cont) • Mapping function: where p(i)is the PDF of the intensity level i, obtained from cumulative histogram. SCCS 476

  33. Histogram Equalization: Procedure Example: Suppose a 4-bit grayscale image has the histogram associated with a table of the numbers ni of gray values. (page 78) SCCS 476

  34. Histogram Equalization: Example BEFORE AFTER http://www.mathworks.com/access/helpdesk/help/toolbox/images/histeq.html SCCS 476

  35. MATLAB: Histogram Equalization • Command: histeq • Syntax: histeq(image, target_hist) histeq(image, #bin) histeq(indexed_im, #bin, target_hist) histeq(indexed_im, map, #bin) • Default: #bin = 64 • Output: output_im,[output_im, transform], new_map, [new_map, transform] SCCS 476

  36. Lookup Tables • Improve the performance of point processing • Why? • one intensity is always mapped to the same value • reduce the computing time • Lookup table: array Input intensity: index in the array Output intensity: value of the member SCCS 476

  37. Ex: Lookup Table (1) • Function: output = input/2; • MATLAB >> T = uint8(floor(0:255)/2); >> output = T(input); SCCS 476

  38. Ex: Lookup Table in MATLAB (2) • Function: • MATLAB >> T1 = 0.6667*[0:95]; >> T2 = 2*[96:160] – 128; >> T3 = 0.6632*[161:255] + 85.8947; >> T = uint8(floor([T1 T2 T3])); SCCS 476

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