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Chapter 5

Chapter 5. Digital Image Processing Fundamentals. Learning Goals. The human visual system Digitizing images Display of Images. Trading an eye for an ear. An eye is a Multi-mega pixel camera. It has a lens (adjustable zoom) It has an automatic f-stop (iris 2-8 mm)

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Chapter 5

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  1. Chapter 5 Digital Image Processing Fundamentals

  2. Learning Goals • The human visual system • Digitizing images • Display of Images

  3. Trading an eye for an ear

  4. An eye is a Multi-mega pixel camera • It has a lens (adjustable zoom) • It has an automatic f-stop (iris 2-8 mm) • It has a sensor plane (100 million pixels) • The sensor has a transfer function senstive to mesopic range; 380 to about 700 nm

  5. The eyes have a USB2 data rate! • 250,000 neurons in the optic nerve • variable voltage output on EACH nerve • 17.5 million neural samples per second • 12.8 bits per sample • 224 Mbps, per eye (a 1/2 G bps system!). • Compression using lateral inhibition between the retinal neurons

  6. Response curves • Eye has Gaussian response to light. • Gives rise to biologically motivated image processing

  7. Quantization of an Image • Computers use digital cameras -> quantization

  8. Delta-function

  9. Sampling an Image

  10. Sampling=convolution w pulse train

  11. Quantization Error is visible

  12. Displays • Color Monitors are made for people

  13. Chapter 6-7 • Opening and Saving Images

  14. Chapter 8 Convolutionwith a kernel, g(x)

  15. Convolution 1D and 2D signal processing

  16. Consider the delta function

  17. Time-shift delta

  18. Sample the input (it’s a convolution!)

  19. What does sampling do to spectrum?

  20. What is the spectrum?

  21. Fourier Coefficients

  22. CTFT

  23. Euler’s identity

  24. Sine-cos Rep

  25. Harmonic Analysis

  26. Convolution=time-shift&multi

  27. Convolution Thm multiplication in the time domain = convolution in the frequency domain

  28. Sample

  29. Spectrum reproduced spectrum to be reproduced at intervals

  30. Summary

  31. Example of 1D convoln

  32. 2D Convolution

  33. Region of Support • The region of support is defined as that area of the .kernel which is non-zero • linear convolution:=signal has infinite extent but kernel has finite support • If function has finite region of support we have compact support

  34. Real images have finite region of support • But we treat them as periodic and infinite! • We repeat kernels so that they have the same period as the images. • We call this cyclic convolution.

  35. Convolution in 2D

  36. Avoid the Mod op

  37. What is wrong with avoiding the mod op? • How do I find the center of the kernel?

  38. Cyclic Convolution

  39. Implementing Convolution for(int y = 0; y < height; y++) { for(int x = 0; x < width; x++) { sum = 0.0; for(int v = -vc; v <= vc; v++) for(int u = -uc; u <= uc; u++) sum += f[cx(x-u) ][cy(y-v)] * k[ u+uc][v+vc]; if (sum < 0) sum = 0; if (sum > 255) sum = 255; h[x][y] = (short)sum; } }

  40. What happens to the image if you ignore the wrap?

  41. Cyclic Convolution keeps the edges

  42. Can you think of a better way to implement convolution? • Keep the edges! • Don’t use the mod operation. • How about growing the image by the size of the kernel*2?

  43. Convolution is slow, how can I speed it up? • JAI! • FFT!? • Other ideas?

  44. Chapter 9 • Spatial Filters • Blurring • Median Filtering • Hi-pass filtering • SpatialFilterFrame and JAI

  45. Blurring=Low-pass Filters

  46. Why Blur an Image? • Remove Noise • Other ideas?

  47. Average=low-pass

  48. Want Unity Gain

  49. Many variations on LP filters

  50. Gaussian Blur

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