[200 opencv routines] 100 Adaptive local noise reduction filter

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【OpenCV routine 200 piece 】100. Adaptive local noise reduction filter

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3.7 Adaptive local noise reduction filter

The aforementioned filter is directly applied to image processing , The features of the image itself are not considered . Characteristics of adaptive filter $m\ast n$ Rectangular neighborhood $Sxy$ The statistical characteristics of the image in the defined filtering region change . Usually , The performance of adaptive filter is better than that of the above filter , However, the complexity and computation of the filter are also greater .

Mean and variance are the most basic statistics of random variables . In image processing , The mean is the average gray level of the pixel neighborhood , Variance is the image contrast of the pixel neighborhood .

Make $Sxy$ Indicates that the center is at the point $(x,y)$ 、 The size is $m\ast n$ Rectangular sub window （ Neighborhood ）, The filter is controlled by $Sxy$ Defined neighborhood operations .

Noise image at point $(x,y)$ Value $g(x,y)$, The variance of the noise ${\sigma }_{\eta }^2$ Estimated from noisy images ;$Sxy$ The local average gray level of pixels in the is ${\bar{z}}_{Sxy}$, The local variance of gray scale is ${\sigma }_{Sxy}^2$.

Image restored using adaptive local noise reduction filter $\hat{f}$ At point $(x,y)$ Value , Described by the following adaptive expression ：
$$\hat{f}(x,y)=g(x,y)-\frac{{\sigma }_{\eta }^2}{{\sigma }_{Sxy}^2}[g(x,y)-\overline{z_{Sxy}}]$$

routine 9.14： Adaptive local noise reduction filter

    # 9.14:  Adaptive local noise reduction filter  (Adaptive local noise reduction filter)
    img = cv2.imread("../images/Fig0507b.tif", 0)  # flags=0  Read as grayscale image 
    hImg = img.shape[0]
    wImg = img.shape[1]

    m, n = 5, 5
    imgAriMean = cv2.boxFilter(img, -1, (m, n))  #  Arithmetic average filtering 

    #  Edge fill 
    hPad = int((m-1) / 2)
    wPad = int((n-1) / 2)
    imgPad = np.pad(img.copy(), ((hPad, m-hPad-1), (wPad, n-wPad-1)), mode="edge")

    #  Estimate the noise variance of the original image  sigmaEta
    mean, stddev = cv2.meanStdDev(img)
    sigmaEta = stddev ** 2
    print(sigmaEta)

    #  Adaptive local noise reduction 
    epsilon = 1e-8
    imgAdaLocal = np.zeros(img.shape)
    for i in range(hImg):
        for j in range(wImg):
            pad = imgPad[i:i+m, j:j+n]  #  Neighborhood  Sxy, m*n
            gxy = img[i,j]  #  Pixels of noisy image 
            zSxy = np.mean(pad)  #  Local average gray level 
            sigmaSxy = np.var(pad)  #  Local variance of gray level 
            rateSigma = min(sigmaEta / (sigmaSxy + epsilon), 1.0)  #  Additive noise hypothesis ：sigmaEta/sigmaSxy < 1
            imgAdaLocal[i, j] = gxy - rateSigma * (gxy - zSxy)

    plt.figure(figsize=(9, 6))
    plt.subplot(131), plt.axis('off'), plt.title("Original")
    plt.imshow(img, cmap='gray', vmin=0, vmax=255)
    plt.subplot(132), plt.axis('off'), plt.title("Arithmentic mean filter")
    plt.imshow(imgAriMean, cmap='gray', vmin=0, vmax=255)
    plt.subplot(133), plt.axis('off'), plt.title("Adaptive local filter")
    plt.imshow(imgAdaLocal, cmap='gray', vmin=0, vmax=255)
    plt.tight_layout()
    plt.show()

（ At the end of this section ）

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Copyright 2021 youcans, XUPT

Crated：2022-2-1

Welcome to your attention 『OpenCV routine 200 piece 100 piece 』 series , Ongoing update
Welcome to your attention 『Python Small white OpenCV Learning lessons 』 series , Ongoing update

【OpenCV routine 200 piece 】01. Image reading （cv2.imread）
【OpenCV routine 200 piece 】02. Image saving （cv2.imwrite）
【OpenCV routine 200 piece 】03. Image display （cv2.imshow）
【OpenCV routine 200 piece 】04. use matplotlib Display images （plt.imshow）
【OpenCV routine 200 piece 】05. The properties of the image （np.shape）
【OpenCV routine 200 piece 】06. Pixel editing （img.itemset）
【OpenCV routine 200 piece 】07. Image creation （np.zeros）
【OpenCV routine 200 piece 】08. Copy of image （np.copy）
【OpenCV routine 200 piece 】09. Image clipping （cv2.selectROI）
【OpenCV routine 200 piece 】10. Image stitching （np.hstack）
【OpenCV routine 200 piece 】11. Split of image channel （cv2.split）
【OpenCV routine 200 piece 】12. Merging of image channels （cv2.merge）
【OpenCV routine 200 piece 】13. The addition of images （cv2.add）
【OpenCV routine 200 piece 】14. The image is added to the scalar （cv2.add）
【OpenCV routine 200 piece 】15. Weighted addition of images （cv2.addWeight）
【OpenCV routine 200 piece 】16. Addition of images of different sizes
【OpenCV routine 200 piece 】17. Gradient switching between two images
【OpenCV routine 200 piece 】18. Mask addition of images
【OpenCV routine 200 piece 】19. The circular mask of the image
【OpenCV routine 200 piece 】20. Bitwise operation of image
【OpenCV routine 200 piece 】21. Image overlay
【OpenCV routine 200 piece 】22. Add non Chinese text to the image
【OpenCV routine 200 piece 】23. Add Chinese text to the image
【OpenCV routine 200 piece 】23. Add Chinese text to the image
【OpenCV routine 200 piece 】24. Affine transformation of image
【OpenCV routine 200 piece 】25. Translation of image
【OpenCV routine 200 piece 】26. The rotation of the image （ Centered on the origin ）
【OpenCV routine 200 piece 】27. The rotation of the image （ Centered on any point ）
【OpenCV routine 200 piece 】28. The rotation of the image （ Right angle rotation ）
【OpenCV routine 200 piece 】29. Image flipping （cv2.flip）
【OpenCV routine 200 piece 】30. Image zooming （cv2.resize）
【OpenCV routine 200 piece 】31. Image pyramid （cv2.pyrDown）
【OpenCV routine 200 piece 】32. Image distortion （ Crosscutting ）
【OpenCV routine 200 piece 】33. Composite transformation of image
【OpenCV routine 200 piece 】34. Projection transformation of image
【OpenCV routine 200 piece 】35. Projection transformation of image （ Border filling ）
【OpenCV routine 200 piece 】36. Conversion of rectangular coordinates and polar coordinates
【OpenCV routine 200 piece 】37. Gray processing and binary processing of image
【OpenCV routine 200 piece 】38. Inverse color transformation of image （ Image reversal ）
【OpenCV routine 200 piece 】39. Linear transformation of image gray
【OpenCV routine 200 piece 】40. Image piecewise linear gray scale transformation
【OpenCV routine 200 piece 】41. Gray scale transformation of image （ Grayscale stratification ）
【OpenCV routine 200 piece 】42. Gray scale transformation of image （ Bit plane layering ）
【OpenCV routine 200 piece 】43. Gray scale transformation of image （ Logarithmic transformation ）
【OpenCV routine 200 piece 】44. Gray scale transformation of image （ Gamma transform ）
【OpenCV routine 200 piece 】45. Gray histogram of the image
【OpenCV routine 200 piece 】46. Histogram equalization
【OpenCV routine 200 piece 】47. Image enhancement — Histogram matching
【OpenCV routine 200 piece 】48. Image enhancement — Color histogram matching
【OpenCV routine 200 piece 】49. Image enhancement — Local histogram processing
【OpenCV routine 200 piece 】50. Image enhancement — Histogram statistics image enhancement
【OpenCV routine 200 piece 】51. Image enhancement — Histogram back tracking
【OpenCV routine 200 piece 】52. Image correlation and convolution
【OpenCV routine 200 piece 】53. Scipy Realize image two-dimensional convolution
【OpenCV routine 200 piece 】54. OpenCV Realize image two-dimensional convolution
【OpenCV routine 200 piece 】55. Separable convolution kernel
【OpenCV routine 200 piece 】56. Low pass cartridge filter
【OpenCV routine 200 piece 】57. Low pass Gaussian filter
【OpenCV routine 200 piece 】58. Nonlinear filtering — median filtering
【OpenCV routine 200 piece 】59. Nonlinear filtering — Bilateral filtering
【OpenCV routine 200 piece 】60. Nonlinear filtering — Joint bilateral filtering
【OpenCV routine 200 piece 】61. Guided filtering （Guided filter）
【OpenCV routine 200 piece 】62. Sharpen the image —— Passivation masking
【OpenCV routine 200 piece 】63. Sharpen the image ——Laplacian operator
【OpenCV routine 200 piece 】64. Sharpen the image ——Sobel operator
【OpenCV routine 200 piece 】65. Sharpen the image ——Scharr operator
【OpenCV routine 200 piece 】66. Low pass of image filtering / qualcomm / Band stop / Bandpass
【OpenCV routine 200 piece 】67. Comprehensive application of image enhancement in spatial domain
【OpenCV routine 200 piece 】68. Comprehensive application of image enhancement in spatial domain
【OpenCV routine 200 piece 】69. Discontinuous Fourier coefficients
【OpenCV routine 200 piece 】70. Fourier transform of one-dimensional continuous function
【OpenCV routine 200 piece 】71. Sampling of continuous functions
【OpenCV routine 200 piece 】72. One dimensional discrete Fourier transform
【OpenCV routine 200 piece 】73. Two dimensional continuous Fourier transform
【OpenCV routine 200 piece 】74. Anti aliasing of images
【OpenCV routine 200 piece 】75. Numpy Realize image Fourier transform
【OpenCV routine 200 piece 】76. OpenCV Realize image Fourier transform
【OpenCV routine 200 piece 】77. OpenCV Realize fast Fourier transform
【OpenCV routine 200 piece 】78. Fundamentals of image filtering in frequency domain
【OpenCV routine 200 piece 】79. The basic steps of image filtering in frequency domain
【OpenCV routine 200 piece 】80. Detailed steps of image filtering in frequency domain
【OpenCV routine 200 piece 】81. Gaussian low pass filter in frequency domain
【OpenCV routine 200 piece 】82. Butterworth low pass filter in frequency domain
【OpenCV routine 200 piece 】83. Low pass filtering in frequency domain ： Printed text character repair
【OpenCV routine 200 piece 】84. The high pass filter is obtained from the low pass filter
【OpenCV routine 200 piece 】85. Application of high pass filter in frequency domain
【OpenCV routine 200 piece 】86. Frequency domain filtering applications ： Fingerprint image processing
【OpenCV routine 200 piece 】87. Frequency domain passivation masking
【OpenCV routine 200 piece 】88. Laplace high pass filter in frequency domain
【OpenCV routine 200 piece 】89. Transfer function of band stop filter
【OpenCV routine 200 piece 】90. Frequency domain notch filter
【OpenCV routine 200 piece 】91. Gaussian noise 、 rayleigh noise 、 Irish noise
【OpenCV routine 200 piece 】92. Exponential noise 、 Uniform noise 、 Salt and pepper noise
【OpenCV routine 200 piece 】93. Histogram of noise model
【OpenCV routine 200 piece 】94. Arithmetic average filter
【OpenCV routine 200 piece 】95. Geometric mean filter
【OpenCV routine 200 piece 】96. Harmonic averaging filter
【OpenCV routine 200 piece 】97. Anti harmonic averaging filter
【OpenCV routine 200 piece 】98. Statistical sorting filter
【OpenCV routine 200 piece 】99. Modified alpha mean filter
【OpenCV routine 200 piece 】100. Adaptive local noise reduction filter