Image Processing with Fourier Transform Filters

This script performs various image processing tasks using Fourier Transform filters.

Step 1: Import Libraries

Importing necessary libraries such as cv2 for computer vision operations, numpy for numerical computations, matplotlib.pyplot for plotting, and math for mathematical functions.

Step 2: Load and Display Images

Two images are loaded using cv2.imread function. The first image is loaded grayscale. These images are then displayed using matplotlib.pyplot.

Step 3: Fourier Transform

The images are transformed into the frequency domain using Fourier Transform (np.fft.fft2). The zero frequency component is shifted to the center (np.fft.fftshift). Then, the inverse operations are performed to bring back the image to its original position (np.fft.ifftshift, np.fft.ifft2).

Step 4: Plotting Spectrums

Here, plots various spectrums of the images including the original spectrum, centered spectrum, and decentralized spectrum using matplotlib.pyplot.

Step 5: Implementing Filters

Several types of filters are implemented:

• Ideal Low-pass and High-pass Filters
• Butterworth Low-pass and High-pass Filters
• Gaussian Low-pass and High-pass Filters

These filters are defined as functions taking parameters such as cutoff frequency (D0) and image shape.

Step 6: Applying Filters

One of the images is chosen, and a low-pass filter is applied to it. The steps include centering the spectrum, applying the filter, and then reversing the operations to obtain the processed image.

Step 7: Plotting Results

The original image, its spectrum, centered spectrum, multiplied spectrum with the low-pass filter, decentralized spectrum, and the processed image are plotted using matplotlib.pyplot.

Conclusion

This code provides a comprehensive demonstration of image processing techniques using Fourier Transform filters.