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ENDS 375

ENDS 375. Foundations of Visualization 9/7/04 Notes. Image Statistics. Useful input into computational algorithms measures of image quality basis for automated decisions about images. Image Statistics. Arithmetic Mean mean = sum(P xy )/(x*y) Variance

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ENDS 375

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  1. ENDS 375 Foundations of Visualization 9/7/04 Notes Visualization Laboratory, Texas A&M University

  2. Image Statistics • Useful input into computational algorithms • measures of image quality • basis for automated decisions about images Visualization Laboratory, Texas A&M University

  3. Image Statistics • Arithmetic Mean mean = sum(Pxy)/(x*y) • Variance variance = (sum(Pxy*Pxy)/(x*y)-mean*mean) Visualization Laboratory, Texas A&M University

  4. Image Statistics • Standard Deviation stdev = square root (variance) • Histogram • two axis plot of pixel values vs number of pixels • basis for deciding - contrast range, overall brightness, thresholding, ... Visualization Laboratory, Texas A&M University

  5. Visualization Laboratory, Texas A&M University

  6. Point Operations on Images • Numeric Transformations • Transfer Functions • Often implemented using look-up tables Visualization Laboratory, Texas A&M University

  7. Specific Operations (not usually reversible) Unity Invert Visualization Laboratory, Texas A&M University

  8. Specific Operations Contrast Adjustment Higher Lower Visualization Laboratory, Texas A&M University

  9. Specific Operations Threshold Gamma Visualization Laboratory, Texas A&M University

  10. Color Modification Less Red More Yellow Visualization Laboratory, Texas A&M University

  11. Arithmetic Operations Two or more images Cxy = Axy< operation > Bxy • Addition • Subtraction • Averaging, etc ... Visualization Laboratory, Texas A&M University

  12. Logical Operations and, or nand, nor xor, xnor Visualization Laboratory, Texas A&M University

  13. Image Averaging Add corresponding pixels from multiple images then divide by the number of images Visualization Laboratory, Texas A&M University

  14. Alpha Blending Cxy = Axy*Mxy + Bxy*(max -Mxy ) “Blends” two images Need a “matte” image Basis for image compositing Visualization Laboratory, Texas A&M University

  15. Compositing Visualization Laboratory, Texas A&M University

  16. Visualization Laboratory, Texas A&M University

  17. Neighborhood Operations • Each output pixel depends on its neighbors in the original • Convolution - the basic operation • Image Filters • Sampling Visualization Laboratory, Texas A&M University

  18. Convolution Each pixel the sum of neighborhood and kernel Visualization Laboratory, Texas A&M University

  19. Image Filters low-pass filters Box or Gaussian filters Visualization Laboratory, Texas A&M University

  20. High-pass Visualization Laboratory, Texas A&M University

  21. Edge detection LaPlacian Filter also Sobel and Prewitt Visualization Laboratory, Texas A&M University

  22. Embossing Visualization Laboratory, Texas A&M University

  23. Object Correlation Pattern matching to find specific shapes in an image Use shape specific kernels Orientation sensitive Visualization Laboratory, Texas A&M University

  24. Other Filters • Statistical median, max, min • Sharpening unsharpening mask combine two versions of the same image Visualization Laboratory, Texas A&M University

  25. Degraining Uses “maxmin” or “minmax “ filters Visualization Laboratory, Texas A&M University

  26. Visualization Laboratory, Texas A&M University

  27. Sampling • Creating a new image based on multi-pixel information from the original image • Sub-pixel information Visualization Laboratory, Texas A&M University

  28. Sampling • Forward Transformation from source to destination • Inverse Transformation from destination to source Visualization Laboratory, Texas A&M University

  29. Sampling Nearest Neighbor Visualization Laboratory, Texas A&M University

  30. Bilinear Interpolation Visualization Laboratory, Texas A&M University

  31. Geometric Operations • Scaling • Rotation • Translation • Operation ordering important Visualization Laboratory, Texas A&M University

  32. Warping • Polynomial warping • Morphing Visualization Laboratory, Texas A&M University

  33. Morphological Operations • Usually on one-bit images • Erosion • Dilation • Hit-or-Miss • Outlining Visualization Laboratory, Texas A&M University

  34. “Pipelined” Operations • Sequences of operations Shrinking - center of “mass” Thinning - equidistant from boundaries Skeletonization - “burn” together Visualization Laboratory, Texas A&M University

  35. Readings • Course notes section 1-7 • Course notes section 1-8 • Course notes section 1-9 • Textbook - Chapter 14 Visualization Laboratory, Texas A&M University

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