JPEG uses DCT, quantization, and entropy coding to provide lossy compression of images. It can operate in several modes, including sequential, lossless, progressive, and hierarchical. Sequential mode encodes an image in a single left-to-right, top-to-bottom scan. Lossless mode uses predictive coding to encode images without loss. Progressive mode transmits an initial coarse version that is progressively improved over multiple transmissions.
Cycle’s topological optimizations and the iterative decoding problem on gener...Usatyuk Vasiliy
We consider several problem related to graph model related to error-correcting codes. From base problem of cycle broken, trapping set elliminating and bypass to fundamental problem of graph model. Thanks to the hard work of Michail Chertkov, Michail Stepanov and Andrea Montanari which inspirit me...
Slides presented at Applied Mathematics Day, Steklov Mathematical Institute of the Russian Academy of Sciences September 22, 2017 http://www.mathnet.ru/conf1249
Cycle’s topological optimizations and the iterative decoding problem on gener...Usatyuk Vasiliy
We consider several problem related to graph model related to error-correcting codes. From base problem of cycle broken, trapping set elliminating and bypass to fundamental problem of graph model. Thanks to the hard work of Michail Chertkov, Michail Stepanov and Andrea Montanari which inspirit me...
Slides presented at Applied Mathematics Day, Steklov Mathematical Institute of the Russian Academy of Sciences September 22, 2017 http://www.mathnet.ru/conf1249
Modified approximate 8-point multiplier less DCT like transformIJERA Editor
Discrete Cosine Transform (DCT) is widely usedtransformation for compression in image and video standardslike H.264 or MPEGv4, JPEG etc. Currently the new standarddeveloped Codec is Highly Efficient Video Coding (HEVC) orH.265. With the help of the transformation matrix the computational cost can be dynamically reduce. This paper proposesa novel approach of multiplier-less modified approximate DCT like transformalgorithm and also comparison with exact DCT algorithm and theapproximate DCT like transform. This proposed algorithm willhave lower computational complexity. Furthermore, the proposedalgorithm will be modular in approach, and suitable for pipelinedVLSI implementation.
Efficient Implementation of Low Power 2-D DCT ArchitectureIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
When Discrete Optimization Meets Multimedia Security (and Beyond)Shujun Li
Invited talk at the FoT-RSS: Faculty of Technology Research Seminar Series, De Montfort University, UK, co-sponsored by the IEEE UK & Ireland Signal Processing Chapter, 25 May 2016
Abstract:
Selective encryption has been widely used for image and video encryption due to many practical reasons such as to achieve format compliance and perceptual encryption, to avoid negative impact on compression efficiency, and to make the multimedia processing pipeline more modular and thus reconfigurable. The seminar will present research on modelling recovery of missing information with different structures in digital images as a discrete optimization problem. In the context of selective encryption, the structure of missing information is defined by the underlying selective encryption algorithm, where the selectively encrypted information is considered missing from an attacker's point of view. Experimental results showed that the new approach can significantly improve the performance of error-concealment attacks compared to the state of the art in terms of visual quality of the recovered images. The approach can be applied to other areas of multimedia security and multimedia processing in general where the structure of missing information in digital signals is known. An example of adapting the model to self-recovery image authentication watermarking will be shown.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Modified approximate 8-point multiplier less DCT like transformIJERA Editor
Discrete Cosine Transform (DCT) is widely usedtransformation for compression in image and video standardslike H.264 or MPEGv4, JPEG etc. Currently the new standarddeveloped Codec is Highly Efficient Video Coding (HEVC) orH.265. With the help of the transformation matrix the computational cost can be dynamically reduce. This paper proposesa novel approach of multiplier-less modified approximate DCT like transformalgorithm and also comparison with exact DCT algorithm and theapproximate DCT like transform. This proposed algorithm willhave lower computational complexity. Furthermore, the proposedalgorithm will be modular in approach, and suitable for pipelinedVLSI implementation.
Efficient Implementation of Low Power 2-D DCT ArchitectureIJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
When Discrete Optimization Meets Multimedia Security (and Beyond)Shujun Li
Invited talk at the FoT-RSS: Faculty of Technology Research Seminar Series, De Montfort University, UK, co-sponsored by the IEEE UK & Ireland Signal Processing Chapter, 25 May 2016
Abstract:
Selective encryption has been widely used for image and video encryption due to many practical reasons such as to achieve format compliance and perceptual encryption, to avoid negative impact on compression efficiency, and to make the multimedia processing pipeline more modular and thus reconfigurable. The seminar will present research on modelling recovery of missing information with different structures in digital images as a discrete optimization problem. In the context of selective encryption, the structure of missing information is defined by the underlying selective encryption algorithm, where the selectively encrypted information is considered missing from an attacker's point of view. Experimental results showed that the new approach can significantly improve the performance of error-concealment attacks compared to the state of the art in terms of visual quality of the recovered images. The approach can be applied to other areas of multimedia security and multimedia processing in general where the structure of missing information in digital signals is known. An example of adapting the model to self-recovery image authentication watermarking will be shown.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
ER(Entity Relationship) Diagram for online shopping - TAEHimani415946
https://bit.ly/3KACoyV
The ER diagram for the project is the foundation for the building of the database of the project. The properties, datatypes, and attributes are defined by the ER diagram.
1.Wireless Communication System_Wireless communication is a broad term that i...JeyaPerumal1
Wireless communication involves the transmission of information over a distance without the help of wires, cables or any other forms of electrical conductors.
Wireless communication is a broad term that incorporates all procedures and forms of connecting and communicating between two or more devices using a wireless signal through wireless communication technologies and devices.
Features of Wireless Communication
The evolution of wireless technology has brought many advancements with its effective features.
The transmitted distance can be anywhere between a few meters (for example, a television's remote control) and thousands of kilometers (for example, radio communication).
Wireless communication can be used for cellular telephony, wireless access to the internet, wireless home networking, and so on.
This 7-second Brain Wave Ritual Attracts Money To You.!nirahealhty
Discover the power of a simple 7-second brain wave ritual that can attract wealth and abundance into your life. By tapping into specific brain frequencies, this technique helps you manifest financial success effortlessly. Ready to transform your financial future? Try this powerful ritual and start attracting money today!
Multi-cluster Kubernetes Networking- Patterns, Projects and GuidelinesSanjeev Rampal
Talk presented at Kubernetes Community Day, New York, May 2024.
Technical summary of Multi-Cluster Kubernetes Networking architectures with focus on 4 key topics.
1) Key patterns for Multi-cluster architectures
2) Architectural comparison of several OSS/ CNCF projects to address these patterns
3) Evolution trends for the APIs of these projects
4) Some design recommendations & guidelines for adopting/ deploying these solutions.
Multi-cluster Kubernetes Networking- Patterns, Projects and Guidelines
M4L1.ppt
1. 1
Image Compression: JPEG
Multimedia Systems (Module 4 Lesson 1)
Summary:
r JPEG Compression
m DCT
m Quantization
m Zig-Zag Scan
m RLE and DPCM
m Entropy Coding
r JPEG Modes
m Sequential
m Lossless
m Progressive
m Hierarchical
Sources:
r The JPEG website:
http://www.jpeg.org
r My research notes
2. 2
Why JPEG
r The compression ratio of lossless methods (e.g.,
Huffman, Arithmetic, LZW) is not high enough for
image and video compression.
r JPEG uses transform coding, it is largely based on
the following observations:
m Observation 1: A large majority of useful image contents
change relatively slowly across images, i.e., it is unusual
for intensity values to alter up and down several times in
a small area, for example, within an 8 x 8 image block.
A translation of this fact into the spatial frequency
domain, implies, generally, lower spatial frequency
components contain more information than the high
frequency components which often correspond to less
useful details and noises.
m Observation 2: Experiments suggest that humans are
more immune to loss of higher spatial frequency
components than loss of lower frequency components.
3. 3
JPEG Coding
Y
Cb
Cr
DPCM
RLC
Entropy
Coding
Header
Tables
Data
Coding
Tables
Quant…
Tables
DCT
f(i, j)
8 x 8
F(u, v)
8 x 8
Quantization
Fq(u, v)
Zig Zag
Scan
Steps Involved:
1. Discrete Cosine
Transform of each 8x8
pixel array
f(x,y) T F(u,v)
2. Quantization using a
table or using a constant
3. Zig-Zag scan to exploit
redundancy
4. Differential Pulse Code
Modulation(DPCM) on
the DC component and
Run length Coding of the
AC components
5. Entropy coding
(Huffman) of the final
output
4. 4
DCT : Discrete Cosine Transform
DCT converts the information contained in a block(8x8) of
pixels from spatial domain to the frequency domain.
m A simple analogy: Consider a unsorted list of 12 numbers
between 0 and 3 -> (2, 3, 1, 2, 2, 0, 1, 1, 0, 1, 0, 0). Consider a
transformation of the list involving two steps (1.) sort the list
(2.) Count the frequency of occurrence of each of the numbers
->(4,4,3,1 ). : Through this transformation we lost the spatial
information but captured the frequency information.
m There are other transformations which retain the spatial
information. E.g., Fourier transform, DCT etc. Therefore
allowing us to move back and forth between spatial and
frequency domains.
1-D DCT: 1-D Inverese DCT:
5. 5
Example and Comparison
0
2 0
4 0
6 0
8 0
0 1 2 3 4 5 6 7
100 -52 0 -5 0 -2 0 0.4 36 10 10 6 6 4 4 4
36 10 10 6 6 4 4 4
100 -52 0 -5 0 -2 0 0.4
24 12 20 32 40 51 59 48
8 15 24 32 40 48 57 63
0
2 0
4 0
6 0
8 0
0 1 2 3 4 5 6 7
0
2 0
4 0
6 0
8 0
0 1 2 3 4 5 6 7
DCT FFT
Inverse DCT Inverse FFT
Example Description:
r f(n) is given from n = 0 to 7; (N=8)
r Using DCT(FFT) we compute F(ω) for ω = 0 to 7
r We truncate and use Inverse Transform to compute f’(n)
6. 6
2-D DCT
r Images are two-dimensional; How do you perform 2-D DCT?
m Two series of 1-D transforms result in a 2-D transform as
demonstrated in the figure below
1-D
Row-
wise
1-D
Column-
wise
8x8 8x8 8x8
j)
f(i,
v)
F(u,
r F(0,0) is called the DC component and the rest of F(i,j) are called
AC components
7. 7
2-D Transform Example
r The following example will demonstrate the idea behind a 2-
D transform by using our own cooked up transform: The
transform computes a running cumulative sum.
1
1-D
Row-
wise
1-D
Column-
wise
8x8
8x8
8x8
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8 7 6 5 4 3 2 1
8 7 6 5 4 3 2 1
8 7 6 5 4 3 2 1
8 7 6 5 4 3 2 1
8 7 6 5 4 3 2 1
8 7 6 5 4 3 2 1
8 7 6 5 4 3 2 1
8 7 6 5 4 3 2 1
64 56 48 40 32 24 16 8
56
48
40
32
24
16
8
49
42
35
28
21
14
7
42
36
30
24
18
12
6
35
30
25
20
15
10
5
28
24
20
16
12
8
4
21
18
15
12
9
6
3
14
12
10
8
6
4
2
7
6
5
4
3
2
1
8
n
my (n)
f
)
(
F
My Transform:
j)
f(i,
v)
(u,
my
F
Note that this is only a hypothetical
transform. Do not confuse this with DCT
8. 8
Quantization
r Why? -- To reduce number of bits per sample
F’(u,v) = round(F(u,v)/q(u,v))
r Example: 101101 = 45 (6 bits).
Truncate to 4 bits: 1011 = 11. (Compare 11 x 4 =44 against 45)
Truncate to 3 bits: 101 = 5. (Compare 8 x 5 =40 against 45)
Note, that the more bits we truncate the more precision we lose
r Quantization error is the main source of the Lossy
Compression.
r Uniform Quantization:
m q(u,v) is a constant.
r Non-uniform Quantization -- Quantization Tables
m Eye is most sensitive to low frequencies (upper left corner in
frequency matrix), less sensitive to high frequencies (lower right
corner)
m Custom quantization tables can be put in image/scan header.
m JPEG Standard defines two default quantization tables, one
each for luminance and chrominance.
9. 9
Zig-Zag Scan
r Why? -- to group low frequency coefficients in top of vector
and high frequency coefficients at the bottom
r Maps 8 x 8 matrix to a 1 x 64 vector
8x8
. . .
1x64
10. 10
DPCM on DC Components
r The DC component value in each 8x8 block is large and varies
across blocks, but is often close to that in the previous block.
r Differential Pulse Code Modulation (DPCM): Encode the
difference between the current and previous 8x8 block.
Remember, smaller number -> fewer bits
45
54
48
32
45
9
-6
12
36 4
.
.
.
.
.
.
1x64
1x64
1x64
1x64
1x64
1x64
1x64
1x64
1x64
1x64
11. 11
RLE on AC Components
r The 1x64 vectors have a lot of zeros in them, more so towards
the end of the vector.
m Higher up entries in the vector capture higher frequency (DCT)
components which tend to be capture less of the content.
m Could have been as a result of using a quantization table
r Encode a series of 0s as a (skip,value) pair, where skip is the
number of zeros and value is the next non-zero component.
m Send (0,0) as end-of-block sentinel value.
. . .
1x64
0 0 0 0 0 1 1 0 0 0 0 0
5,1
0 0
7,2
0 . . .
2
12. 12
Entropy Coding: DC Components
SIZE Value Code
0 0 ---
1 -1,1 0,1
2 -3, -2, 2,3 00,01,10,11
3 -7,…, -4, 4,…, 7 000,…, 011, 100,…111
4 -15,…, -8, 8,…, 15 0000,…, 0111, 1000,…, 1111
. .
. .
11 -2047,…, -1024, 1024,… 2047 …
r DC components are differentially coded as (SIZE,Value)
m The code for a Value is derived from the following table
Size_and_Value Table
13. 13
Entropy Coding: DC Components (Contd..)
SIZE Code
Length
Code
0 2 00
1 3 010
2 3 011
3 3 100
4 3 101
5 3 110
6 4 1110
7 5 11110
8 6 111110
9 7 1111110
10 8 11111110
11 9 111111110
r DC components are differentially coded as (SIZE,Value)
m The code for a SIZE is derived from the following table
Example: If a DC component is 40
and the previous DC
component is 48. The
difference is -8. Therefore it
is coded as:
1010111
0111: The value for representing –8
(see Size_and_Value table)
101: The size from the same table
reads 4. The corresponding
code from the table at left is
101.
Huffman Table for DC component SIZE field
14. 14
Entropy Coding: AC Components
r AC components (range –1023..1023) are coded as (S1,S2 pairs):
m S1: (RunLength/SIZE)
• RunLength: The length of the consecutive zero values [0..15]
• SIZE: The number of bits needed to code the next nonzero AC component’s value. [0-A]
• (0,0) is the End_Of_Block for the 8x8 block.
• S1 is Huffman coded (see AC code table below)
m S2: (Value)
• Value: Is the value of the AC component.(refer to size_and_value table)
Run/
SIZE
Code
Length
Code
0/0 4 1010
0/1 2 00
0/2 2 01
0/3 3 100
0/4 4 1011
0/5 5 11010
0/6 7 1111000
0/7 8 11111000
0/8 10 1111110110
0/9 16 1111111110000010
0/A 16 1111111110000011
Run/
SIZE
Code
Length
Code
1/1 4 1100
1/2 5 11011
1/3 7 1111001
1/4 9 111110110
1/5 11 11111110110
1/6 16 1111111110000100
1/7 16 1111111110000101
1/8 16 1111111110000110
1/9 16 1111111110000111
1/A 16 1111111110001000
… 15/A More Such rows
15. 15
Entropy Coding: Example
Example: Consider encoding the AC components by
arranging them in a zig-zag order -> 12,10, 1, -7
2 0s, -4, 56 zeros
12: read as zero 0s,12: (0/4)12 10111100
1011: The code for (0/4 from AC code table)
1100: The code for 12 from the
Size_and_Value table.
10: (0/4)10 10111010
1: (0/1)1 001
-7: (0/3)-7 100000
2 0s, -4: (2/3)-4 1111110111011
1111110111: The 10-bit code for 2/3
011: representation of –4 from Size_and_Value
table.
56 0s: (0,0) 1010 (Rest of the components are
zeros therefore we simply put the EOB to
signify this fact)
40 12 0 0 0 0 0 0
10 -7 -4 0 0 0 0 0
1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
16. 16
JPEG Modes
Sequential Mode:
r Each image is encoded in a single left-to-right,
top-to-bottom scan.
m The technique we have been discussing so far is an
example of such a mode, also referred to as the Baseline
Sequential Mode.
m It supports only 8-bit images as opposed to 12-bit images
as described before.
17. 17
JPEG Modes
Lossless Mode:
r Truly lossless
r It is a predictive coding mechanism as opposed to the
baseline mechanism which is based on DCT and
quantization(the source of the loss).
r Here is the simple block diagram of the technique:
Predictive
Difference
Huffman
EnCoder
Lossless
Coding
18. 18
Lossless Mode (Contd..)
Predictive Difference:
m For each pixel a predictor (one of 7 possible) is used that best predicts
the value contained in the pixel as a combination of up to 3 neighboring
pixels.
m The difference between the predicted value and the actual value
(X)contained in the pixel is used as the predictive difference to
represent the pixel.
m The predictor along with the predictive difference are encoded as the
pixel’s content.
m The series of pixel values are encoded using huffman coding
C B
A X
Predictor Prediction
P1 A
P2 B
P3 C
P4 A+B-C
P5 A + (B-C)/2
P6 B + (A-C)/2
P7 (A+B)/2
Notes:
r The very first pixel in location (0, 0)
will always use itself.
r Pixels at the first row always use P1,
r Pixels at the first column always use
P2.
r The best (of the 7) predictions is
always chosen for any pixel.
19. 19
JPEG Modes
Progressive Mode: It allows a coarse version of an
image to be transmitted at a low rate, which is
then progressively improved over subsequent
transmissions.
m Spectral Selection : Send DC component and first few
AC coefficients first, then gradually some more ACs.
Spectral Selection:
First Scan:
Second Scan:
Third Scan:
.
.
Nth Scan:
Image Pixels
20. 20
Progressive Mode
r Successive Approximation : All the DCT components are
sent few bits at a time: For example, send n1 (say,4) bits
(starting with MSB) of all pixels in the first scan, the next
n2(say 1) bits of all pixels in the second and so on.
Pixels ordered (zig-zag-wise)
First Scan:
Second Scan:
Third Scan:
5th Scan:
7 6 5 4 0
3 2 1
MSB LSB
.
.
. . .
. . .
. . .
. . .
.
.
One Pixel
21. 21
Hierarchical Mode
r Used primarily to support multiple resolutions of the same
image which can be chosen from depending on the target’s
capabilities.
r The figure here shows a description of how a 3-level
hierarchical encoder/decoder works:
2x2 Encode
Decode
4x4 Encode
Decode
2x2
2x2
+
-
+ +
+
-
L4
L2
L1
I
Encode
Decode
Decode
Decode
Decoding
Encoding
4x4
2x2
2x2
+
+
I4
I2
I’4
I’2
I’