Module V35
Image Compression
fundamentals in Digital Image
Processing
 Introduction
 What is Image Compression?
• Image Compression is the art and science of reducing the amount
of data required to represent an image.
• Data required for two hour standard definition(SD) television
movie using 720×480×24 bits pixel arrays is 224 GB of data.
•
The images are compressed to save storage space and reduce
transmission time.
 Image compression fundamentals
 What is Data Compression?
• Data compression refers to the process of reducing the amount of data
required to represent a given quantity of information.
• Data contains irrelevant or repeated information called redundant data.
Types of Compression
Lossless compression
• This do not lose any information.
• For eg. Run-length encoding, Huffman coding,
Lempel Ziv coding(LZW) etc.
Lossy compression
• This loses part of information in a controlled way.
• For eg. JPEG, MPEG, MP3 etc.
 Image compression fundamentals
• Let b and b’ denote the number of bits in two representations of the same
information, the Relative data redundancy R of the representation with b bits is,
R = 1 – 1/CR where CR commonly called the compression ratio is defined as
CR = b/b’
• b=b’, R = 0, and CR= 1, R = 0, no data redundancy.
• b>>b’ and CR>>1, R≅1 highly redundant data.
• If CR = 10 (or 10:1), for instance, means larger representation has 10 bits of data
for every 1 bit of data in the smaller representation.
• Corresponding relative data redundancy of the larger representation is 0.9
indicating 90% of its data is redundant.
 Principal types of data redundancies
Data redundancies
Coding Redundancy
Spatial and temporal
redundancy
Irrelevant information
◦ Each piece of information or ◦ Pixels of most 2-D intensity arrays are ◦ Most 2-D intensity arrays contain
event is assigned a sequence of
correlated spatially (i.e. each pixel is
information that is ignored by
code symbols, called a code
similar to or dependent on neighboring
human visual system and/or
word.
pixels.
extraneous to the intended use of
◦ Number of symbols in each ◦ Information is unnecessarily replicated
the image.
code word is its length.
in the representations of the correlated ◦ It is redundant in the sense that it
pixels.
is not used.
 Image compression Model (Encoder)
• Encoder: is the device that is used for compression.
• Mapper: The function of the mapper is to reduce the spatial or
temporal redundancy. The operation is generally reversible. e.g. DCT.
• Quantizer: It reduces the accuracy of mapper’s output in accordance with
some preestablished fidelity criterion. It reduces the psychovisual
redundancies and it is a irreversible process.
• Symbol coder: creates a fixed- or variable-length code to represent
the quantizer output and maps the output in accordance with the code.
The term symbol coder distinguishes this coding operation from the
overall source encoding process. In most cases, a variable-length code is
used to represent the mapped and quantized data set. e.g. VLE (Variable
Length Encoder).
• Channel: May be wired or wireless.
 Image compression Model (Decoder)
• Decoder: is the device that is used for decompression.
• Symbol decoder: Performs the reverse operation of the symbol coder. It
decodes the code back. e.g. VLD (Variable Length Decoder).
• Inverse mapper: Performs the reverse operation of the mapper. It restores the
spatial or temporal redundancy in the image. e.g. DCT-1
• The Channel Encoder and Decoder: The channel encoder and decoder play
an important role in the overall encoding-decoding process when the channel is
noisy or prone to error. They are designed to reduce the impact of channel
noise by inserting a controlled form of redundancy into the source encoded
data. As the output of the source encoder contains little redundancy, it would
be highly sensitive to transmission noise without the addition of this "controlled
redundancy."
2
1
3
2
2
2
1
1
2
16
16
16
16
16
16
16
16
16
0.125 0.0625
-3
-4
0.1875
0.125 0.125 0.125 0.0625 0.0625 0.125
2.4150374992
7884
-3
-3
-3
-4
-4
-3
-0.375 -0.25 -0.452819531 -0.375 -0.375 -0.375 -0.25
3.0778
-0.25 -0.375
2
39Huffman coding
in Digital Image Processing
 Huffman coding
• The most popular technique for removing coding redundancy is due to Huffman
(Huffman [1951]). When coding the symbols of an information source
individually, Huffman coding yields the smallest possible number of code symbols
per source symbol.
• Huffman coding is a variable length coding and it achieves error-free/lossless
compression as it is reversible. It exploits only coding and inter-pixel redundancy
to achieve compression.
• In terms of the noiseless coding theorem, the resulting code is optimal for a fixed
value of n, subject to the constraint that the source symbols be coded one at a time.
• The length of the code should be inversely proportional to its probability of
occurrence.
 Steps of Huffman coding:
1. Sort the symbols according to decreasing order of their probabilities.
2. Combine the lowest probable symbols to form a composite symbol with
probability equal to sum of the respective probabilities.
3. Repeat step 2 until you are left with only 2 symbols.
4. Extract the codewords from the resulting binary tree representation of the code.
Image Size 10x10 (5 bit image)
Given Frequency:
a1=10, a2=40, a3=6, a4=10, a5=4 a6=30
Encoded String :
010100111100
• The first step in Huffman's approach is to create a series of source reductions by
ordering the probabilities of the symbols under consideration and combining
the lowest probability symbols into a single symbol that replaces them in the
next source reduction.
• At the far left, a hypothetical set of source symbols and their probabilities are
ordered from top to bottom in terms of decreasing probability values. To form
the first source reduction, the bottom two probabilities, 0.06 and 0.04, are
combined to form a "compound symbol" with probability 0.1.
• This compound symbol and its associated probability are placed in the first
source reduction column so that the probabilities of the reduced source are also
ordered from the most to the least probable. This process is then repeated until
a reduced source with two symbols (at the far right) is reached.
• The second step in Huffman's procedure is to code each reduced source,
starting with the smallest source and working back to the original source. The
minimal length binary code for a two-symbol source, of course, is the symbols 0
and 1.
• These symbols are assigned to the two symbols on the right (the assignment is
arbitrary; reversing the order of the 0 and 1 would work just as well). As the
reduced source symbol with probability 0.6 was generated by combining two
symbols in the reduced source to its left, the 0 used to code it is now assigned to
both of these symbols, and a 0 and 1 are arbitrarily appended to each to
distinguish them from each other. This operation is then repeated for each
reduced source until the original source is reached. The final code appears at
the far left.
• The entropy of the source is 2.1435 bits/symbol. The resulting Huffman code
efficiency is 97.43 %.
•
Huffman's procedure creates the optimal code for a set of symbols and probabilities
subject to the constraint that the symbols be coded one at a time. After the code has
been created, coding and/or decoding is accomplished in a simple lookup table
manner.
•
The code itself is an instantaneous uniquely decodable block code. It is called a block
code because each source symbol is mapped into a fixed sequence of code symbols. It
is instantaneous, because each code word in a string of code symbols can be decoded
without referencing succeeding symbols.
•
It is uniquely decodable, because any string of code symbols can be decoded in only
one way. Thus, any string of Huffman encoded symbols can be decoded by examining
the individual symbols of the string in a left to right manner. For the binary code, a
left-to-right scan of the encoded string 010100111100 reveals that the first valid code
word is 01010, which is the code for symbol a3 .The next valid code is 011, which
corresponds to symbol a1. Continuing in this manner reveals the completely decoded
message to be a3a1a2a2a6.
RUN-LENGTH
CODING
 Run-length encoding (RLE)
• RLE is one of the simplest lossless data compression techniques. It reduces
interpixel redundancy. It consists of replacing a sequence (Run) of identical
symbols by a pair containing the symbol and the run length.
• It is used as the primary compression technique in the 1-D CCITT Group 3
Fax standard, bitmap images such as computer icons and in conjunction with
other techniques in the JPEG image compression standard.
• Scan the image horizontally or vertically and while scanning assign a group of
pixel with the same intensity into a pair (G ,L) where G is the intensity and L
is the length of the “run”. This method can also be used for detecting edges
and boundaries of an object. It is mostly used for images with a small number
of gray levels and is not effective for highly textured images.
STR=[ 5 5 5 5 5 5 4 4 4 3 3 2 ];
str=[1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1];
• Run-length coding (RLC) works by counting adjacent pixels with the same gray
level value called the run-length, which is then encoded and stored
• RLC works best for binary, two-valued, images
• RLC can also work with complex images that have been preprocessed by
thresholding to reduce the number of gray levels to two
RLC can be implemented in various ways, but the first step is to define the
required parameters
• Horizontal RLC (counting along the rows) or vertical RLC (counting along the
columns) can be used .
• This technique is especially successful in compressing bi-level images since the
occurrence of a long run of a value is rare in ordinary gray-scale images. A solution
to this is to decompose the gray-scale image into bit planes and compress every bitplane separately.
LOSSLESS COMPRESSION
AND
LOSSY COMPRESSION
JPG 52 KB
PNG 545KB
Sr. Parameter
No:
Lossless compression
Lossy compression
1.
Definition
The technique in which no data loss occurs and The technique in which there is data loss and the
output image is same as input image is called output image is not same(size, visually) as input
lossless image compression.
image is called lossy image compression.
2.
Removal
It removes only the redundant information It removes visually irrelevant
(coding and inter-pixel redundancy).
(Psychovisual redundancy).
3.
Information loss
There is no information loss.
There is always a loss of information.
4.
Other name
It is also called reversible compression.
It is also called irreversible compression.
5.
Compression ratio
CR is low.
CR can be very high.
6.
Algorithms/
Techniques used
Bit-plane coding, Run-length coding, Huffman Transform coding, DCT, DWT etc.
coding, LZW coding, Arithmetic coding etc.
7.
RMS error
Erms between original and reconstructed image is Erms between original and reconstructed image is
always zero.
never equal to zero.
8.
Advantages
It retains the file quality in smaller size.
9.
Drawbacks
The file size is much large as compared to lossy The quality of file is low, file is degraded. Original
and hence the data holding capacity is very less.
file cannot be recovered with decompression.
10.
Applications
Text files, medical images, space images etc.
Images, speech and videos.
11.
Examples
PNG, TIFF, BMP etc.
JPG, MPEG, MP3 etc.
information
It gives significantly reduced file size. It is supported
by many tools and software. Here we can choose
preferred degree of compression.
Predictive coding
Lossless Predictive Coding
 Consider the pixel {23, 34, 39, 47, 55, 63}. Demonstrate Predictive coding
 Consider the pixel {23, 64, 39, 47, 55, 63}. Demonstrate Predictive coding
Lossy Predictive Coding
• This process can be extended further by using only one bit
to encode the difference between the adjacent pixels.
• This scheme is known as Delta Modulation
45
BLOCK TRANSFORM
CODING
 Transform Coding
• The lossless compression techniques discussed till now operate
directly on the pixels of an image and so are spatial domain
techniques.
• For transform coding, we modify the transform of an image. A
reversible linear transform (such as DCT/DFT ) is used to map the
image into a set of transform coefficients.
• These coefficients are then quantized and coded.
• The goal of transform coding is to decorrelate pixels and pack as
much information into small number of transform coefficients.
• Compression is achieved during quantization not during the
transform step.
 Block diagram of Transform Coding
A transform coding system: (a) encoder; (b) decoder
 Procedure for Transform Coding
• Divide the image into n × n sub-images.
• Transform each sub-image using a reversible transform (e.g., the Hartley
transform, the discrete Fourier transform (DFT) or the discrete cosine
transform (DCT)).
• Quantify, i.e., truncate the transformed image (e.g., by using DFT, and DCT
frequencies with small amplitude can be removed without much information
loss). The quantification can be either image dependent (IDP) or image
independent (IIP).
• Code the resulting data, normally using some kind of “variable length coding”,
e.g., Huffman code.
• The coding is not reversible (unless step 3 is skipped).
• Transform coding, is a form of block coding done in the transform domain.
The image is divided into blocks, or sub images, and the transform is
calculated for each block.
• Any of the previously defined transforms can be used, frequency (e.g. Fourier)
or sequency (e.g. Walsh-Hadamard), but it has been determined that the
discrete cosine transform (DCT) is optimal for most images.
• The newer JPEG2000 algorithms uses the wavelet transform, which has been
found to provide even better compression. After the transform has been
calculated, the transform coefficients are quantized and coded.
• This method is effective because the frequency/sequency transform of images is
very efficient at putting most of the information into relatively few coefficients,
so many of the high frequency coefficients can be quantized to 0 (eliminated
completely).
• This type of transform is a special type of mapping that uses spatial frequency
concepts as a basis for the mapping.
• The main reason for mapping the original data into another mathematical space
is to pack the information (or energy) into as few coefficients as possible.
• The simplest form of transform coding is achieved by filtering or eliminating
some of the high frequency coefficients.
• However, this will not provide much compression, since the transform data is
typically floating point and thus 4 or 8 bytes per pixel (compared to the original
pixel data at 1 byte per pixel), so quantization and coding is applied to the
reduced data
• Quantization includes a process called bit allocation,which determines the
number of bits to be used to code each coefficient based on its importance.
• Typically, more bits are used for lower frequency components where the energy
is concentrated for most images, resulting in a variable bit rate or nonuniform
quantization and better resolution.
• Two particular types of transform coding have been widely explored:
1. Zonal coding
2. Threshold coding
• These two vary in the method they use for selecting the transform coefficients to
retain (using ideal filters for transform coding selects the coefficients based on
their location in the transform domain).
Image taken from the book Digital Image Processing(Third Edition) by R. C. Gonzalez & R. E. Woods
ZONAL
CODING
• It involves selecting specific coefficients based on maximal variance.
• A zonal mask is determined for the entire image by finding the variance for
each frequency component.
• This variance is calculated by using each sub-image within the image as a
separate sample and then finding the variance within this group of subimages.
• The zonal mask is a bitmap of 1's and 0', where the 1's correspond to the
coefficients to retain, and the 0's to the ones to eliminate.
• As the zonal mask applies to the entire image, only one mask is required.
THRESHOLD
CODING
• It selects the transform coefficients based on specific value.
• A different threshold mask is required for each block, which increases file
size as well as algorithmic complexity.
• In practice, the zonal mask is often predetermined because the low frequency
terms tend to contain the most information, and hence exhibit the most
variance.
• In this case we select a fixed mask of a given shape and desired compression
ratio, which streamlines the compression process.
• It also saves the overhead involved in calculating the variance of each group
of sub-images for compression and also eases the decompression process.
• Typical masks may be square, triangular or circular and the cutoff frequency
is determined by the compression ratio.
JPEG
COMPRESSION
 Transform Selection
• T(u,v) can be computed using various transformations, for example:
• DFT (Discrete Fourier Transform), DCT (Discrete Cosine Transform), KLT
(Karhunen-Loeve Transformation) etc.
• DCT is a real transform, while DFT is a complex transform.
• Blocking artifacts are less pronounced in the DCT than the DFT.
• The DCT is a good approximation of the Karhunen Loeve Transform(KLT)
which is optimal in terms of energy compaction.
• However unlike KLT the DCT has image independent basis functions.
• The DCT is used in JPEG compression standard.
 JPEG Encoding
• It is used to compress pictures and graphics.
• In JPEG, a picture is divided into 8x8 pixel blocks to decrease the number of
calculations.
• The basic idea is to change the picture into a linear (vector) sets of numbers that
reveals the redundancies. The redundancies is then removed by one of lossless
compression methods.
 DCT (Discrete Cosine Transform)
Forward:
Inverse:
if u=0
if u>0
if v=0
if v>0
 DCT (cont’d)
Basis functions for a 4x4 image (i.e., cosines of different frequencies).
 DCT (cont’d)
Using
8 x 8 sub-images
yields 64 coefficients
per sub-image.
DFT
WHT
DCT
RMS error: 2.32
1.78
1.13
Reconstructed images
by truncating
50% of the
coefficients
More compact
transformation
 Quantization:
• In JPEG, each F[u,v] is divided by a constant q(u,v).
Table of q(u,v) is called quantization table T.
• After T table is created, the values are quantized to
reduce the number of bits needed for encoding.
• Quantization divides the number of bits by a constant,
then drops the fraction. This is done to optimize the
number of bits and the number of 0s for each
particular application.
Block diagram of (a) JPEG encoder, (b) JPEG decoder
 Compression:
• Quantized values are read from the table and
redundant 0s are removed.
• To cluster the 0s together, the table is read diagonally
in an zigzag fashion. The reason is if the table doesn’t
have fine changes, the bottom right corner of the table
is all 0s.
• JPEG usually uses lossless run length encoding and
Huffman coding at the compression phase.
Block diagram of (a) JPEG encoder and
Decoder for color images
JPEG compression for color images
 STEPS IN JPEG COMPRESSION
1. Pre-process image. (8*8 blocks subdivision
and level shifting for grayscale images, color
transformation, down-sampling and 8*8
blocks subdivision for color images.
2. Apply 2D forward DCT. Each block is
represented by 64 frequency components,
one of which (the DC component) is the
average color of the 64 pixels in the block.
3. Quantize DCT coefficients.
and
Huffman
4. Apply
RLE
encoding(Entropy encoding).
 8*8 block of an image
f=
183
160
94
153
194
163
132
165
183
153
116
176
187
166
130
169
179
168
171
182
179
170
131
167
177
177
179
177
179
165
131
167
178
178
179
176
179
164
130
171
179
180
180
179
182
164
130
171
179
179
180
182
183
170
129
173
180
179
181
179
181
170
130
169
 Level Shifting
fs = f - 128
55
32
-34
25
66
35
4
37
55
25
-12
48
59
38
2
41
51
40
43
54
51
42
3
39
49
49
51
49
51
37
3
39
50
50
51
48
54
36
2
43
51
52
52
51
55
36
2
43
51
51
52
54
55
42
1
45
52
51
53
51
53
42
2
41
 Computing the DCT
312
56
-27
17
79
-60
26
-26
-38
-28
13
45
31
-1
-24
-10
-20
-18
10
33
21
-6
-16
-9
-11
-7
9
15
10
-11
-13
1
1
6
5
-4
-7
-5
5
3
3
0
-2
-7
-4
1
2
3
5
0
-4
-8
-1
2
4
3
1
-1
-2
-3
-1
4
1
DCT=round(dct2(fs)) -6
 The Quantization Matrix
16
11 10
12
12 14
14
16
24
40
51
61
19
26
58
60
55
13 16
24
40
57
69
56
Qmat = 14
17 22
29
51
87
80
62
18
22 37
56
68
109
103
77
24
35 55
64
81
104
113
92
49
64 78
87
103
121
120
101
72
92 95
98
112
100
103
99
Quantization Table
312/16
= 20
16
11
10
16
24
40
51
61
12
12
14
19
26
58
60
55
14
13
16
24
40
57
69
56
14
17
22
29
51
87
80
62
18
22
37
56
68
109
103
77
24
35
55
64
81
104
113
92
49
64
78
87
103
121
120
101
72
92
95
98
112
100
103
99
20
5
-3
1
3
-2
1
0
-3
-2
1
2
1
0
0
0
-1
-1
1
1
1
0
0
0
-1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
312
56
-27
17
79
-60
26
-26
-38
-28
13
45
31
-1
-24
-10
-20
-18
10
33
21
-6
-16
-9
-11
-7
9
15
10
-11
-13
1
-6
1
6
5
-4
-7
-5
5
3
3
0
-2
-7
-4
1
2
0
0
0
0
0
0
0
0
3
5
0
-4
-8
-1
2
4
0
0
0
0
0
0
0
0
3
1
-1
-2
-3
-1
4
0
0
0
0
0
0
0
0
DCT matrix
1
Quantized value
 Thresholding/Threshold coding:
t=round(dcts./Qmat) =
20
5
-3
1
3
-2
1
0
-3
-2
1
2
1
0
0
0
-1
-1
1
1
1
0
0
0
-1
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
 Zig- Zag Scanning of the Coefficients
20 5
-3
1
3
-2
1
0
-3
-2
1
2
1
0
0
0
-1
-1
1
1
1
0
0
0
-1
0
0
1
0
0
0
0 [20,5,-3,-1,-2,-3,1,1,-1,-1,0,0,1,2,3,-2,1,1,0,0,0,0,0,0,1,1,0,1,0,EOB]
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
• Here the EOB symbol denotes the end-of-block condition. A special EOB
Huffman code word is provided to indicate that the remainder of the coefficients
in a reordered sequence are zeros.
 Decoding the Coefficients
ds_hat = t * Qmat =
320
55
-30
16
72
-80
51
0
-36
-24
14
38
26
0
0
0
-14
-13
16
24
40
0
0
0
-14
0
0
29
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
 Computing the IDCT
fs_hat=round(idct2(ds_hat))
67
12
-9
20
69
43
-8
42
58
25
15
30
65
40
-4
47
46
41
44
40
59
38
0
49
41
52
59
43
57
42
3
42
44
54
58
40
58
47
3
33
49
52
53
40
61
47
1
33
53
50
53
46
63
41
0
45
55
50
56
53
64
34
-1
57
 Shifting Back the Coefficients
195
140
119
148
197
171
120
170
186
153
143
158
193
168
124
175
174
169
172
168
187
166
128
177
169
180
187
171
185
170
131
170
182
186
168
186
175
131
161
177
180
181
168
189
175
129
161
181
178
181
174
191
169
128
173
183
178
184
181
192
162
127
185
f_hat=fs_hat+128 172
f=
183
160
94
153
194
163
132
165
183
153
116
176
187
166
130
169
179
168
171
182
179
170
131
167
177
177
179
177
179
165
131
167
178
178
179
176
182
164
130
171
179
180
180
179
183
164
130
171
179
179
180
182
183
170
129
173
180
179
181
179
181
170
130
169
Reconstructed image
Original image
A 4×4 grayscale image is given with the following pixel intensity values:
Perform the following steps for JPEG compression:
1.Subtract 128 from each pixel value (center the values around zero).
2.Compute the Discrete Cosine Transform (DCT) using the standard formula.
3.Quantize the transformed values using the following quantization matrix:
4.Round the values to obtain the compressed representation.
5.Reconstruct the approximate image by dequantization (multiplying by QQQ) and
applying Inverse DCT (IDCT).
Wavelet Based Compression
 Limitations of JPEG Standard
• Low bit-rate compression: JPEG offers an excellent quality at high and mid
bit-rates. However, the quality is unacceptable at low bit-rates (e.g. below
0.25 bpp)
• Lossless and lossy compression: JPEG cannot provide a superior
performance at lossless and lossy compression in a single code-stream.
• Transmission in noisy environments: the current JPEG standard provides
some resynchronization markers, but the quality still degrades when biterrors are encountered.
• Different types of still images: JPEG was optimized for natural images. Its
performance on computer generated images and bi-level (text) images is
poor.
 JPEG 2000
• JPEG 2000 is based on the DWT(Discrete Wavelet Transform). DWT
decomposes the image using functions called wavelets.
• The main advantage of wavelet is that it offers both time and frequency
information.
• The idea here is to have more localized analysis of the information which
is not possible using cosine functions whose spatial supports are identical
to the data.
• JPEG 2000 distinguishes itself from JPEG compression standards not only
by virtue of its higher compression ratios, but also by its many new
functionalities.
• The most noticeable among them is its scalability. From a compressed
JPEG 2000 bitstream, it is possible to extract a subset of the bitstream that
decodes to an image of variable quality and resolution.
 What is Wavelet Transform ?
• Wavelets are functions that are defined in time as well as in frequency around a
certain point.
• Wavelet is a localize image transform. Because of localize process LF and HF
component are get scanned row wise as well as column wise.
• Wavelets based transform are mathematical tools which are used to extract
information from images. A significant benefit it has over Fourier transforms is
temporal(time) resolution which signifies that it can captures both frequency and
location information of the images.
• Wavelet transform can be viewed as the projection of a signal into a set of basis
functions named wavelets. Such basis functions offer localization in the frequency
domain.
• The wavelet transform is designed in such a way that we get good frequency
resolution for low frequency components(average intensity values of image) and
high temporal resolution for high frequency components(edges of image).
 Steps of Wavelet Transform
Step1: Start with a mother wavelet such as Haar, Morlet, Daubechies etc. The image
is then translated into shifted and scaled versions of this mother wavelet. First
original image have to been passed through high pass filter and low pass filter by
applying filter on each row. We know when we apply LPF we get approximation
and when we apply HPF we get the details.
Step2: Now to the horizontal approximation, we again apply LPF and HPF to the
columns. Hence we get the approximate image (LL) and vertical detail of the
horizontal approximation(LH).
Step3: Next we apply LPF and HPF to the horizontal detail. Hence we get
horizontal detail of the image (HL) and the diagonal detail of the image (HH).
If the 3 detail sub-signals i.e. LH, HL and HH are small, they can be assumed to be
zero, without any significant change in the image. Hence large compression can be
achieved using wavelet transform.
 Features of JPEG 2000
• Lossless and lossy compression: the standard provides lossy compression with a
superior performance at low bit-rates. It also provides lossless compression with
progressive decoding. Applications such as digital libraries/databases and
medical imagery can benefit from this feature.
• Protective image security: the open architecture of the JPEG2000 standard
makes easy the use of protection techniques of digital images such as
watermarking, labeling, stamping or encryption.
• Region-of-interest coding: in this mode, regions of interest (ROI’s) can be
defined. These ROI’s can be encoded and transmitted with better quality than
the rest of the image .
• Robustness to bit errors: the standard incorporate a set of error resilient tools to
make the bit-stream more robust to transmission errors.
 Block diagram of JPEG 2000
Sr. Parameter
No:
JPEG
1.
Definition
It was created by Joint Photographic Expert It was created by JPEG in year 2000 and is a new
Group in 1986.
standard.
2.
Lossy/Lossless
JPEG uses lossy compression.
JPEG 2000 offers both lossless & lossy compression.
3.
Complexity
JPEG codec has low complexity.
JPEG 2000 codec is highly complex.
4.
Resolution
Quality
5.
Compression ratio
JPEG gives CR around 10 to 20.
JPEG 2000 can give CR around 30 to 200.
6.
Algorithms/
Techniques used
JPEG uses DCT.
JPEG 2000 uses DWT.
7.
Computation
It requires less computational complexity and It requires more computational complexity and
computation time is less.
computation time is also more.
8.
Image Quality
Blocking artifacts are present in the image and Blocking artifacts are not present in the image, image
regions of interest can also be not selected.
quality is very good and regions of interest can also
be selected for quality.
9.
Applications
JPEG is used widely on World Wide Web and in
digital cameras.
JPEG 2000 is widely in use in the medical and
wireless multimedia arenas. Most diagnostic imagery,
such as MRI, CT scans, and X-rays, are encoded as
JPEG 2000.
10.
File extension
JPEG/JPG.
J2K/JP2/ JPX.
and JPEG gives single resolution and single quality.
JPEG 2000
JPEG 2000 gives multiple resolution and full quality
scalability.
 Comparison
JPEG (DCT based)
JPEG-2000 (Wavelet based)
 Comparison
JPEG-2000(1.83KB)
Original(979 KB)
JPEG (6.21 KB)