CS 519 Signal & Image Processing
Human Vision
Human Vision
Some properties of human vision that affect image perception:
Linear and non-linear parts Non-linear (approx. logarithmic) encoding of input Adaptation Relative-contrast encoding Varying sensitivi
CS 519 Signal & Image Processing
Sampling
Sampling
f(t) Continuous t
g(t) Discrete t
1
Sampling: Spatial/Temporal Domain
Sampling a continuous function f at time/space interval t to produce a discrete function g g[n] = f(nt) is the same as multiplying it
CS 519 Signal & Image Processing
Video
Storing Video
Simplest: Store fully-encoded frames (2-D images) as a
sequence
Better: Individually compress each frame
Still Better: Take advantage of inter-frame redundancy
Simple frame subtraction and encode/com
CS 519 Signal & Image Processing
Reconstruction
Image Reconstruction
Reconstruction is the process of attempting to recreate the original signal given a corrupted one Terms:
Scene: the real world Image: a (possibly corrupted) picture of a scene
Image reco
CS 519 Signal & Image Processing
Other Transforms
Other Transforms
A transform is a change in the numeric representation
of a signal that preserves all of the signals information
Transforms can be thought of as a change of
coordinates into some coordina
CS 519 Signal & Image Processing
The Fourier Transform: Examples & Properties
Magnitude and Phase
Remember: complex numbers can be thought of in two ways: (real, imaginary) or (magnitude, phase)
Magnitude: F = ( F ) 2 + ( F ) 2 Phase: Intuition:
( F ) (
CS 519 Signal & Image Processing
The Fourier Transform: Linear Systems
Linear Systems and Responses
Input
Time/Spatial
f
Frequency
F
Output
g
G
Impulse Response
h
Transfer Function
Relationship
H
g=f*h
G = FH
1
The Convolution Theorem
Let F, G, and H deno
CS 519 Signal & Image Processing
The 2-D Fourier Transform
2-D Continuous Fourier Transform
Basic functions are sinusoids with frequency u in one
direction times sinusoids with frequency v in the other:
F (u , v) =
f ( x, y ) e
i 2 (ux + vy )
dx dy
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