DFT Image Processing

Description

This project implements image processing in the frequency domain using the Discrete Fourier Transform (DFT) with Python and Tkinter.

Features

• Discrete Fourier Transform (DFT)
• Inverse DFT (image reconstruction)
• Amplitude spectrum visualization
• Circular filtering (low-pass / high-pass)
• Mean filter (frequency domain)
• Gaussian filter (frequency domain)

How it works

The image is transformed to the frequency domain using fft2, then centered with fftshift.

Filtering is applied by multiplying the frequency representation with a mask, and the final image is reconstructed using ifft2.

Key concepts

• Frequency domain representation

• Circular masks for filtering

• Convolution theorem:

  TF(image × filter) = TF(image) × TF(filter)

Types of filtering

Low-pass filter

Keeps low frequencies and removes high frequencies, producing a smoother image.

High-pass filter

Keeps high frequencies to enhance edges and fine details.

Mean and Gaussian filters

Filters are created as masks and applied in the frequency domain.

How to run

pip install numpy pillow matplotlib
python dft-image-processing.py