Chapter4 Image Enhancement

Transcription

1 Chapter4 Image Enhancement Preview 4.1 General introduction and Classification 4.2 Enhancement by Spatial Transforming(contrast enhancement) 4.3 Enhancement by Spatial Filtering (image smoothing) 4.4 Enhancement by Frequency Filtering (image sharpening) 4.5 Color Enhancement Summary 1

2 41G 4.1 General lintroduction ti and dclassification 411Purposes improve the visual effects easy to edge extracting Methods spatial domain: point operations, local operations frequency domain: DFT Filter IDFT 2

3 4.1 General Introduction and Classification contents contrast enhancement: linear transform non-linear transform, histogram equalization histogram matching local enhancement image smoothing: averaging mask, order-statistics filter lowpass filter. image sharpening: derivatives, highpass gp filter color image enhancement: pseudo color processing, full color processing 3

4 4.2 Contrast Enhancement Introduction: Histogram Histogram gives an estimate of the probability of the occurrence of gray levels ps ( ) = n / n k= 0,1,, L 1 k k Where s k is the the kth gray level and the n k is the number of Pixels in the image having gray level s k apparently L 1 k = 0 ps ( k ) = 1 4

5 4.2 Contrast Enhancement Introduction: Histogram Horizontal axis: gray level lvalues Vertical axis: probability of gray level values 5

6 4.2 Contrast Enhancement Introduction: Histogram Histograms and images quality Dark image 6

7 4.2 Contrast Enhancement Introduction: Histogram Histograms and images quality Bright image 7

8 4.2 Contrast Enhancement Introduction: Histogram Histograms and images quality Low-contrast image 8

9 4.2 Contrast Enhancement Introduction: Histogram Histograms and images quality Double-peaks image 9

10 4.2 Contrast Enhancement Introduction: Histogram Histograms and images quality Equalized image 10

11 4.2 Contrast Enhancement Introduction: Classification Direct gray level transformations Histogram processing Operations among images 11

12 4.2 Contrast Enhancement Direct gray level transformations: Linear transformations Expression: Formulation: s = T() r = ar+ b r [ A, B] s [ C, D] s D C BC AD = r+ B A B A 255 Example: C=0 D=255 12

13 4.2 Contrast Enhancement Direct gray level transformations : Linear transformations example: A= 69, B=213, C=0, D=255 s = 1.7 r

14 4.2 Contrast Enhancement Direct gray level transformations : Piecewise-linear transformations Formulation: d c c r r [0, a ) a d c s= r+ c r [ a, b) b a 255 d ( r b ) + d r [ b,255) 255 b 14

15 4.2 Contrast Enhancement Direct gray level transformations : Piecewise-linear transformations ( ac, ) = (10,50),( bd, ) = (210,150) Original image ( ac, ) = (50,10),( bd, ) = (150, 210) 15

16 4.2 Contrast Enhancement Direct gray level transformations : image negatives Formulation: s = L 1 r 16

17 4.2 Contrast Enhancement Direct gray level transformations : Log transformations Formulation: s = c log(1 + r) c is a constant t and itis assumed that r 0 17

18 4.2 Contrast Enhancement Direct gray level transformations : Log transformations Example: display of DFT spectrum Direct display After log operation 18

19 4.2 Contrast Enhancement Direct gray level transformations : Power transformations Formulation: s = cr γ c γ Where and are positive constants. 19

20 4.2 Contrast Enhancement Direct gray level transformations : Power transformations Gamma correction 20

21 4.2 Contrast Enhancement Direct gray level transformations : Power transformations 21

22 4.2 Contrast Enhancement Direct gray level transformations : Gray-lever slicing 22

23 4.2 Contrast Enhancement Histogram processing : Histogram equalization If a transform has the form: s = T() r 0 r 1 We hope the Probability Density Function (PDF) of s is p () s = 1 Inverse transform exist p s and, if r1 < r2 then s1 < s2 Tr () satisfies the following conditions: (a) is single-valued and monotonically in the interval (b) 0 s 1 for 0 r 1 0 r 1 s has the same range as the r 23

24 4.2 Contrast Enhancement Histogram processing : Histogram equalization 24

25 4.2 Contrast Enhancement Histogram processing : Histogram equalization Continuous condition s = T() r dr ps() s = pr() r ds ds pr () r = r dr ps () s = 0 r ( ) p () s = 1 s s p x dx namely r Tr () = p() r xdx 0 25

26 4.2 Contrast Enhancement Histogram processing : Histogram equalization Discrete condition In practice k k n j k k r j j= 0 j= 0 n s = Tr ( ) = p( r) = k= 0,1, 2,..., L 1 k j= 0 s = = k T( rk) ( L 1) pr ( rj ) 26

27 4.2 Contrast Enhancement Histogram processing : Histogram equalization Example:page pe:pge78 Suppose that a 64*64, 3bits image has the gray-level distribution as show in the first row, the calculate steps are: 序号 运算步骤和结果 1 列出原始图灰度级, k = 0,1,..., s k 2 统计原始直方图各灰度级象素 n k 3 计算原始直方图 计算累计直方图 取整 t int[( N 1) t + 0.5] k = k 6 确定映射对应关系 ( sk t k ) ,4 6 5,6,7 7 7 统计新直方图各灰度级象素 n k 用计算新直方图

28 4.2 Contrast Enhancement Histogram processing : Histogram equalization Histograms (b) (a) original histogram transformation function (c) equalized histogram 28

29 4.2 Contrast Enhancement Histogram processing : Histogram equalization Experimental e results s 29

30 4.2 Contrast Enhancement Histogram processing : Histogram equalization Experimental results 30

31 4.2 Contrast Enhancement Histogram processing : Histogram equalization Experimental results 31

32 4.2 Contrast Enhancement Histogram processing : Histogram equalization Experimental results 32

33 4.2 Contrast Enhancement Histogram processing : Histogram equalization Experimental results 33

34 4.2 Contrast Enhancement Histogram processing : Histogram equalization question: page 99, 4.2 Why the discrete histogram equalization technique does not yield a flat histogram? 34

35 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) 35

36 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) Histogram equalization: r s k s = Tr ( ) = p( r) k= 0,1, 2 L 1 k k r j j=0 Histogram equalization: z v k k v = G( z ) = p ( z ) k = 0,1,2 L 1 k k z i i= 0 let v = s then r z k z = G ( v ) = G ( s ) = G ( T( r )) k k k k 36

37 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) G(z k ) Pz v,,v z,pv z, T(r k ) 37

38 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) Example:page pe:pge80 Suppose that a 64*64, 3bits image has the gray-level distribution as show in the first row, and the 5 th row is the specified gray-level distribution. The calculate steps are: 序 运 算 步骤和结果 号 1 列出原始图灰度级, k = 0,1,..., s k 2 统计原始直方图各灰度级象素 n k 3 计算原始直方图 计算原始累计直方图 规定直方图 p ( u ) = n / n, n = u k k 6 计算规定累计直方图 s SML 映射 s 确定映射对应关系 0,1 3 2,3,4 5 5,6,7 7 9s 变换后直方图

39 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) (a) (b) specified histogram original ii lhit histogram (c) resulting histogram 39

40 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) 40

41 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) 41

42 4.2 Contrast Enhancement Histogram processing : Histogram matching (specification) Example original ii equalized matched 42

43 4.2 Contrast Enhancement Direct gray level transformations : Bit-plane slicing eg: b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 一个 8bit 的字节 位面 7.. 位面 B7 B6 B5 B4 B3 B2 B1 B0 43

44 4.2 Contrast Enhancement Direct gray level transformations : Bit-plane slicing b 7 b 6 b 5 b 4 b 3 b 2 b 1 b 0 44

45 4.3 Image Smoothing Introduction Smoothing linear filters Order- statistic filters Low-pass filter in frequency domain 45

46 4.3.1 Introduction 4.3 Image Smoothing Purposes: removing noise Request: keeping edges and details Noise Edges Details Gray levels change greatly in neighborhood Having the same texture in a region Having the similar grads directions in a segment Random in gray levels and spatial location Salt-pepper noise Gaussian noise 46

47 4.3 Image Smoothing Introduction: Noise models PDF of Gaussian noise: pz ( ) = 1 e 2πσ 2 2 ( z μ ) /2σ 47

48 4.3 Image Smoothing Introduction: Noise models Gaussian Guss noise ose g ( x, y) = f( x, y) +η ( x, y) 48

49 4.3 Image Smoothing Introduction: Noise models PDF of salt-pepper noise: Pa z= a pz () = Pb z= b 0 otherwise 49

50 4.3 Image Smoothing Introduction: Noise models salt-pepper noise: 50

51 4.3 Image Smoothing Introduction: Smoothing filters (1) Smoothing linear filters: neighbor ihb averaging out range pixel smoothing Maximum homogeneity smoothing (2)Order- statistic filters: Max filters Min filters Midpoint i filters Median filters Alpha-trimmed mean filter (3)Low-pass filters: Idea low-pass filter (ILPF) Butterworth low-pass filter (BLPF) Gaussian low-pass filter (GLPF) 51

52 4.3 Image Smoothing Mask Smoothing linear filters: neighbor averaging Spatial filter: mask, kernel, e template, e, window Mask coefficients w(-1,-1) w(-1,0) w(-1,1) w(0,-1) w(0,0) w(0,-1) w(1,-1) w(1,0) w(1,1) mask f(x,y) f(x-1,y-1) 1) f(z-1,y) f(x-1,y+1) Pixels under mask f(x,y-1) f(x,y) f(x,y+1) f(x+1,y-1) f(x+1,y) f(x+1,y+1) 52

53 4.3 Image Smoothing Smoothing linear filters: neighbor averaging Spatial filter: operating steps: (page 83) (1) Moving the filter mask from point to point in an image (2) Multiplying the filter coefficient and the corresponding image pixels (3) Adding all the products (4) The sum is the response of the filter at a given point a b gxy (, ) = wijf (, ) ( x+ iy, + j) i= a j = b 53

54 4.3 Image Smoothing Smoothing linear filters: neighbor averaging Typical mask:

55 4.3 Image Smoothing Smoothing linear filters: neighbor averaging Experimental results: different masks 55

56 4.3 Image Smoothing Smoothing linear filters: neighbor averaging Experimental results:different sizes 56

57 4.3 Image Smoothing Smoothing linear filters: out range pixel smoothing formulate a b gxy (, ) = wijf (, ) ( x+ iy, + j) i= a j= b gxy ˆ(, ) gxy (, ) gxy (, )- f( xy, ) > T = f( x, y) others Advantage: keep details in the image with salt-pepper noise 57

58 4.3 Image Smoothing Smoothing linear filters: out range pixel smoothing Experimental results 58

59 4.3 Image Smoothing Smoothing linear filters: Maximum homogeneity smoothing Advantage: keep edges 59

60 4.3 Image Smoothing Order- statistic filters: Max filters formulate g( x, y) = { f( x+ i, y+ j)} max (, i j= 0, ± 1 ) Advantage: removes pepper noise 60

61 4.3 Image Smoothing Order- statistic filters: Min filters formulate g ( x, y ) = { f ( x+ i, y + j )} min (, i j= 0, ± 1 ) Advantage: removes salt noise 61

62 4.3 Image Smoothing Order- statistic filters: Midpoint filter formulate 1 g ( x, y ) = [ { ( x+ i, + )} + { ( x+ i, + )}] 2 max f y j min f y j (, i j= 0, ± 1 ) (, i j= 0, ± 1 ) Advantage: removes Gausian noise 62

63 4.3 Image Smoothing Order- statistic filters: Median filter 1-D: replace the signal value by the median value of neighborhood L=5 X=[ ] Adv vantage e: keep edges [ ] [ ] 63

64 4.3 Image Smoothing Order- statistic filters: Median filter Replaces the value of a pixel by the median of the gray levels in the neighborhood of that pixel gxy (, ) = { f( x+ iy, + j)} median (, i j= 0, ± 1 ) Shapes of 2-D filter 64

65 4.3 Image Smoothing Order- statistic filters: Median filter Experiment result 65

66 4.3 Image Smoothing Order- statistic filters: alpha-trimmed mean filter Delete the α lowest and α highest gray-level values of a sub-image, averaging the remaining pixels as output Let the pixels in a sub-image: A A A 0 1 N 1 Then: gxy (, ) N 1 = N 2 α α i = α A i 66

67 4.3 Image Smoothing Low-pass filters: Idea low-pass filter (ILPF) formulate gxy (, ) = hxy (, )* f( xy, ) Guv (, ) = HuvFuv (, ) (, ) D 0 : cutoff frequency where Huv (, ) 1 if D( u, v) D = 0 if D( u, v) > D 0 0 D 2 ( u, v) = [( u M / 2) + ( v N / 2) 2 ] 1/ 2 67

68 4.3 Image Smoothing Low-pass filters: Idea low-pass filter(ilpf) 68

69 4.3 Image Smoothing Low-pass filters: Idea low-pass filter (ILPF) Properties: es: total image power

70 4.3 Image Smoothing Low-pass filters: Idea low-pass filter (ILPF) Properties: blurring and ringing h(x,y) 70

71 4.3 Image Smoothing Low-pass filters: Idea low-pass filter (ILPF) Experiment result cutoff frequencies set at radii values of

72 4.3 Image Smoothing Low-pass filters: Butterworth low-pass filter formulate Huv (, ) 1 = [ Duv (, )/ D] n 0 where D 2 ( u, v ) = [( u M / 2) + ( v N / 2) 2 ] 1/ 2 72

73 4.3 Image Smoothing Low-pass filters: Butterworth low-pass filter H(u,v)=0.5 when D(u,v)=D D 0 73

74 4.3 Image Smoothing Low-pass filters: Butterworth low-pass filter Properties: blurring and ringing 74

75 4.3 Image Smoothing Low-pass filters: Butterworth low-pass filter Experiment result cutoff frequencies set at radii values of

76 4.3 Image Smoothing Low-pass filters: Gaussian low-pass filter formulate 2 2 (, )/2 0 H ( u, v ) = e D uv D where D 2 ( u, v ) = [( u M / 2) + ( v N / 2) 2 ] 1/ 2 76

77 4.3 Image Smoothing Low-pass filters: Gaussian low-pass filter Inverse Fourier transform of the Gaussian lowpass filter also is Gaussian 77

78 4.3 Image Smoothing Low-pass filters: Gaussian low-pass filter Applications: machine perception 78

79 4.3 Image Smoothing 434L Low-pass filters: Gaussian low-pass filter Applications: printing and publishing industry 79

80 4.3 Image Smoothing Low-pass filters: Gaussian low-pass filter Experiment result cutoff frequencies set at radii values of

81 4.3 Image Smoothing Low-pass filters: Comparisons (cutoff 5) Origin Ideal filter Butterworth filter Gaussian filter 81

82 4.3 Image Smoothing Low-pass filters: Comparison (cutoff 30) Origin Ideal filter Butterworth filter Gaussian filter 82

83 4.3 Image Smoothing Low-pass filters: Comparison (cutoff 80) Origin Ideal filter Butterworth filter Gaussian filter 83

84 The End 84