Tutorial 1

• For a real-valued function, show that its Fourier transform is conjugate symmetric
• Prove the shift theorem in DFT
• Proof of rotation and scaling theorem in continuous Fourier transforms
• Demo of visualization of Fourier transform magnitude for an image
• Demo of finding the translation between two images efficiently using Fourier transforms

Tutorial 2

• Analysis of Fourier transform of a 3 x 3 spatial mask of the form [0 1/4 0; 1/4 0 1/4; 0 1/4 0]
• Homomorphic filtering (section 4.9.6 of Gonzalez)
• Discussion on blur kernel estimation given pairs of blurred images (all with the same blur kernel) and their "clean" versions

Tutorial 3

• Prove that the Radon transform is a linear operator
• Radon transform of f(x-x0,y-y0) in terms of the Radon transform of f(x,y) - applications in efficient image alignment
• Radon transform of rotated image
• Question 1 from last year's final exam (see solutions also)