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In the name of Allah In the name of Allah
the compassionate, the merciful
In the name of Allah In the name of Allah the compassionate, the - - PowerPoint PPT Presentation
In the name of Allah In the name of Allah the compassionate, the - - PowerPoint PPT Presentation
In the name of Allah In the name of Allah the compassionate, the merciful Digital Video Processing S. Kasaei S. Kasaei Room: CE 307 Department of Computer Engineering Sharif University of Technology E-Mail: skasaei@sharif.edu Web Page:
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Digital Video Processing
- S. Kasaei
- S. Kasaei
Room: CE 307 Department of Computer Engineering Sharif University of Technology
E-Mail: skasaei@sharif.edu Web Page: http://sharif.edu/~skasaei http://mehr.sharif.edu/~ipl
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Chapter 3 Chapter 3
Video Sampling Video Sampling
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Video Sampling Main Concerns
- 1. What are the necessary sampling
frequencies in the spatial & temporal directions?
- 2. Given an overall sampling rate (i.e.,
product of the horizontal, vertical, & temporal sampling rates), how do we sample in the 3-D space to obtain the best representation?
- 3. How can we avoid aliasing?
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Basics of Lattice Theory
A lattice, , in the real K-D space, ,is
the set of all possible vectors that can be represented as integer-weighted combinations of a set of K linearly independent basis vectors, that is: with generating matrix:
[ ] [ ]
1 2
, , ,
k
= L V v v v
1
| ,
K k k k k k
n n
=
Λ = ∈ = ∀ ∈
∑
x x v R Z
k
R
Λ
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Basics of Lattice Theory
One can find more than one basis or
generating matrix that can generate the same lattice.
Given a lattice, one can find a unit cell
such that its translations to all lattice points form a tiling of the entire space.
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Basics of Lattice Theory
Unit cells are of two types: fundamental
parallelepiped & Voronoi cell.
There are many fundamental parallelepipeds
associated with a lattice (because of the nonuniqueness of the generating matrix).
The volume of the unit cell is unique.
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Basics of Lattice Theory
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Basics of Lattice Theory
Determination of Voronoi cell:
Draw a straight line between the
- rigin & each one of the closest
nonzero lattice points.
Draw a perpendicular line that is
the half way between the 2 points.
This line is the equidistance line
between the origin & this lattice point.
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Basics of Lattice Theory
Given a lattice, its reciprocal lattice, , is defined
as a lattice that its basis vector is orthonormal to that of the lattice.
- r =I
The denser the lattice, the sparser its reciprocal. A generalized Nyquist sampling theory exists,
which governs the necessary density & structure
- f the sampling lattice for a given signal
spectrum.
[ ]
1
( )
T −
= U V
T
V
[ ]
U
*
Λ
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Sampling over Lattices
To avoid aliasing, the sampling lattice
must be designed so that the Voronoi cell
- f its reciprocal lattice completely cover
the signal spectrum.
To minimize the sampling density, it
should cover the signal spectrum as tightly as possible.
Most real-world signals are symmetric in
frequency contents (spherical support).
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Sampling Efficiency
( ) d Λ
( ) ρ Λ
Sampling density: Sampling efficiency:
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Sampling of Video Signals
Most motion picture cameras sample a
scene in the temporal direction (store a sequence of analog frames on film).
Most TV cameras capture a video
sequence by sampling it in temporal & vertical directions (1-D raster scan).
To obtain a full digital video:
Sample analog frames in 2-D. Sample analog raster scan in 1-D. Acquire discrete video frames directly using a digital
camera, by sampling a scene in 3-D.
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Required Sampling Rates
Governed factors:
Frequency content of the underlying signal. Visual thresholds in terms of the spatial &
temporal cut-off frequencies.
Capture & display device characteristics. Affordable processing, storage, & transmission
costs.
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Sampling Video in 2-D
- 1. The same 2-D sampling density.
- 2. The same 2-D nearest aliasing.
- 3. Different nearest aliasing along the
temporal frequency axis (less flickering for interlaced).
- 4. Different mixed aliases (the nearest off-
axis alias component).
- 5. For a signal with isotropic spectral
support, the interlaced scan is more efficient.
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Sampling of Video Signals
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Filtering Operations
How practical cameras & display devices
accomplish the required prefiltering & reconstruction filters in a crude way.
How the HVS partially accomplishes the
required interpolation task.
Camera aperture consists of:
Temporal aperture. Spatial aperture. Combined aperture.
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