lecture04: Sampling and transforms in 2D

This lecture extends our work on the DFT into 2D. We see that the DFT naturally generalizes to higher dimensions, and this can be very useful in image processing.

Topics covered

• Transforms in 2D
• 2D signals = images
• Displaying 2D signals
• The DFT in 2D
• Examples (i)
• Examples (i): {\tt fftshift}
• Examples (ii)
• Examples (iii): superposition
• Examples (iv)
• DFT and symmetry
• Examples (iv-b)
• 2D DFT of a sinusoid
• Examples (v)
• Examples (v-b) %
• Examples (v)
• Examples (vi)
• Examples (vii)
• Examples (viii)
• Examples (viiib)
• Radial symmetry
• Examples (Lena)
• Aliasing in images
• Jaggies
• Jaggies (reduced by enhanced resolution)
• Jaggies (reduced by pre-filtering)
• Moire patterns
• Anti-aliased fonts
• Anti-aliased CGI
• Aliasing: crawling ants
• Resampling applications: video
• Resampling applications: printing
• Newsprint
• Resampling applications: printing
• Half-toning
• Halftoning
• Dithering
• Examples of Dithering
• Extreme example: ascii art
• Application: JPEG compression
• JPEG algorithm
• Color in images
• JPEG compression (color transform)
• JPEG compression (blocks)
• The Discrete Cosine Transform (DCT)
• JPEG compression -- quantization
• Quantization
• Quantization matrix
• JPEG compression -- Encoding %
• JPEG compression (example)
• JPEG compression properties
• Application: JPEG compression
• Steganography
• Applications: digital watermarks
• Watermarks
• Watermarks in the frequency domain
• Applications: digital watermarks