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ENDS 375

Explore the foundational concepts of image statistics and operations in a visualization laboratory at Texas A&M University. Learn about arithmetic mean, variance, standard deviation, histograms, point operations, color modification, neighborhood operations, convolution, image filters, edge detection, morphological operations, and more. Gain insight into the principles behind automated decisions about images and useful input for computational algorithms. Discover techniques like image averaging, alpha blending, geometric operations, and morphing. Dive into readings covering course notes and relevant textbook chapters to enhance your understanding of visual data processing.

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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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