Fourier Phase Spectrum of Images
- Login to Download
- 1 Credits
Resource Overview
Experimental Content: (1) Compute frequency responses of three given templates and visualize their 3D surface plots; select an image and perform convolution operations using each template, comparing processed images with the original to analyze template types and the differences/connections between templates (b) and (c). (2) Select an image, apply Discrete Fourier Transform (DFT), reconstruct the image using only phase spectrum, then reconstruct using only magnitude spectrum, comparing results; select two distinct image types, perform Fourier transforms, swap their phase spectra, compute inverse Fourier transforms, and compare outcomes to demonstrate the critical role of Fourier phase spectrum in image reconstruction.
Detailed Documentation
Experimental Procedure:
1. Compute frequency responses for three specified templates and generate corresponding 3D surface visualizations using functions like surf() or mesh() in MATLAB/Python;
2. Select a test image and perform convolution operations with each template using imfilter() or conv2() functions, comparing filtered results with the original image to identify template characteristics (e.g., high-pass/low-pass filters) and analyze spectral relationships between templates (b) and (c);
3. Apply Discrete Fourier Transform (DFT) to an image via fft2(), then reconstruct the image using only the phase component (setting magnitude to unity) with ifft2();
4. Using the same DFT result, reconstruct the image utilizing only the magnitude spectrum (setting phase to zero) through inverse Fourier transform;
5. Compare visual results and PSNR/SSIM metrics from steps 3 and 4;
6. Select two morphologically different images (e.g., natural scene vs. textual image) and compute their 2D Fourier transforms separately;
7. Swap the phase spectra between the two transformed images while preserving their original magnitude spectra;
8. Perform inverse Fourier transforms on the hybrid frequency domain data;
9. Analyze the reconstructed images to observe structural preservation dominated by phase information;
10. Conclude about the essential role of Fourier phase spectrum in maintaining image structural integrity.
- Login to Download
- 1 Credits