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What is image processing?

Analog Image. CAMERA. x ( n 1 , n 2 ). STORAGE. PROCESS. DIGITIZER. Sampling + Quantization. x ( t 1 , t 2 ). Display Perform analysis Reconstruct x ( t 1 , t 2 ). What is image processing?. x ( t 1 , t 2 ) : ANALOG SIGNAL x : real value

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What is image processing?

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  1. Analog Image CAMERA x(n1,n2) STORAGE PROCESS DIGITIZER Sampling + Quantization x(t1,t2) • Display • Perform analysis • Reconstruct x(t1,t2) What is image processing? • x(t1,t2) : ANALOG SIGNAL x : real value (t1,t2) : pair of real continuous space (time) variables • x(n1,n2) : DISCRETE SIGNAL (DIGITAL) x : discrete (quantized) real or integer value (n1,n2) : pair of integer indices Sensor with RGB color filters 1

  2. Examples • Sampled Black & White Photograph: x(n1,n2) x (n1,n2) scalar indicating piel intensity at location (n1,n2) For example: x = 0 Black x = 1 White 0 < x < 1 In-between • Sampled color video/TV signal xR(n1, n2, n3) xG(n1, n2, n3) xB(n1, n2, n3) 2

  3. Examples 3

  4. How do we process images? • Use DSP concepts as tools • Exploit visual perception properties 4

  5. Visual Perception • We represent pixels as amplitude values (gray scale). 256 levels 1 0 128 levels 1 0 64 levels 1 0 32 levels 1 0 • How much to sample (quantize) the gray scale? • Humans can distinguish in the order of 100 levels of gray (about 40 to 100). 5

  6. Visual Perception: Examples Original image, 8 bits per pixel Processed image, 0.35 bits per pixel 6

  7. Visual Perception RMSE = 8.5 RMSE = 9.0 7

  8. Image Enhancement • Image Enhancement • Objective: accentuate or improve appearance of features, for subsequent analysis or display (possibly, but not necessarily degraded by some phenomenon). • Examples of features: edges, boundaries, dynamic range and contrast. • Examples of applications: • TV: enhance image for viewer (image quality, intelligibility, visual appearance). • Preprocessing for machine identification. • Enhancement is not necessarily needed because of degradation but can be used possibly to remove degradation. 8

  9. Image Enhancement Noise Blurred or faint edges Low contrast or dynamic range  Sharpen faint or blurred edges Modify low dynamic range   Remove noise 9

  10. Image Enhancement • Types of distortions to correct: • Blur (Blurring due to camera motion, defocusing, …) • Noise (assumed to be additive often for simplicity, although not necessarily the case). • Contrast • Blocking artifacts in block-based transform coders. • Examples: • Space photography • Underwater photography • Film grain noise 10

  11. p(x) Number of occurrences of pixel with a particular intensity x x b a Contrast and Dynamic Range Modification • Contrast stretching • Degradation is commonly due to poor lighting. • Image probability distribution function (pdf) has narrow peak  poor contrast. • Image intensities are clustered in a small region  available dynamic range is not very well utilized. 11

  12. p(xnew) xnew Contrast and Dynamic Range Modification • Possible solution: increase overall dynamic range •  resulting image would appear to have a grater contrast •  expand the amplitudes from a to b to cover available intensity range. 12

  13. xnew slope  b’ slope  a’ a b L x slope  Contrast and Dynamic Range Modification • Idea: Gray scale or intensity level of an input image x(n1,n2) is modified according to a specific transformation (function) f(·). • Note: f(·) is usually constrained to be a monotonically non-decreasing function of x ensures that a pixel with higher intensity than another will not became a pixel with a lower intensity in output image xnew. • Typical stretching operator: 13

  14. Contrast and Dynamic Range Modification • Specific desired transformation depends on the application Example: compensation of display non-linearity  most suitable transformation depends on display non-linearity. • In most applications, a good or suitable transformation can be identified by computing and analyzing the histogram of the input image to be enhanced. • The histogram is a scaled version of the image pdf. • The histogram gives pdf when scaled by the total number of pixels in the image. 14

  15. normalized Histogram Modification and Equalization • Definition: The histogram of an image h(x) represents the number of pixels that have a specific intensity x number of pixels as a function of intensity x. h(x) = scaled version of pdf p(x) Normalization ensures that 15

  16. hd(xnew) Desired histogram of output image xnew = f(x) xnew Lmin Lmax hi(x) x Histogram Modification and Equalization • Remarks: • Histogram modification methods popular because computing and modifying histogram of an image requires little computations. • Experienced person can easily determine needed transformation by analyzing histogram characteristics. But if too many images  automatic method is desired. • For typical natural images, the desired histogram has a maximum around the middle of the dynamic range and decreases slowly as the intensity increases or decreases. • Problem: Determine f(·) such that houtput(xnew) = hd(xnew) 16

  17. hd(x) Redistribute pixels by assigning pixels uniformly to the given levels. const xnew Lmin Lmax pixels assigned to each level Histogram Modification and Equalization • Histogram equalization: special case of histogram modification where hd(x) = constant • For a 256256 image, with 256 intensity levels: • How can we do assignment? 17

  18. 16 h(x) 35 35 16 21 21 7 7 1 1 x 0 L1 1 L2 2 L3 3 L4 4 L5 5 L6 6 L7 7 L8 ho(x) 16 16 16 16 16 16 16 16 x 0 L1 1 L2 2 L3 3 L4 4 L5 5 L6 6 L7 7 L8 Histogram Modification and Equalization • Method 1: Collect and redistribute pixels Example: 128 pixels at 8 levels Collect and redistribute pixels. Get bundles of 16 regardless of their position in image. 18

  19. Histogram Modification and Equalization • How to group them? • One approach is to split bins  can choose pixels within a bin randomly  poor results that tend to be noisy. • Compute average values of neighboring pixels and match to closest average  better, but still noisy. • A better approach is to use a cumulative method. 19

  20. hi(xi) ho(xo) xo = f(xi) const xi xo 0 L-1 xmin xmax Histogram Modification and Equalization • Cumulative method for histogram equalization • Histogram equalization  desired histogram is constant at all levels. • Problem: Find transformation xo=f(xi) such that that houtput(xo) = const If normalized histogram    uniform distribution 20

  21. = normalized histogram = cumulative probability distribution of xi Histogram Modification and Equalization • Solution: • Compute input pdf • Choose • Why? if  y uniformly distributed between (0,1)  histogram uniformly distributed  need also to scale y because y  (0,1) instead of (0,L-1) or (Lmin,Lmax) + scaling needed 21

  22. Histogram Modification and Equalization • Note: if y uniformly distributed between (0,1) Proof: 22

  23. only approximately uniformly distributed (because of discretization) Histogram Modification and Equalization • Since xi is a discrete variable, integral is replaced by summation:  ymin not necessarily 0 since • Scaling can be done as follows 23

  24. where - rounding operation Histogram Modification and Equalization • If input and output range from 0 to L – procedure can be described as follows: • Procedure: xk = k; k=0,…, L = input amplitude levels yk; k=0,…, L = output amplitude levels • Compute the histogram of the image to be improved. • Normalize histogram; • Normalize amplitudes so that the sum of all values is equal to one and you have a pdf,pi(·). • Compute • Move bins in xk to locations in yk. • Scale yk to desired amplitude range (linear mapping). 24

  25. pi(xk) 0.25 0.25 0.2 0.20 0.15 0.15 0.14 0.1 0.07 0.10 0.05 0.04 0.05 xk; 0≤xk≤7 0 1 2 3 4 5 6 7 Histogram Modification and Equalization • Example: L = 7 Find yk such that xk maps into yk: 25

  26. po(yk) 0.25 0.25 0.25 0.2 0.20 0.16 0.14 0.15 0.10 0.05 0 1 3 5 6 7 Histogram Modification and Equalization yk; 0≤yk≤7 26

  27. Histogram Modification and Equalization Original Image Equalized Image 27

  28. Thresholding • Thresholding can be used to extract objects from image (segmentation) • Histogram statistics can be used to define single or multiple thresholds to classify an image pixel-by-pixel. • A simple approach: • Bimodal histogram  set the threshold to gray value corresponding to the deepest point in the histogram value. • Multimodal histogram  set thresholds to correspond to points in “valleys” of histogram. • Classify every pixel f(x,y) by comparing its gray level to the selected threshold. 28

  29. Original image Image histogram Thresholded, T=12 Thresholded, T=166 Thresholded, T=225 Pixel-based direct classification methods 29

  30. Thresholding 30

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