[OpenCV complete routine] 83 Low pass filtering in frequency domain: character restoration of printed text

Posted by Magestic on Sat, 29 Jan 2022 07:31:27 +0100

[OpenCV complete routine] 83 Frequency domain low-pass filtering case: printed text character repair

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3.5 low pass filtering in frequency domain: character restoration of printed text

Low pass filtering technology is mainly used in printing and publishing industry. This section presents the practical application of low-pass filtering in frequency domain: character restoration of printed text. The case comes from figure 4.48 of P194 of Gonzalez's digital image processing (Fourth Edition).

The original image is a sample of a low resolution text image. We will encounter such text in fax, copy or historical documents. The text in the picture does not have stains, creases and tears, but the characters in the text are distorted due to insufficient resolution, many of which are broken. One way to solve this problem is to bridge these small gaps by blurring the input image.

The routine shows how to use different D 0 D_0 The repair effect of D0 # Gaussian low-pass filter after simple processing. Of course, this is only one step of repair. Next, other processing, such as threshold processing and thinning processing, will be carried out. These methods will be discussed in the follow-up content.

In order to facilitate future use, the routine encapsulates the optimal extended fast Fourier transform and Gaussian low-pass filter as functions.

Routine 8.22: GLPF low-pass filtering case: text character recognition

# OpenCVdemo08.py
# Demo08 of OpenCV
# 8. Image frequency domain filtering
# Copyright 2021 Youcans, XUPT
# Crated: 2021-12-15
   
# 8.22: GLPF low-pass filtering case: text character recognition
    def gaussLowPassFilter(shape, radius=10):  # Gaussian low pass filter
        # Gaussian filter:# Gauss = 1/(2*pi*s2) * exp(-(x**2+y**2)/(2*s2))
        u, v = np.mgrid[-1:1:2.0/shape[0], -1:1:2.0/shape[1]]
        D = np.sqrt(u**2 + v**2)
        D0 = radius / shape[0]
        kernel = np.exp(- (D ** 2) / (2 *D0**2))
        return kernel

    def dft2Image(image):  #Optimal extended fast Fourier transform
        # Centralized 2D array f (x, y) * - 1 ^ (x + y)
        mask = np.ones(image.shape)
        mask[1::2, ::2] = -1
        mask[::2, 1::2] = -1
        fImage = image * mask  # f(x,y) * (-1)^(x+y)

        # Optimal DFT expansion size
        rows, cols = image.shape[:2]  # The height and width of the original picture
        rPadded = cv2.getOptimalDFTSize(rows)  # Optimal DFT expansion size
        cPadded = cv2.getOptimalDFTSize(cols)  # For fast Fourier transform

        # Edge extension (complement 0), fast Fourier transform
        dftImage = np.zeros((rPadded, cPadded, 2), np.float32)  # Edge expansion of the original image
        dftImage[:rows, :cols, 0] = fImage  # Edge expansion, 0 on the lower and right sides
        cv2.dft(dftImage, dftImage, cv2.DFT_COMPLEX_OUTPUT)  # fast Fourier transform 
        return dftImage


    # (1) Read original image
    imgGray = cv2.imread("../images/Fig0419a.tif", flags=0)  # flags=0 read as grayscale image
    rows, cols = imgGray.shape[:2]  # The height and width of the picture

    plt.figure(figsize=(10, 6))
    plt.subplot(2, 3, 1), plt.title("Original"), plt.axis('off'), plt.imshow(imgGray, cmap='gray')

    # (2) Fast Fourier transform
    dftImage = dft2Image(imgGray)  # Fast Fourier transform (rPad, cPad, 2)
    rPadded, cPadded = dftImage.shape[:2]  # Fast Fourier transform size, original image size optimization
    print("dftImage.shape:{}".format(dftImage.shape))


    D0 = [10, 30, 60, 90, 120]  # radius
    for k in range(5):
        # (3) Construct Gaussian low pass filter
        lpFilter = gaussLowPassFilter((rPadded, cPadded), radius=D0[k])

        # (5) Modify Fourier transform in frequency domain: Fourier transform point multiplication low-pass filter
        dftLPfilter = np.zeros(dftImage.shape, dftImage.dtype)  # Size of fast Fourier transform (optimized size)
        for j in range(2):
            dftLPfilter[:rPadded, :cPadded, j] = dftImage[:rPadded, :cPadded, j] * lpFilter

        # (6) The inverse Fourier transform is performed on the low-pass Fourier transform, and only the real part is taken
        idft = np.zeros(dftImage.shape[:2], np.float32)  # Size of fast Fourier transform (optimized size)
        cv2.dft(dftLPfilter, idft, cv2.DFT_REAL_OUTPUT + cv2.DFT_INVERSE + cv2.DFT_SCALE)

        # (7) Centralized 2D array g (x, y) * - 1 ^ (x + y)
        mask2 = np.ones(dftImage.shape[:2])
        mask2[1::2, ::2] = -1
        mask2[::2, 1::2] = -1
        idftCen = idft * mask2  # g(x,y) * (-1)^(x+y)

        # (8) Intercept the upper left corner, the size is equal to the input image
        result = np.clip(idftCen, 0, 255)  # Truncation function, limiting the value to [0255]
        imgLPF = result.astype(np.uint8)
        imgLPF = imgLPF[:rows, :cols]

        plt.subplot(2,3,k+2), plt.title("GLPF rebuild(n={})".format(D0[k])), plt.axis('off')
        plt.imshow(imgLPF, cmap='gray')

    print("image.shape:{}".format(imgGray.shape))
    print("lpFilter.shape:{}".format(lpFilter.shape))
    print("dftImage.shape:{}".format(dftImage.shape))

    plt.tight_layout()
    plt.show()

(end of this section)

youcans@xupt Original works, reprint must be marked with the original link: [OpenCV complete routine] 82 Butterworth low pass filter in frequency domain

Crated: 2022-1-25

Welcome to pay attention "100 complete OpenCV routines" Series, continuously updating
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Topics: Python OpenCV Algorithm Computer Vision image processing

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[OpenCV complete routine] 83 Low pass filtering in frequency domain: character restoration of printed text

[OpenCV complete routine] 83 Frequency domain low-pass filtering case: printed text character repair

3.5 low pass filtering in frequency domain: character restoration of printed text

Routine 8.22: GLPF low-pass filtering case: text character recognition

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