[OpenCV complete routine] 86 Application of frequency domain filtering: fingerprint image processing

Posted by phpian on Tue, 01 Feb 2022 01:30:48 +0100

[OpenCV complete routine] 86 Application of frequency domain filtering: fingerprint image processing

Welcome to pay attention "100 complete OpenCV routines" Series, continuously updating
Welcome to pay attention "Python Xiaobai's OpenCV learning course" Series, continuously updating

4. High pass filter in frequency domain

Image edge and other sharp changes of gray level are related to high-frequency components, so image sharpening can be realized by high pass filtering in frequency domain. High pass filtering attenuates the low-frequency components in the Fourier transform without interfering with the high-frequency information.

Simply, by subtracting the transfer function of the low-pass filter from 1 in the frequency domain, the corresponding high-pass filter transfer function can be obtained:
H H P ( u , v ) = 1 − H L P ( u , v ) H_{HP}(u,v) = 1- H_{LP}(u,v) HHP(u,v)=1−HLP(u,v)
Where, H H P ( u , v ) H_{HP}(u,v) HHP(u,v), H L P ( u , v ) H_{LP}(u,v) HLP (u,v) represents the transfer functions of high pass filter and low-pass filter respectively.

The transfer function of Gaussian high pass filter (GHPF) is:
H ( u , v ) = 1 − e − D 2 ( u , v ) / 2 D 0 2 H(u,v)=1-e^{-D^2 (u,v)/2D_0^2} H(u,v)=1−e−D2(u,v)/2D02

Routine 8.25: fingerprint image processing (high pass filtering + threshold processing)

(1) Optimal extended fast Fourier transform;
(2) Construct a Gaussian low pass filter;
(3) Modify Fourier transform in frequency domain: Fourier transform point multiplication Gaussian high pass filter;
(4) Performing an inverse Fourier transform on the high pass Fourier transform;
(5) Threshold processing to obtain a sharpened image.

# OpenCVdemo08.py
# Demo08 of OpenCV
# 8. Image frequency domain filtering
# Copyright 2021 Youcans, XUPT
# Crated: 2021-12-15

    # 8.25: fingerprint image processing (high pass filtering + threshold processing)
    def gaussHighPassFilter(shape, radius=10):  # Gaussian Highpass 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 = 1 - 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


    def imgHPFilter(image, D0=50):  #Image high pass filtering
        rows, cols = image.shape[:2]  # The height and width of the picture
        # fast Fourier transform 
        dftImage = dft2Image(image)  # Fast Fourier transform (rPad, cPad, 2)
        rPadded, cPadded = dftImage.shape[:2]  # Fast Fourier transform size, original image size optimization

        # Construct Gaussian low pass filter
        hpFilter = gaussHighPassFilter((rPadded, cPadded), radius=D0)  # Gaussian Highpass Filter 

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

        # The inverse Fourier transform is performed on the high 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(dftHPfilter, idft, cv2.DFT_REAL_OUTPUT + cv2.DFT_INVERSE + cv2.DFT_SCALE)

        # 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)

        # 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]
        imgHPF = result.astype(np.uint8)
        imgHPF = imgHPF[:rows, :cols]
        return imgHPF


    imgGray = cv2.imread("../images/Fig0457a.tif", flags=0)  # flags=0 read as grayscale image
    rows, cols = imgGray.shape[:2]  # The height and width of the picture
    imgHPF = imgHPFilter(imgGray, D0=50)
    imgThres = np.clip(imgHPF, 0, 1)

    plt.figure(figsize=(10, 5))
    plt.subplot(131), plt.imshow(imgGray, 'gray'), plt.title('origial'), plt.xticks([]), plt.yticks([])
    plt.subplot(132), plt.imshow(imgHPF, 'gray'), plt.title('GaussHPF'), plt.xticks([]), plt.yticks([])
    plt.subplot(133), plt.imshow(imgThres, 'gray'), plt.title('Threshold'), plt.xticks([]), plt.yticks([])
    plt.tight_layout()
    plt.show()

(end of this section)

youcans@xupt Original works, reprint must be marked with the original link

Crated: 2022-1-30

Welcome to pay attention "100 complete OpenCV routines" Series, continuously updating
Welcome to pay attention "Python Xiaobai's OpenCV learning course" Series, continuously updating

Topics: Python OpenCV Algorithm Computer Vision image processing

Programmer Think

[OpenCV complete routine] 86 Application of frequency domain filtering: fingerprint image processing