Slide đa phương tiện chương 2 image

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

ng

th

an

co

ng

Digital Image Communication

cu

u

du
o

Tien Pham Van, Dr. rer. nat.
Hanoi University of Science and
Technology

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

cu

u

du
o

ng

th

an

co

ng

• Image processing
• Image coding

• Image communications

.c
om

Agenda

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

cu

u

du
o

ng

th

an

co

ng

.c
om

Image processing

3

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

What are images?

cu

u

du
o

ng

th

an

co

ng

• An image is a 2-d rectilinear array of pixels

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Pixels as samples

cu

u

du
o

ng

th

an

co

ng

• A pixel is a sample of a continuous function

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c

om

Images are Ubiquitous

ng

• Input

du
o

• Output

ng

th

an

co

– Optical photoreceptors
– Digital camera CCD array
– Rays in virtual camera

cu

u

– TVs

– Computer monitors
– Printers

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Properties of Images

ng

• Spatial resolution

th

• Intensity resolution

an

co

– Width pixels/width cm and height pixels/ height cm

ng

– Intensity bits/intensity range (per channel)

du
o

• Number of channels

cu

u

– RGB is 3 channels, grayscale is one channel

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Image errors

• Spatial aliasing

co

ng

– Not enough spatial resolution

an

• Intensity quantization

cu

u

du
o

ng

th

– Not enough intensity resolution

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Two issues

• Sampling and reconstruction

an

co

ng

– Creating and displaying images while reducing
spatial aliasing errors

th

• Halftoning techniques

cu

u

du
o

ng

– Dealing with intensity quantization

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

cu

u

du
o

ng

th

an

co

ng

.c
om

Sampling and reconstruction

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Aliasing

cu

u

du

o

ng

th

an

co

ng

• Artifacts caused by too low sampling frequency
(undersampling) or improper reconstruction
• Undersampling rate determined by Nyquist limit
(Shannon’s sampling theorem)

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Aliasing in computer graphics

• In graphics, two major types

co

ng

– Spatial aliasing

th

– Temporal aliasing

an

• Problems in individual images

cu

u

du
o

ng

• Problems in image sequences (motion)

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Spatial Aliasing

cu

u

du
o

ng

th

an

co

ng

• “Jaggies”

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

cu

u

du
o

ng

th

an

co

ng

.c
om

Spatial aliasing

Ref: SIGGRAPH aliasing tutorial

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

cu

u

du
o

ng

th

an

co

ng

• Texture disintegration

.c
om

Spatial aliasing

Ref: SIGGRAPH aliasing tutorial

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Temporal aliasing

ng

• Strobing

co

– Stagecoach wheels in movies

th

an

• Flickering

cu

u

du
o

ng

– Monitor refresh too slow
– Frame update rate too slow

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Antialiasing

• Sample at a higher rate

th

an

co

ng

– What if the signal isn’t bandlimited?
– What if we can’t do this, say because the sampling
device has a fixed resolution?

ng

• Pre-filter to form bandlimited signal

u

du

o

– Low pass filter
– Trades aliasing for blurring

cu

• Non-uniform sampling
– Not always possible, done by your visual system,
suitable for ray tracing
– Trades aliasing for noise
CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Sampling Theory

• Two issues

cu

u

du
o

ng

th

an

co

ng

– What sampling rate suffices to allow a given
continuous signal to be reconstructed from a
discrete sample without loss of information?
– What signals can be reconstructed without loss
for a given sampling rate?

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Spectral Analysis

Frequency domain:

cu

u

du
o

ng

th

an

co

ng

Spatial (time) domain:

Any (spatial, time) domain signal (function) can be written as
a sum of periodic functions (Fourier)

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

cu

u

du
o

ng

th

an

co

ng

.c
om

Fourier Transform

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Fourier Transform

∞

co

ng

• Fourier transform:

an

F (u ) = ∫ f ( x)e

−i 2πxu

ng

th

−∞

dx

cu

u

du
o

• Inverse Fourier transform:
∞

f ( x) = ∫ F (u )e
−∞

CuuDuongThanCong.com

i 2πxu

du

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Sampling theorem

cu

u

du
o

ng

th

an

co

ng

• A signal can be reconstructed from its samples if
the signal contains no frequencies above ẵ the

sampling frequency.
-Claude Shannon
ã The minimum sampling rate for a bandlimited
signal is called the Nyquist rate
• A signal is bandlimited if all frequencies above a
given finite bound have 0 coefficients, i.e. it
contains no frequencies above this bound.

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Filtering and convolution

ng

• Convolution of two functions (= filtering):

co

∞

an

g ( x) = f ( x) ⊗ h( x) = ∫ f (λ )h( x − λ )dλ

du
o

ng

th

−∞

• Convolution theorem:

cu

u

– Convolution in the frequency domain is the same as
multiplication in the spatial (time) domain, and
– Convolution in the spatial (time) domain is the same as
multiplication in the frequency domain

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group

Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

Filtering, sampling and image processing

co
an
th

cu

u

du
o

ng

– Blurring
– Edge detection
– Scaling
– Rotation
– Warping

ng

.c
om

• Many image processing operations basically
involve filtering and resampling.

CuuDuongThanCong.com

/>

Pham Van Tien, Dr. rer. nat. , Embedded Networking Research Group
Faculty of Elec. and Telecom, Hanoi University of Science and Technology

Email:
C9-411 Dai Co Viet str. 1, Hanoi

.c
om

Resampling

cu

u

du
o

ng

th

an

co

ng

• Consider reducing the image resolution:

CuuDuongThanCong.com

/>