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Chapter 5 – Image Pre-processing

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  1. 5.1 Brightness Transformations 5.2 Geometric Transformations 5.3 Local Pre-processing 5.4 Image Restoration Chapter 5 – Image Pre-processing

  2. Objectives of image pre-processing: (a) Suppress image information that is not relevant to later work (b) Enhancing information that is useful for later analysis

  3. Classes of Image Pre-processing Methods (a) Brightness Transformations (b) Geometric transformations 5.1 Brightness Transformations Categorization: (1) Point processing, Neighborhood processing (2) Position invariant, Position variant (3) Image Enhancement, Image Restoration

  4. Histogram • Histogram Equalization– image enhancement, position variant, point processing

  5. Contrast Stretching Transform function

  6. Theorem: Let T be a differentiable strictly increasing or strictly decreasing function. Letr be a random variable having density Let having density or Then,

  7. Let transform function be Then Called equalizationorlinearization. Discrete case: Let , , Transformation: 5-7

  8. ○ Example: L = 16, n = 360

  9. ○ Examples:

  10. Specified Histogram Equalization -- Specify the shape of the histogram that we wish the processed image to have. Histogram equalization Histogram specification Input image 5-12

  11. 5-13

  12. Let : gray levels of the input image I : gray levels of the output image O : the probability density function of r thatcanbe estimated from I : the given specified probability density function of z that we wish O to have Let and Then and Both are known 5-14

  13. Procedure: Given: input image (I), specification ( ) 1. Compute from I 2. Compute from 3. Compute from 4. Compute 5. Transform I into O by 5-15

  14. Discrete case: 5-16

  15. 5.2. Geometric Transformations Distorted grid image Scene grid Recovered grid image A geometric transform is a vector function T defined by Two steps: i) Pixel coordinate transformation ii) Brightness interpolation Applications: Remotely sensed image registration Bird-view generation Document skew 5-17

  16. Remotely Sensed Image Registration 5-18

  17. 5.2.1. Pixel Coordinate Transformations Geometric distortion types : a. variable distance, b. panoramic c. skew, e. scale, f. perspective Transformation model: where 5-19

  18. Polynomial transformation: Bilinear transformation: Affine transformation: Rotation: Scale change: Skewing : 5-20

  19. Example: Bilinear transform Needs at least 4 pairs of corresponding points to determine the parameters 5-21

  20. Solve x by the least square error method. 5-22

  21. Image Registration: Steps: 1. Detect salient points of images 2. Determine the point correspondences between the two images 3. Compute the parameters of the transformation functions 5-23

  22. 5.2.2. Brightness Interpolation 5-24

  23. (a)Nearest-Neighbor Interpolation (b) Linear Interpolation 5-25

  24. 。 Bilinear Interpolation 5-26

  25. ◎ Generalization○ Interpolation functionR ○ Examples: 5-27

  26. ○Substituting into NN-interpolation 5-28

  27. ○Substituting into linear interpolation 5-29

  28. ○Cubic interpolation function 5-30

  29. ○ Bi-cubic Interpolation -- Apply cubic interpolation first along the rows and then down the columns 5-31

  30. 5.3 Local (Neighborhood) Pre-Processing -- Applies a function to a neighborhood of each pixel -- Different functions  different objectives e.g., noise removal (smoothing), edge detection, corner detection 5-32

  31. Neighborhood (window, mask) Function+ Window = Filter 5-33

  32. Filtration (Filtering) Convolution: 5-34

  33. 5.3.1 Image Smoothing Objective: noise removal • Linear Smoothing Filters 1-D case: Input data Mean filter Smoothed data 2-D case:

  34. Gaussian Smoothing 1D: 2D: Discrete case:

  35. Separable Filters Convolution: e.g., Laplacian filter n × n filter: 2 (n × 1)filters: 5-38

  36. Non-linear Smoothing Filters 。 K-nearest neighbors (K-NN) mean filter 。 Alpha-trimmed mean filter i) Order elements, ii) Trim off end elements iii) Take mean 。 Smoothing by a rotating masker

  37. Dispersion 5-40

  38. 。 Mean Filters (i) Arithmetic mean: (ii) Geometric mean: (iii) Harmonic mean: 5-41

  39. (iv) Contra-harmonic mean: 。 Median filter 5-42

  40. 5.3.2 Edge Detectors -- Edges are important information for image understanding Origin of edges Line drawing

  41. Typical edge profiles: Step edge (jump edge) Ramp edge Roof edge (crease edge) Smooth edge Line

  42. ○ Derivatives

  43. 2D case: Gradient Magnitude Direction

  44. 。 Prewitt filters Consider Horizontal filter: , Smooth filter: Combine Vertical filter: , Smooth filter: Combine

  45. Input Horizontal Vertical Edge image Binary image Thinning