Frequency Domain

Image
 enhancement
 in
 the
  frequency
 domain
 

What
 exactly
 is
 “frequency”
 

1 k= λ
k = u +v
2 2

€

Spa;al
 frequencies
 

Fourier
 series
 and
 
  the
 Fourier
 transform
 

Proper;es
 of
 the
 Fourier
 transform
 
•  •  •  •  •  •  •  •  •  Separability
  Linearity
  Transla;on
 /
 shiBing
  Periodicity
 and
 symmetry
  Rota;on
  Scaling
  Convolu;on
  Projec;on
 (central
 slice
 theorem)
  Energy
 

Orien;ng
 ourselves…
 

How
 to
 calculate
 the
 2D
 Fourier
  transform
 

Ac;vity
 7.2
 

Window
 func;ons
 

MRI
 trouble…
 

More
 MRI
 trouble
 

Cross-­‐correla;on
 
CCF = f ( x, y ) * h ( x, y )
*

€

FT [ f ( x, y ) * h ( x, y )] = F ( u,v )G ( u,v )
* *

€

Template
 matching
 

Ac;vity
 7.6
 

Filtering
 in
 the
 frequency
 domain
 
•  Convolu;on
 in
 the
 spa;al
 domain
 corresponds
  to
 
 

Ac;vity
 7.7
 

Ac;vity
 7.8