The Fourier Transform

The Fourier Transform (FT) is a fundamental mathematical tool used in image processing to analyze the frequency components of an image. It allows us to transform an image from the spatial domain (where pixel values are represented directly) to the frequency domain (where we analyze patterns and structures based on their frequency). This is useful for tasks like image filtering, edge detection, and noise reduction.

First, we need to convert the image to grayscale:

To compute the 2D Fourier Transform:

Here, fft2() converts the image from the spatial domain to the frequency domain, and fftshift() moves low-frequency components to the center.

To visualize the magnitude spectrum:

Since Fourier Transform outputs complex numbers, we take the absolute values (np.abs()) for a meaningful visualization.

The np.log function enhances visibility, as raw magnitude values vary greatly in scale.