Image Transforms Lecture

Abstract

This lecture overviews Image Transforms that are instrumental in image filtering, compression and power spectrum estimation.   It covers the following topics in detail: 2D Discrete Space Fourier Transform, 2D Discrete Fourier Transform and their properties. 2D FFT algorithms: Row-column FFT (RCFFT) algorithm, Vector-radix FFT (VRFFT) algorithm, Polynomial Transform FFT (PTFFT). 2D convolution calculation using 2D FFT algorithms. 2D DFT memory problems. 2D Power Spectrum estimation. Discrete Cosine Transform (DCT), 2D DCT and their use in image compression.

Image LENA and its power spectrum.

Image-Transforms-v3.4.1-Summary

Understanding Questionnaire

https://docs.google.com/forms/image-transforms

Tutorial Exercises

1. 2D Inverse Discrete Fourier Transform Tutorial Exercise
2. 3D Discrete Fourier Transform Tutorial Exercise
3. Continuous Signal Fourier Transform
4. DFT Coefficients Exercise
5. Discrete Fourier Transform Tutorial Exercise
6. FIR Frequency Response Tutorial Exercise
7. Frequency Response Tutorial Exercise
8. Separable Filter Frequency Response Tutorial Exercise
9. Seperable 2D DFT Calculation Tutorial Exercise

Programming Exercise

1. Video frame frequency Spectrum