image theory
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This document provides an overview of topics to be covered in an image processing course, including image formation, point processing, color correction, Fourier transforms, convolution, sampling and warping, spatial and frequency domain filtering, noise reduction, mathematical morphology, and image compression. Example images are used to illustrate concepts like color perception, color balance, filtering, noise removal, and image compositing.
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image theory
- 1. EECE/CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester 2007 Lecture Notes: Introduction and Overview This work is licensed under the Creative Commons Attribution-Noncommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/2.5/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA.
- 2. Introduction and Overview This presentation is an overview of some of the ideas and techniques to be covered during the course.
- 3. 1. image formation 2. point processing and equalization 3. color correction 4. the fourier transform 5. convolution 6. image sampling and warping 7. spatial filtering 8. noise reduction 9. mathematical morphology 10. image compression Topics
- 4. Wallace and Gromit Wallace and Gromit will be subjects of some of the imagery in this introduction. Wallace Gromit likes cheese reads Electronics for Dogs http://www.aardman.com/wallaceandgromit/index.shtml Visit:
- 5. Image Formation object image plane lens
- 6. Image Formation light source
- 7. Image Formation projection through lens image of object
- 8. Image Formation projection onto discrete sensor array. digital camera
- 9. Image Formation sensors register average color. sampled image
- 10. Image Formation continuous colors, discrete locations. discrete real-valued image
- 11. Digital Image Formation: Quantization continuous color input discrete color output continuous colors mapped to a finite, discrete set of colors.
- 12. Sampling and Quantization pixel grid sampled real image quantized sampled & quantized
- 13. Digital Image a grid of squares, each of which contains a single color each square is called a pixel (for picture element ) Color images have 3 values per pixel; monochrome images have 1 value per pixel.
- 14. Color Images Are constructed from three intensity maps. Each intensity map is pro-jected through a color filter ( e.g., red, green, or blue, or cyan, magenta, or yellow) to create a monochrome image. The intensity maps are overlaid to create a color image. Each pixel in a color image is a three element vector.
- 15. Color Images On a CRT
- 16. Point Processing original + gamma - gamma + brightness - brightness original + contrast - contrast histogram EQ histogram mod
- 17. Color Processing requires some knowledge of how we see colors
- 18. Eye’s Light Sensors #(blue) << #(red) < #(green) cone density near fovea
- 19. Color Sensing / Color Perception These are approximations of the responses to the visible spectrum of the “red”, “green”, and “blue” receptors of a typical human eye.
- 20. Color Sensing / Color Perception These are approximations of the responses to the visible spectrum of the “red”, “green”, and “blue” receptors of a typical human eye. The simultaneous red + blue response causes us to perceive a continuous range of hues on a circle. No hue is greater than or less than any other hue.
- 21. Color Sensing / Color Perception luminance hue saturation photo receptors brain The eye has 3 types of photoreceptors: sensitive to red, green, or blue light. The brain transforms RGB into separate brightness and color channels ( e.g. , LHS).
- 22. Color Perception all bands luminance chrominance red green blue 16 × pixelization of: luminance and chrominance (hue+saturation) are perceived with different resolutions, as are red, green and blue.
- 23. Color Perception all bands luminance chrominance red green blue 16 × pixelization of:
- 24. Color Balance and Saturation Uniform changes in color components result in change of tint. E.g., if all G pixel values are multiplied by > 1 then the image takes a green cast.
- 25. Color Transformations Image aging: a transformation, , that mapped:
- 26. The 2D Fourier Transform of a Digital Image Let I ( r,c ) be a single-band (intensity) digital image with R rows and C columns. Then, I ( r,c ) has Fourier representation where are the R x C Fourier coefficients. these complex exponentials are 2D sinusoids.
- 27. 2D Sinusoids: ... are plane waves with grayscale amplitudes, periods in terms of lengths, ... A = phase shift r c orientation
- 28. 2D Sinusoids: ... specific orientations, and phase shifts. orientation r c r c
- 29. The Value of a Fourier Coefficient … … is a complex number with a real part and an imaginary part. If you represent that number as a magnitude, A , and a phase, , … ..these represent the amplitude and offset of the sinusoid with frequency and direction .
- 30. The Sinusoid from the Fourier Coeff. at ( u , v )
- 31. The Fourier Transform of an Image I | F { I } | [ F { I }] magnitude phase
- 32. Continuous Fourier Transform The continuous Fourier transform assumes a continuous image exists in a finite region of an infinite plane. The BoingBoing Bloggers
- 33. Discrete Fourier Transform The discrete Fourier transform assumes a digital image exists on a closed surface, a torus. The BoingBoing Bloggers
- 34. Convolution Sum times 1/5 Sums of shifted and weighted copies of images or Fourier transforms.
- 35. Convolution Property of the Fourier Transform The Fourier Transform of a product equals the convolution of the Fourier Transforms. Similarly, the Fourier Transform of a convolution is the product of the Fourier Transforms
- 36. Sampling, Aliasing, & Frequency Convolution aliasing (the jaggies) no aliasing (smooth lines)
- 37. Sampling, Aliasing, & Frequency Convolution (a) (b) (c) (d) a) aliased b) power spectrum c) unaliased d) power spectrum
- 38. Resampling 8 × 16 × nearest neighbor nearest neighbor bicubic interpolation bicubic interpolation (resizing)
- 39. Rotation and motion blur
- 40. Image Warping
- 41. Frequency Domain (FD) Filtering Gaussian LPF in FD Original Image Power Spectrum Image size: 512x512 SD filter sigma = 8
- 42. FD Filtering: Lowpass Original Image Filtered Image Filtered Power Spectrum Image size: 512x512 SD filter sigma = 8
- 43. FD Filtering: Highpass Original Image Filtered Image Filtered Power Spectrum Image size: 512x512 FD notch sigma = 8
- 44. FD Filtering: Highpass Original Image Filtered Image Filtered Power Spectrum Image size: 512x512 FD notch sigma = 8 signed image with 0 at middle gray
- 45. Spatial Filtering original blurred sharpened
- 46. Spatial Filtering bandpass filter unsharp masking original
- 47. Spatial Filtering bandpass filter unsharp masking original signed image with 0 at middle gray
- 48. Motion Blur vertical regional zoom rotational original
- 49. Noise Reduction color noise blurred image color-only blur
- 50. Noise Reduction 5x5 Wiener filter color noise blurred image
- 51. Noise Reduction original periodic noise frequency tuned filter
- 52. Shot Noise or Salt & Pepper Noise + shot noise - shot noise s&p noise
- 53. Nonlinear Filters: the Median s&p noise original median filter
- 54. Nonlinear Filters: Min and Maxmin + shot noise min filter maxmin filter
- 55. Nonlinear Filters: Max and Minmax - shot noise max filter minmax
- 56. Nonlinear Processing: Binary Morphology Cross-hatched pixels are indeterminate. “ L” shaped SE O marks origin Foreground: white pixels Background: black pixels
- 57. Used after opening to grow back pieces of the original image that are connected to the opening. Permits the removal of small regions that are disjoint from larger objects without distorting the small features of the large objects. Nonlinear Processing: Binary Reconstruction original opened reconstructed
- 58. Nonlinear Processing: Grayscale Morphology Cross-hatched pixels are indeterminate. “ L” shaped SE O marks origin Foreground: white pixels Background: black pixels
- 59. Grayscale Morphology: Opening opening: erosion then dilation opened & original
- 60. Grayscale Morphology: Opening erosion & opening erosion & opening & original
- 61. Nonlinear Processing: Grayscale Reconstruction reconstructed opening original
- 62. Forensic Analysis of Photographs Photographs by Robert Fenton of a battlefield in the Crimean war taken on 23 April 1855. From Morris, Errol, “Which Came First, the Chicken or the Egg?”, Parts 1-3, New York Times , Zoom Editorial Section , 25 Sept. 2007 (pt.1), 7 Oct. 2007 (pt.2), 30 Oct. 2007 (pt.3). Which came first?
- 63. Forensic Analysis of Photographs Photographs by Robert Fenton of a battlefield in the Crimean war taken on 23 April 1855. From Morris, Errol, “Which Came First, the Chicken or the Egg?”, Parts 1-3, New York Times , Zoom Editorial Section , 25 Sept. 2007 (pt.1), 7 Oct. 2007 (pt.2), 30 Oct. 2007 (pt.3). Which came first?
- 64. Forensic Analysis of Photographs Photographs by Robert Fenton of a battlefield in the Crimean war taken on 23 April 1855. From Morris, Errol, “Which Came First, the Chicken or the Egg?”, Parts 1-3, New York Times , Zoom Editorial Section , 25 Sept. 2007 (pt.1), 7 Oct. 2007 (pt.2), 30 Oct. 2007 (pt.3). Which came first?
- 65. Image Compression Yoyogi Park, Tokyo, October 1999. Photo by Alan Peters. Original image is 5244w x 4716h @ 1200 ppi: 127MBytes
- 66. Image Compression: JPEG JPEG quality level File size in bytes
- 67. Image Compression: JPEG JPEG quality level File size in bytes
- 68. Image Compositing Combine parts from separate images to form a new image. It’s difficult to do well. Requires relative positions, orientations, and scales to be correct. Lighting of objects must be consistent within the separate images. Brightness, contrast, color balance, and saturation must match. Noise color, amplitude, and patterns must be seamless.
- 69. Image Compositing Example Prof. Peters in his home office. Needs a better shirt.
- 70. Image Compositing Example This shirt demands a monogram.
- 71. Image Compositing Example He needs some more color.
- 72. Image Compositing Example Nice. Now for the way he’d wear his hair if he had any.
- 73. Image Compositing Example He can’t stay in the office like this.
- 74. Image Compositing Example Where’s a hepcat Daddy-O like this belong?
- 75. Image Compositing Example In the studio! Collar this jive, Jackson. Like crazy , Man !