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ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
ECE 516 / CS 532
Computer Vision
Pradeep Sen Advanced Graphics Lab
Class 8 February 16, 2009
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Last time
Linear filters
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Today
Fourier Transforms
Correlation filters
Edge detection
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Fourier transforms
Projection of function into sinusoidal basis i.e. write a signal as a sum of sinusoids
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
1-D Example
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
2-D Fourier basis elements
Real component of the Fourier basis elements
(u,v) = (0,0.4) (^) (u,v) = (1,2) (u,v) = (10,-5)
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Magnitude vs phase
original magnitude phase magnitude + other phase
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Properties of Fourier transforms
Linear operator Important property: multiplication in the time domain becomes convolution in the frequency domain and vice-versa
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Sampling
Fundamental to images, hence important in computer vision (as well as image processing, computer graphics, etc)
Basic idea: take continuous signal and measure “samples” of it to record
Converts a continuous signal into a discrete signal
“Aliasing” occurs when high frequency information masquerades as low frequency information because of sampling
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Sufficient sampling
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Under sampling
ECE516 / CS532 Computer Vision Pradeep Sen Class 8 – February 16, 2009
Sampling
So in order to properly sample a signal without aliasing, we must band-limit it depending on the sampling rate
