IEG4160_Part4 - IEG 4160 Image and Video Processing...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Linear & Shift Invariant Systems IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu Linearity and shift invariance Delta function and its properties Point spread function Convolution Discrete LSI systems
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Page 2 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Linearity
Background image of page 2
Page 3 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Shift invariance 1D 2D Linear, shift invariant systems (LSI systems) I f () , then ( ) ( ) f t g t f tT g →− t t f t gt t t f gt T T T If ( , ) ( , ), then ( , ) ( , ) f x yg x y fx y gx y α βα β −→
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Page 4 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Delta function
Background image of page 4
Page 5 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Delta function Can be defined as the limit of a sequence of functions ± each member has some area, but getting narrower & higher A “ sharp spike ”atorigin
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Page 6 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Delta function Examples in 1D ± ± 0 1 ( ) lim rect a t t aa δ ⎛⎞ = ⎜⎟ ⎝⎠ t () t 0 1/2 t rect( ) t 1 /2 a /2 a t 1 rect( ) a t a 1/ a
Background image of page 6
Page 7 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Delta function Examples in 2D ± ± ( , ) lim ( , ) N N xy δ →∞ = 2 rect( , ), | | 1/2 , |y| 1/2 (, ) 0, elsewhere N NN x N y x N N ≤≤ = x y x y (0,0)
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Page 8 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Delta function Properties ± It’s 0 everywhere except at the origin ± Its volume = 1 x y (, ) x y δ (0,0)
Background image of page 8
Page 9 IEG 4160: Image and Video Processing. Lecturer: Jianzhuang Liu 4. Linear & Shift Invariant Systems Delta function
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 24

IEG4160_Part4 - IEG 4160 Image and Video Processing...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online