Image and speech processing

Module 2

IMAGE COMRESSION

Part b

1)Differentiate Lossless and Lossy compression.

Lossless compression is a type of data compression in which the original data can

be reconstructed exactly from the compressed data. This means that there is no loss

of quality or data when the file is decompressed. Lossless compression is used for

data that needs to be stored or transmitted exactly as it is, such as medical images,

text files, and financial data.

On the other hand, lossy compression is a type of data compression in which some

of the original data is lost during the compression process. Lossy compression is

used for data that can tolerate some loss of quality, such as audio and video files.

While lossy compression can achieve higher levels of compression than lossless

compression, it does so at the expense of some loss of quality in the original data.

In general, lossless compression is used for data that needs to be preserved exactly,

while lossy compression is used for data that can tolerate some loss of quality in

exchange for a smaller file size.

2)Demonstrate run length encoding with example.

Run length encoding is a lossless data compression technique that encodes data by

representing a sequence of repeated values as a single value and a count of the number

of times the value appears.

For example, consider the following string of characters:

"WWWWWWBBBBRRR"

Using run length encoding, this string can be compressed to the following:

"6W3B4R"

In this example, the letter "W" appears 6 times in a row, so it is represented as "6W". The

letter "B" appears 3 times in a row, so it is represented as "3B". The letter "R" appears 4

times in a row, so it is represented as "4R".

Overall, this results in a compression ratio of 1:4, as the original string has a length of 14

characters and the compressed string has a length of 4 characters.

Note that run length encoding is most effective on data that contains long sequences of

repeated values, as it can significantly reduce the size of the data. It is less effective on

data that does not have many repeated values, as the compressed data may not be

much smaller than the original data.

3)Explain the need for image compression .How run length

encoding approach is used for compression? Is it lossy? Justify

There is a need for image compression because images are often very large files that

take up a lot of space and can be difficult to transmit over the internet or other networks.

Image compression is a way of reducing the file size of an image while maintaining as

much quality as possible.

One approach to image compression is run length encoding, which is a lossless data

compression technique that encodes data by representing a sequence of repeated

values as a single value and a count of the number of times the value appears. In the

context of image compression, run length encoding can be used to compress an image

by identifying and encoding sequences of pixels that have the same color.
For example, consider an image with the following pixel values:

(255, 255, 255, 255, 255, 0, 0, 0, 0, 0, 255, 255, 255, 255, 255)

Using run length encoding, this image can be compressed to the following:

(5, 255, 5, 0, 5, 255)

In this example, the pixel value "255" appears 5 times in a row, so it is represented as "5,

255". The pixel value "0" appears 5 times in a row, so it is represented as "5, 0".

Run length encoding is a lossless compression technique because the original data can

be exactly reconstructed from the compressed data. This means that there is no loss of

quality or data when the image is decompressed.

Overall, the use of run length encoding for image compression can help to reduce the file

size of an image, making it easier to store and transmit over the internet or other

networks.

4)Demonstrate arithmetic coding with example.

Arithmetic coding is a lossless data compression technique that encodes data by

representing it as a single fractional value within a range of values.

Here is an example of how arithmetic coding works:

Suppose we have the following string of characters: "ABBCCCDEE"

We can assign probabilities to each character based on their frequency of occurrence in

the string. For example:

● A: 0.1
● B: 0.2
 ● C: 0.3
● D: 0.1
● E: 0.3

We can then use these probabilities to assign a range of values to each character. For

example:

● A: 0.0 - 0.099
● B: 0.1 - 0.299
● C: 0.3 - 0.599
● D: 0.6 - 0.699
● E: 0.7 - 0.999

To encode the string "ABBCCCDEE", we can start with the range 0.0 - 1.0 and then

continually update the range based on the character being encoded. For example:

● Start with range 0.0 - 1.0

● Encode "A": Update range to 0.0 - 0.099
● Encode "B": Update range to 0.1 - 0.299
● Encode "B": Update range to 0.1 - 0.249
● Encode "C": Update range to 0.25 - 0.499
● Encode "C": Update range to 0.25 - 0.399
● Encode "C": Update range to 0.4 - 0.599
● Encode "D": Update range to 0.6 - 0.699
● Encode "E": Update range to 0.7 - 0.899
● Encode "E": Update range to 0.7 - 0.849

The final range, 0.7 - 0.849, represents the encoded string "ABBCCCDEE". This range can

be represented as a single fractional value, such as 0.752, which can be stored or

transmitted as the compressed version of the original string.

To decode the string, we can use the same probabilities and ranges to reconstruct the

original string from the encoded value.

Arithmetic coding is a lossless compression technique because the original data can be

exactly reconstructed from the compressed data. This means that there is no loss of

quality or data when the data is decompressed.

5)Explain the average length of the code. Is Huffman code uniquely

decodable? If so , Justify your answer

The average length of the code in a Huffman coding system is the average number of

bits used to represent each symbol in the original data. In a Huffman coding system, the

average length of the code is directly related to the probabilities of the symbols in the

original data.

Symbols with higher probabilities will be assigned shorter codes, while symbols with

lower probabilities will be assigned longer codes. This means that the average length of

the code will be lower for data with a more balanced distribution of symbol probabilities,

and higher for data with a skewed distribution of symbol probabilities.

Huffman coding is a uniquely decodable code, which means that there is a unique way

to decode the compressed data to obtain the original data. This is because the Huffman

coding system assigns a unique code to each symbol in the original data, and the codes

are designed in such a way that they can be easily distinguished from one another.

For example, consider the following Huffman coding system:

Symbol Code

A 0
 B 10

C 110

D 111

In this example, the codes for the symbols A, B, C, and D are all distinct from one

another, and there is no overlap between the codes. This means that it is always

possible to unambiguously decode the compressed data to obtain the original data.

Overall, the uniquely decodable nature of Huffman coding makes it an effective and

widely used data compression technique.

6)How an image is compressed using JPEG image compression

standard?

JPEG (Joint Photographic Experts Group) is a widely used image compression standard

that is designed to reduce the file size of digital images while maintaining as much

visual quality as possible.

Here is an overview of how an image is compressed using the JPEG standard:

1. The image is divided into small blocks called "macroblocks."

2. The macroblocks are transformed from the spatial domain (i.e., the pixel values in
the original image) to the frequency domain using a discrete cosine transform
(DCT).
3. The DCT coefficients are quantized using a quantization table, which reduces the
precision of the coefficients and results in data reduction.
4. The quantized DCT coefficients are encoded using a lossless compression
technique, such as Huffman coding.
 5. The compressed data is stored or transmitted.

To decompress the image, the process is reversed: the compressed data is decoded

using the Huffman coding, the quantized DCT coefficients are dequantized, the DCT

coefficients are transformed back to the spatial domain using an inverse discrete cosine

transform (IDCT), and the macroblocks are combined to form the decompressed image.

Overall, the use of the DCT and quantization in the JPEG compression process allows for

a high level of data reduction while maintaining relatively good image quality, making it a

popular choice for storing and transmitting digital images.

7)Explain in detail about the arithmetic coding

Arithmetic coding is a lossless data compression technique that encodes data by

representing it as a single fractional value within a range of values.

The basic idea behind arithmetic coding is to assign a range of values to each symbol in

the original data, and then to update the range based on the symbol being encoded. The

final range, which can be represented as a single fractional value, is the encoded version

of the original data. To decode the data, the process is reversed: the encoded value is

used to reconstruct the original range, and the original data is obtained by decoding the

symbols within the range.

Here is a more detailed explanation of how arithmetic coding works:

1. Assign probabilities to each symbol in the original data based on their frequency
of occurrence.
2. Use the probabilities to assign a range of values to each symbol. The range of
values for each symbol should be a contiguous subrange of the overall range of
possible values.
3. Initialize the range to the full range of possible values (e.g., 0.0 to 1.0).
 4. Encode each symbol in the original data by updating the range based on the
symbol's range of values. For example, if the symbol is "A" and its range of values
is 0.0 to 0.499, the overall range would be updated to 0.0 to 0.499.
5. The final range, which can be represented as a single fractional value, is the
encoded version of the original data.
6. To decode the data, the process is reversed: the encoded value is used to
reconstruct the original range, and the original data is obtained by decoding the
symbols within the range.

Arithmetic coding is a lossless compression technique because the original data can be

exactly reconstructed from the compressed data. This means that there is no loss of

quality or data when the data is decompressed.

Overall, arithmetic coding is a powerful data compression technique that can achieve

very high levels of compression, particularly for data with a skewed distribution of

symbol probabilities. However, it can be more complex to implement than other data

compression techniques, and may not be as efficient in terms of computational

resources.

8)Describe run length encoding with examples

Run length encoding is a lossless data compression technique that encodes data by

representing a sequence of repeated values as a single value and a count of the number

of times the value appears.

Here are some examples of how run length encoding works:

Example 1:

Consider the following string of characters:

"WWWWWWBBBBRRR"

Using run length encoding, this string can be compressed to the following:
"6W3B4R"

In this example, the letter "W" appears 6 times in a row, so it is represented as "6W". The

letter "B" appears 3 times in a row, so it is represented as "3B". The letter "R" appears 4

times in a row, so it is represented as "4R".

Overall, this results in a compression ratio of 1:4, as the original string has a length of 14

characters and the compressed string has a length of 4 characters.

Example 2:

Consider the following string of characters:

"AAAAABBBBCCCCDDDDEEEE"

Using run length encoding, this string can be compressed to the following:

"5A4B5C4D4E"

In this example, the letter "A" appears 5 times in a row, so it is represented as "5A". The

letter "B" appears 4 times in a row, so it is represented as "4B". The letter "C" appears 5

times in a row, so it is represented as "5C". The letter "D" appears 4 times in a row, so it is

represented as "4D". The letter "E" appears 4 times in a row, so it is represented as "4E".

Overall, this results in a compression ratio of 1:9, as the original string has a length of 20

characters and the compressed string has a length of 9 characters.

Run length encoding is most effective on data that contains long sequences of repeated

values, as it can significantly reduce the size of the data. It is less effective on data that

does not have many repeated values, as the compressed data may not be much smaller

than the original data.

Run length encoding is a lossless compression technique because the original data can

be exactly reconstructed from the compressed data. This means that there is no loss of

quality or data when the data is decompressed.

9)What is mean by bit plane slicing and write the applications of it

Bit plane slicing is a technique used in image processing and data compression that

involves dividing an image into its individual bit planes.

An image can be thought of as a matrix of pixel values, where each pixel value is a digital

representation of the color and intensity of the pixel. The pixel values are typically

represented as a fixed number of bits, such as 8 bits (for a 256-color image) or 24 bits

(for a full-color image).

Bit plane slicing involves separating the individual bits that make up each pixel value into

separate planes or layers. For example, in an 8-bit image, the first bit plane would

contain the least significant bit (LSB) of each pixel value, the second bit plane would

contain the second least significant bit (LSB-1) of each pixel value, and so on up to the

eighth bit plane, which would contain the most significant bit (MSB) of each pixel value.

Bit plane slicing can be used for a variety of purposes, including:

1. Image compression: Bit plane slicing can be used to identify and encode the
most important bits of an image (i.e., the bits that contribute the most to the
overall visual quality of the image), while discarding or encoding less important
bits less efficiently. This can help to reduce the file size of the image while
maintaining as much visual quality as possible.
2. Image enhancement: Bit plane slicing can be used to manipulate the individual
bits of an image to improve its visual quality. For example, the LSBs of an image
can be modified to smooth out noise or to adjust the contrast of the image.
3. Image representation: Bit plane slicing can be used to represent an image in a
compact and efficient way. For example, the LSBs of an image can be used to
encode a rough approximation of the image, while the MSBs can be used to
 encode the fine details of the image. This can be useful for applications such as
image transmission, where the available bandwidth is limited.

Overall, bit plane slicing is a useful technique for manipulating and analyzing the

individual bits that make up an image, and can be an effective tool in image processing

and data compression applications.

10)List out and explain in detail about the image compression

There are several techniques that can be used for image compression, including:

1. Lossless compression: Lossless image compression techniques are designed

to reduce the file size of an image while maintaining the original pixel values
and the original visual quality of the image. Examples of lossless image
compression techniques include run length encoding, Huffman coding, and
arithmetic coding.
2. Lossy compression: Lossy image compression techniques are designed to
reduce the file size of an image by sacrificing some of the visual quality of the
image. These techniques typically achieve higher levels of compression than
lossless techniques, but at the cost of reduced image quality. Examples of
lossy image compression techniques include JPEG, JPEG 2000, and MPEG.
3. Transform coding: Transform coding is a lossy image compression technique
that involves transforming the pixel values of an image from the spatial
domain (i.e., the pixel values in the original image) to the frequency domain
using a mathematical transform, such as a discrete cosine transform (DCT).
The transformed coefficients are then quantized and encoded using a
lossless compression technique, such as Huffman coding. Transform coding
is commonly used in image and video compression standards, such as JPEG
and MPEG.
4. Fractal compression: Fractal compression is a lossy image compression
technique that involves representing an image as a set of self-similar patterns,
called "fractals." The image is divided into small blocks, and the blocks are
compared to a set of pre-computed fractals. The closest matching fractal is
chosen to represent each block, and the resulting set of fractals is used to
reconstruct the image.
11)Relate the JPEG compression standard and the steps involved
in JPEG compression

JPEG (Joint Photographic Experts Group) is a widely used image compression standard

that is designed to reduce the file size of digital images while maintaining as much

visual quality as possible.

Here is an overview of the steps involved in JPEG compression:

1. Divide the image into small blocks called "macroblocks."

2. Transform the macroblocks from the spatial domain (i.e., the pixel values in the
original image) to the frequency domain using a discrete cosine transform (DCT).
3. Quantize the DCT coefficients using a quantization table, which reduces the
precision of the coefficients and results in data reduction.
4. Encode the quantized DCT coefficients using a lossless compression technique,
such as Huffman coding.
5. Store or transmit the compressed data.

To decompress the image, the process is reversed: the compressed data is decoded

using the Huffman coding, the quantized DCT coefficients are dequantized, the DCT

coefficients are transformed back to the spatial domain using an inverse discrete cosine

transform (IDCT), and the macroblocks are combined to form the decompressed image.

Overall, the use of the DCT and quantization in the JPEG compression process allows for

a high level of data reduction while maintaining relatively good image quality, making it a

popular choice for storing and transmitting digital images.

12)Which type of method to generating variable length codes with

an example.

Huffman coding is a technique for generating variable length codes for data
compression. It works by assigning shorter codes to symbols that occur more
frequently in the data, and longer codes to symbols that occur less frequently.

Here is an example of how Huffman coding works:

Consider the following string of characters:

"AAABBCCCCCDDDDDD"

The first step in Huffman coding is to assign probabilities to each symbol

based on their frequency of occurrence. For this string, the probabilities would
be:

Symbol Probability

A 0.2

B 0.2

C 0.4

D 0.2

Next, a binary tree is constructed based on the probabilities of the symbols.

This is done by starting with a node for each symbol, and then repeatedly
combining the two nodes with the lowest probabilities until there is only one
node left. The resulting tree is shown below:

.4
/\
/ \
.2 .2
/ /\
.2 .2 .2
 A B CD

Finally, the symbols are assigned codes based on the path from the root of the tree

to each symbol. In this example, the codes would be:

Symbol Code

A 0

B 10

C 110

D 111

The resulting encoded string would be:

"000110001110111111111"

Overall, Huffman coding is a simple and efficient technique for generating variable

length codes for data compression. It is widely used in a variety of applications,

including image and video compression, data transmission, and data storage.

13)Show arithmetic encoding process with an example.

Arithmetic coding is a lossless data compression technique that encodes data by

representing it as a single fractional value within a range of values.

Here is an example of how arithmetic coding works:

Consider the following string of characters:

"AAABBCCCCCDDDDDD"

The first step in arithmetic coding is to assign probabilities to each symbol based on

their frequency of occurrence. For this string, the probabilities would be:

Symbol Probability

A 0.2

B 0.2

C 0.4

D 0.2

Next, the range of values for each symbol is determined based on the probabilities.

For example, if the overall range of possible values is 0.0 to 1.0, the range of values
for symbol "A" would be 0.0 to 0.2, the range of values for symbol "B" would be 0.2 to

0.4, and so on.

The encoding process then proceeds as follows:

1. Initialize the range to the full range of possible values (e.g., 0.0 to 1.0).
2. Encode the first symbol in the original data by updating the range based on
the symbol's range of values. For example, if the symbol is "A" and its range of
values is 0.0 to 0.2, the overall range would be updated to 0.0 to 0.2.
3. Encode the next symbol in the original data by further updating the range
based on the symbol's range of values. For example, if the next symbol is "B"
and its range of values is 0.2 to 0.4, the overall range would be updated to 0.2
to 0.4.
4. Repeat the process for each remaining symbol in the original data

14)Why LZW coding and what is the need for image relate with an
example.

LZW (Lempel-Ziv-Welch) is a lossless data compression technique that is widely

used in a variety of applications, including image compression. It works by creating a

dictionary of strings (i.e., sequences of symbols) that occur in the data, and

replacing each occurrence of a string in the data with a code that represents the

string in the dictionary.

The basic idea behind LZW is to take advantage of the fact that many strings in the

data are likely to be repeated, and to replace the repeated strings with a single code,

which can be encoded more efficiently than the original string.

Here is an example of how LZW works:

Consider the following string of characters:

"AAABBCCCCCDDDDDD"

The first step in LZW is to initialize the dictionary with the individual symbols in the

data. In this example, the dictionary would be initialized with the symbols "A", "B", "C",

and "D".

Next, the encoding process begins by looking for repeated strings in the data. The

first repeated string in this example is "AA", which can be replaced with a code from

the dictionary. The dictionary is updated to include "AA" and the resulting encoded

string becomes:

"1B"

The encoding process continues by looking for the next repeated string in the data.

In this example, the next repeated string is "CC", which can also be replaced with a

code from the dictionary. The dictionary is updated to include "CC" and the resulting

encoded string becomes:

"1B2D"

The encoding process continues until all strings in the data have been processed. In

this example, the final encoded string is:

"1B2D3"

Overall, LZW is an effective data compression technique that can significantly reduce

the size of the data by replacing repeated strings with compact codes. It is widely

used in a variety of applications, including image compression, data transmission,

and data storage.

15)Relate the JPEG compression standard and the steps involved
in JPEG compression.

JPEG (Joint Photographic Experts Group) is a widely used image compression standard

that is designed to reduce the file size of digital images while maintaining as much

visual quality as possible.

Here is an overview of the steps involved in JPEG compression:

1. Divide the image into small blocks called "macroblocks."

2. Transform the macroblocks from the spatial domain (i.e., the pixel values in the
original image) to the frequency domain using a discrete cosine transform (DCT).
3. Quantize the DCT coefficients using a quantization table, which reduces the
precision of the coefficients and results in data reduction.
4. Encode the quantized DCT coefficients using a lossless compression technique,
such as Huffman coding.
5. Store or transmit the compressed data.

To decompress the image, the process is reversed: the compressed data is decoded

using the Huffman coding, the quantized DCT coefficients are dequantized, the DCT

coefficients are transformed back to the spatial domain using an inverse discrete cosine

transform (IDCT), and the macroblocks are combined to form the decompressed image.

Overall, the use of the DCT and quantization in the JPEG compression process allows for

a high level of data reduction while maintaining relatively good image quality, making it a

popular choice for storing and transmitting digital images.

16)Select and match the Redundancies and their removal methods

with examples

Redundancy Removal Method Example

 Spatial redundancy Lossless compression Run length encoding

Statistical redundancy Lossy compression JPEG image compression

Temporal redundancy Video compression MPEG video compression

1. Spatial redundancy refers to the repetition of patterns or structures within an

image or other data. Lossless compression techniques, such as run length
encoding, can be used to remove spatial redundancy by identifying and encoding
repeated patterns in the data.

For example, consider an image that consists of a large area of solid color. Run length

encoding could be used to represent the image by encoding the length of the solid color

region and the color value, rather than encoding the individual pixels. This would result in

a much smaller file size for the image.

2. Statistical redundancy refers to the presence of patterns in the data that can be
predicted based on the statistical properties of the data. Lossy compression
techniques, such as JPEG image compression, can be used to remove statistical
redundancy by approximating the original data with a simpler representation that
captures the most important features of the data.

For example, consider an image that contains smooth gradations of color. JPEG image

compression could be used to approximate the gradations with a set of discrete colors,

resulting in a smaller file size for the image while maintaining most of the visual quality

of the original image.

3. Temporal redundancy refers to the repetition of patterns or structures over time,

as in a video. Video compression techniques, such as MPEG, can be used to
remove temporal redundancy by identifying and encoding the changes between
frames in the video, rather than encoding each frame independently.
For example, consider a video that shows a person speaking. MPEG video compression

could be used to encode the video by representing the changes in the person's facial

features and mouth movements from frame to frame, rather than encoding each frame

as a separate image. This would result in a much smaller file size for the video.

17)Demonstrate with example source encoder and decoder

A source encoder is a device or system that converts a source of data, such as a video

or audio signal, into a form that can be more efficiently stored or transmitted. A source

decoder is a device or system that converts the encoded data back into its original form.

Here is an example of how a source encoder and decoder might work:

1. The source encoder receives a video signal as input.

2. The source encoder applies a video compression algorithm to the video signal,
such as H.264 or HEVC, to reduce the amount of data required to represent the
video.
3. The source encoder outputs the compressed video data.
4. The compressed video data is transmitted over a network or stored on a storage
device.
5. The source decoder receives the compressed video data as input.
6. The source decoder applies the same video compression algorithm to the
compressed video data to decompress it.
7. The source decoder outputs the decompressed video data, which is the same as
the original video signal.

Overall, source encoders and decoders are essential components of many digital

systems that transmit or store data, such as video streaming platforms, video

conferencing systems, and digital video recording devices. They enable efficient storage

and transmission of data by reducing the amount of data required to represent the

original source.

18)Compare error free compression and lossy compression

Error-free compression and lossy compression are two types of data compression

techniques that are used to reduce the size of a data file or signal.

Error-free compression, also known as lossless compression, is a type of data

compression that allows the original data to be exactly reconstructed from the

compressed data. This means that there is no loss of information or quality when the

data is decompressed. Examples of error-free compression techniques include Huffman

coding and LZW (Lempel-Ziv-Welch).

Lossy compression, on the other hand, is a type of data compression that involves some

loss of information or quality when the data is decompressed. Lossy compression

techniques are designed to remove certain types of redundancy in the data, such as

statistical redundancy or spatial redundancy, in order to achieve a higher level of data

reduction. However, this also means that the decompressed data is not an exact copy of

the original data. Examples of lossy compression techniques include JPEG image

compression and MP3 audio compression.

Overall, error-free compression and lossy compression are useful in different situations

depending on the requirements for the data. Error-free compression is generally

preferred for data that needs to be preserved exactly, such as financial records or

scientific data, while lossy compression is more suitable for data where some loss of

quality is acceptable, such as images or audio.

19)Relate JPEG 2000 standard with merits and demerits

JPEG 2000 is a still image compression standard that was developed by the Joint

Photographic Experts Group (JPEG) in the early 2000s. It is an improvement over the

original JPEG standard and is designed to provide a higher level of image quality and

more efficient compression.

Some of the main advantages of JPEG 2000 include:

 ● Improved image quality: JPEG 2000 uses a more advanced image compression
algorithm than the original JPEG standard, which allows it to achieve a higher
level of image quality for a given file size.
● Higher compression efficiency: JPEG 2000 is generally more efficient at
compressing images than the original JPEG standard, which means that it can
achieve a similar level of image quality with a smaller file size.
● Progressive transmission: JPEG 2000 supports a "progressive" mode of
transmission, which allows an image to be displayed with increasing resolution
as more data is received. This can be useful for applications where low-resolution
images are needed quickly, such as in web browsing.
● Region of interest coding: JPEG 2000 supports the ability to specify a "region of
interest" (ROI) in the image, which can be encoded with higher quality than the
rest of the image. This can be useful for applications where certain parts of the
image are more important than others.

Some of the main drawbacks of JPEG 2000 include:

● Complexity: JPEG 2000 uses a more complex image compression algorithm than
the original JPEG standard, which can make it more difficult to implement and
slower to encode and decode.
● Compatibility issues: JPEG 2000 is not as widely supported as the original JPEG
standard, which can make it more difficult to use in some applications.
● Larger file sizes: In some cases, JPEG 2000 may result in larger file sizes than the
original JPEG standard, particularly for small or simple images.

Overall, JPEG 2000 is a useful image compression standard that offers improved image

quality and higher compression efficiency compared to the original JPEG standard.

However, it may not be the best choice in all situations due to its complexity and

compatibility issues.

20)Draw a transform coding system and relate with image

compression.

A transform coding system is a type of data compression system that converts a

signal from one domain (e.g., the spatial domain of an image) to another domain

(e.g., the frequency domain) and applies a compression algorithm to the transformed
signal in order to reduce its size. Transform coding systems are commonly used in

image and video compression.

Here is a diagram of a simple transform coding system for image compression:

[Input image] ---> [Transform] ---> [Quantization] ---> [Entropy encoding] --->

[Compressed image]

[Compressed image] ---> [Entropy decoding] ---> [Inverse quantization] ---> [Inverse

transform] ---> [Output image]

The input image is first transformed from the spatial domain to the frequency

domain using a transform such as the discrete cosine transform (DCT) or the

wavelet transform. The transformed image is then quantized, which involves

reducing the precision of the transformed coefficients in order to reduce the data

size. The quantized coefficients are then entropy encoded, which involves applying a

lossless compression algorithm such as Huffman coding to the data. The resulting

compressed image is then stored or transmitted.

To decompress the image, the process is reversed: the compressed image is entropy

decoded, the quantized coefficients are dequantized, the transformed image is

transformed back to the spatial domain using an inverse transform, and the output

image is produced.

Overall, transform coding systems are an effective way to compress images and

other signals by exploiting redundancy in the data and representing the data more

efficiently.

Part c

1)What is image compression?

Image compression is the process of reducing the size of a digital image by encoding

the image with fewer bits of information. Image compression is useful because digital

images can be very large in size, making them difficult to store or transmit efficiently. By

compressing an image, it is possible to reduce the amount of storage or bandwidth

required to store or transmit the image, which can save time and resources.

There are two main types of image compression: lossless and lossy. Lossless image

compression techniques allow the original image to be exactly reconstructed from the

compressed data, while lossy techniques involve some loss of information or quality

when the image is decompressed. Lossless techniques are generally used for images

that need to be preserved exactly, such as medical or scientific images, while lossy

techniques are more suitable for images where some loss of quality is acceptable, such

as photographs or web graphics.

There are many different image compression techniques and standards, including JPEG,

JPEG 2000, PNG, GIF, and BMP. Each technique or standard has its own strengths and

limitations, and the best choice for a particular application will depend on the

requirements for the image and the resources available.

2)What is the need for Compression?

There are several reasons why compression is important:

1. Storage: Digital data, such as images, videos, and audio files, can be very large
in size, making it difficult to store large amounts of data efficiently.
Compression can significantly reduce the size of the data, making it more
practical to store.
2. Transmission: When transmitting data over the internet or other networks, the
amount of data that needs to be transferred can be very large. Compression
can reduce the amount of data that needs to be transmitted, which can help to
 reduce the amount of time it takes to transfer the data and the amount of
bandwidth required.
3. Performance: Large data files can take up a lot of memory and processing
power when they are being used or accessed. Compression can help to
reduce the amount of memory and processing power required, which can
improve the overall performance of the system.
4. Cost: Storing and transmitting large amounts of data can be expensive in
terms of hardware, software, and other resources. Compression can help to
reduce the cost of storing and transmitting data by reducing the amount of
resources required.

Overall, compression is a useful tool for reducing the size of digital data and making

it more practical to store, transmit, and use. It is widely used in a variety of

applications, including data storage, data transmission, and image and video

processing.

3)What are the types of redundancy?

Redundancy is the presence of unnecessary or duplicative information in a data file or

signal. There are several types of redundancy that can occur in data:

1. Spatial redundancy: This refers to the repetition of patterns or structures within

an image or other data.
2. Statistical redundancy: This refers to the presence of patterns in the data that can
be predicted based on the statistical properties of the data.
3. Temporal redundancy: This refers to the repetition of patterns or structures over
time, as in a video.
4. Syntactic redundancy: This refers to the repetition of information in the syntax or
structure of a data file or signal, such as the inclusion of unnecessary tags or
formatting.
5. Semantic redundancy: This refers to the repetition of information in the meaning
or content of a data file or signal, such as the inclusion of synonyms or alternate
word forms.
Redundancy can be removed from data using various types of data compression

techniques, such as lossless compression or lossy compression. Removing redundancy

can help to reduce the size of the data and make it more efficient to store and transmit.

4)Define coding redundancy.

Coding redundancy is the presence of unnecessary or duplicative information in a

coded data file or signal. It can occur when a coding scheme or algorithm is used to

represent data in a more compact or efficient form, but some of the information in

the data is not necessary for the intended purpose.

Coding redundancy can be removed by applying a more efficient coding scheme or

algorithm that removes the unnecessary information from the data. This can help to

reduce the size of the coded data and make it more efficient to store and transmit.

For example, consider a data file that consists of a sequence of numbers. A simple

coding scheme might represent each number as a 4-bit binary value, resulting in a

file size of 4 bits per number. However, if the numbers are all between 0 and 15, it

would be more efficient to represent each number as a 4-bit binary value, resulting in

a file size of 4 bits per number. This would remove the coding redundancy in the data

and reduce the file size by 50%.

Overall, coding redundancy is an important concept in data compression and coding

theory, as it can be used to reduce the size of data and improve its efficiency.

5)Define interpixel redundancy.

Interpixel redundancy is a type of redundancy that occurs in digital images

due to the close proximity of neighboring pixels in the image. It is caused by
the fact that the values of neighboring pixels are often correlated, which
means that they are likely to be similar to each other.
Interpixel redundancy can be reduced by applying image compression
techniques that exploit this correlation. For example, lossless image
compression techniques such as run length encoding can be used to identify
and encode runs of pixels with the same value, resulting in a smaller file size
for the image. Lossy image compression techniques such as JPEG can also
be used to remove interpixel redundancy by approximating the values of
neighboring pixels with a simpler representation, resulting in a smaller file size
for the image.

Overall, interpixel redundancy is an important factor in image compression

and can be exploited to achieve a higher level of data reduction while
maintaining relatively good image quality.

6)Define Psychovisual redundancy.

Psychovisual redundancy is a type of redundancy that occurs in digital images

due to the limitations of human perception. It is caused by the fact that the
human visual system is more sensitive to certain types of image features,
such as edges and textures, than to others, and is less sensitive to changes in
color or luminance within a uniform region.

Psychovisual redundancy can be exploited by applying lossy image

compression techniques that remove or approximate image features that are
less important to human perception. For example, JPEG image compression
uses a mathematical model of human perception to approximate the values of
pixels in an image with a simplified representation that preserves the most
important features of the image while reducing the data size.

Overall, psychovisual redundancy is an important factor in image compression

and can be exploited to achieve a high level of data reduction while
maintaining acceptable image quality.

7)What is run length coding?

Run length coding (RLC) is a lossless data compression technique that is used to

encode runs of data with the same value. It is based on the idea that long runs of data

with the same value are more common in many types of data, such as images, and can
be represented more efficiently by encoding the value and the length of the run rather

than each individual value.

Here is an example of how run length coding might work:

Suppose we have the following data:

1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1

Using run length coding, we can represent this data as:

(1, 3), (2, 3), (3, 5), (1, 5)

Each tuple in the encoded data represents a run of data with a particular value, with the

first element of the tuple representing the value and the second element representing

the length of the run.

Run length coding is simple and efficient, and it can be used to compress many types of

data, including images, audio, and text. However, it is not as effective at compressing

data with a high level of randomness or complexity, as it relies on the presence of long

runs of data with the same value.

8)Define compression ratio.

Compression ratio is a measure of the efficiency of a data compression

algorithm or system. It is defined as the ratio of the size of the uncompressed
data to the size of the compressed data.

For example, if a data compression algorithm reduces the size of a data file
from 100 MB to 50 MB, the compression ratio is 100/50 = 2. This means that
the algorithm was able to reduce the size of the data by a factor of 2.

A higher compression ratio indicates that the data compression algorithm was
more effective at reducing the size of the data, while a lower compression
ratio indicates that the data was not as efficiently compressed.
Compression ratio is an important factor to consider when selecting a data
compression algorithm or system, as it can affect the efficiency of storing and
transmitting the data. However, it is not the only factor to consider, as other
factors such as the speed of the algorithm and the quality of the compressed
data may also be important.

9)Define source encoder.

A source encoder is a device or system that converts a data source, such as a video

or audio stream, into a compressed form that is more efficient to store or transmit.

Source encoding is a fundamental part of data compression and is used to reduce

the size of the data by removing redundancy and representing the data more

efficiently.

There are many different source encoding techniques and algorithms that can be

used, depending on the characteristics of the data and the requirements for the

compressed data. Some examples of source encoding techniques include Huffman

coding, LZW (Lempel-Ziv-Welch), and arithmetic coding.

Source encoding is often used in combination with other types of data compression

techniques, such as transform coding or quantization, in order to achieve a higher

level of data reduction.

Overall, source encoding is an important part of many data compression systems

and is used to improve the efficiency of storing and transmitting data.

10)Define channel encoder.

A channel encoder is a device or system that converts a digital data stream into a form

that is more suitable for transmission over a communication channel, such as a wireless

network or a physical cable. Channel encoding is a fundamental part of digital

communication and is used to improve the reliability and efficiency of data transmission.
There are many different channel encoding techniques and algorithms that can be used,

depending on the characteristics of the communication channel and the requirements

for the transmitted data. Some examples of channel encoding techniques include error

correcting codes, forward error correction (FEC), and trellis codes.

Channel encoding is often used in combination with other types of communication

techniques, such as modulation and multiplexing, in order to improve the performance of

the communication system.

Overall, channel encoding is an important part of many digital communication systems

and is used to improve the reliability and efficiency of data transmission.

11)What are the operations performed by error free compression?

Error-free compression is a type of data compression that allows the original data to be

exactly reconstructed from the compressed data. Error-free compression techniques are

generally used for data that needs to be preserved exactly, such as medical or scientific

images, where even a small error in the data could be significant.

There are several operations that are commonly performed by error-free compression

techniques:

1. Redundancy removal: Error-free compression techniques typically remove

redundancy from the data in order to reduce its size. This can involve identifying
and removing duplicative or unnecessary information from the data.
2. Encoding: Once the redundancy has been removed, the data is typically encoded
using a lossless compression algorithm, such as Huffman coding or LZW, which
converts the data into a more compact form.
3. Decoding: To decompress the data, the encoded data is decoded using the same
lossless compression algorithm, which restores the original data exactly.

Overall, error-free compression techniques are designed to preserve the integrity of the

original data and allow it to be exactly reconstructed from the compressed data. They
are used in applications where even a small error in the data could be significant, such

as in medical or scientific imaging.

12)What is Variable Length Coding?

Variable length coding is a data compression technique that uses variable length codes

to represent data symbols or characters. In variable length coding, each symbol or

character is assigned a unique code, and the length of the code is chosen based on the

frequency of the symbol in the data.

For example, consider a data file that consists of the characters "a", "b", and "c". If the

character "a" occurs much more frequently than the characters "b" and "c", it would be

more efficient to assign a shorter code to "a" and longer codes to "b" and "c". This would

result in a smaller data size overall, as the shorter code for "a" would be used more

often.

Variable length coding is used in many data compression techniques, such as Huffman

coding and LZW (Lempel-Ziv-Welch). It is an effective way to reduce the size of data by

assigning shorter codes to the most frequent symbols and longer codes to the less

frequent symbols.

Overall, variable length coding is a useful technique for reducing the size of data and

improving the efficiency of data storage and transmission.

13)What is JPEG?
JPEG (Joint Photographic Experts Group) is a popular image compression standard that

is used to reduce the size of digital image files while maintaining a reasonable level of

image quality. JPEG is designed for compressing photographs and other

continuous-tone images, and it is widely used on the web, in digital cameras, and in other

applications where image quality is important but storage space is limited.

JPEG uses a lossy compression technique, which means that some of the information in

the original image is lost during the compression process. The amount of information

that is lost can be controlled by adjusting the compression level, with higher levels of

compression resulting in smaller file sizes but lower image quality.

The JPEG standard defines a number of different image formats, including JPEG, JPEG

2000, and JPEG XR. Each format has its own strengths and limitations, and the best

choice for a particular application will depend on the requirements for the image and the

resources available.

Overall, JPEG is a widely used image compression standard that is effective at reducing

the size of digital images while maintaining a reasonable level of image quality.

14)What are the coding systems in JPEG?

The JPEG image compression standard uses several different coding systems to

represent and compress digital images. These coding systems include:

1. Discrete Cosine Transform (DCT): JPEG uses the DCT to transform the pixel

values in an image from the spatial domain to the frequency domain, where the

frequencies correspond to the spatial patterns in the image. The DCT is used to

decorrelate the image data, making it easier to compress.

2. Quantization: After the DCT is applied, the resulting coefficients are quantized, or

divided into a set of discrete values. The quantization process reduces the

precision of the coefficients and removes some of the less significant

information from the image.

3. Entropy coding: After quantization, the remaining image data is encoded using an

entropy coding algorithm, such as Huffman coding or arithmetic coding, which

represents the data in a more efficient form. The entropy coding step is used to

further reduce the size of the image data.

Overall, these coding systems are used in combination to represent and compress digital

images according to the JPEG standard.

15)What are the basic steps in JPEG?

The basic steps in JPEG image compression are:

1. Preprocessing: Before the image is compressed, it may undergo

preprocessing to improve the efficiency of the compression process.

This can include resizing the image, adjusting the contrast, or applying

other image processing techniques.

2. Discrete Cosine Transform (DCT): The DCT is applied to the pixel values

in the image to transform them from the spatial domain to the

frequency domain. The DCT is used to decorrelate the image data,

making it easier to compress.

3. Quantization: The DCT coefficients are quantized, or divided into a set of

discrete values, in order to reduce the precision of the coefficients and

remove some of the less significant information from the image.

4. Entropy coding: The quantized image data is then encoded using an

entropy coding algorithm, such as Huffman coding or arithmetic coding,

which represents the data in a more efficient form.

5. Decoding and reconstruction: To decompress the image, the encoded

data is passed through a decoder, which applies the inverse of the DCT

and quantization processes to reconstruct the original image.

Overall, these steps are used to compress and decompress digital images

according to the JPEG standard.

16)State whether the following huffman code 0,01, 10,011 for the given

symbols a1,a2,a3,a4 is uniquely decodable or not

It is not possible to determine whether the given Huffman code is uniquely decodable

based on the information provided.

In order for a Huffman code to be uniquely decodable, it must meet the following

conditions:

1. No code is the prefix of any other code. This means that no code can be the

beginning of another code. For example, if the code for symbol "a" is "01" and the

code for symbol "b" is "011", the code for "a" is not uniquely decodable, because it

is the prefix of the code for "b".

2. The code for each symbol is unique. This means that each symbol must have a

distinct code, and no two symbols can share the same code.

To determine whether the given Huffman code is uniquely decodable, we would need to

know the complete set of symbols and their corresponding codes. Without this

information, it is not possible to determine whether the code satisfies the above

conditions.

17)Match the Lossless compression–coding with example.

Here is a list of lossless compression techniques and their corresponding coding

examples:

1. Run length coding: This technique encodes runs of data with the same value

using a tuple of the form (value, length). For example, the data "1, 1, 1, 2, 2, 2, 3, 3,

3, 3, 3" could be encoded as "(1, 3), (2, 3), (3, 5)".

 2. Huffman coding: This technique assigns variable length codes to data symbols

based on their frequency. For example, the data "aaabbbccc" could be encoded

as "0, 01, 011, 010" if "a" is the most frequent symbol, "b" is the next most

frequent, and "c" is the least frequent.

3. LZW (Lempel-Ziv-Welch): This technique encodes data by replacing repeated

sequences of data with references to earlier occurrences of the same data. For

example, the data "aaabbbaaa" could be encoded as "a, a, a, b, b, b, a, 3" if the

reference to the earlier occurrence of "aaa" is represented by the number 3.

4. Arithmetic coding: This technique encodes data by representing it as a range

within a continuous interval. For example, the data "aaabbbaaa" could be

encoded as a number between 0 and 1, with the most frequent symbol "a" being

represented by a smaller range within the interval and the less frequent symbols

"b" being represented by a larger range.

Overall, these lossless compression techniques can be used to reduce the size of data

while maintaining the integrity of the original data.

18)Explain the Data Compression and Data Redundancy

Data compression is the process of reducing the size of a data file or stream in order

to save storage space or reduce the amount of bandwidth needed to transmit the

data. Data compression is typically achieved by removing redundancy from the data,

which is defined as any information that can be derived from other information in the

data.

There are two main types of data compression: lossless and lossy. Lossless

compression techniques preserve the original data exactly and allow it to be exactly

reconstructed from the compressed data. Lossy compression techniques, on the

other hand, remove some of the information from the original data and do not allow

it to be exactly reconstructed.
Data redundancy is the presence of duplicate or unnecessary information in a data

file or stream. Data redundancy can occur in many forms, such as redundant

symbols, patterns, or structures within the data. Data redundancy can be reduced by

identifying and removing the redundant information, which can improve the

efficiency of data storage and transmission.

Overall, data compression and data redundancy are important concepts in data

management and are used to improve the efficiency of storing and transmitting data.

19)Draw and relate block diagram of Lossy Compression.

In this system, the input data is first preprocessed to improve the efficiency of the

compression process. This can include resizing the data, adjusting the contrast, or

applying other image processing techniques.

Next, the data is transformed using a transform algorithm, such as the Discrete

Cosine Transform (DCT) or the Discrete Wavelet Transform (DWT). The transform
algorithm converts the data from the spatial domain to the frequency domain, where

the frequencies correspond to the spatial patterns in the data.

The transformed data is then quantized, or divided into a set of discrete values, in

order to reduce the precision of the data and remove some of the less significant

information. The quantization step is typically adjustable, with higher levels of

quantization resulting in more data reduction but lower quality.

Finally, the quantized data is encoded using an entropy coding algorithm, such as

Huffman coding or arithmetic coding, which represents the data in a more efficient

form. The encoded data is then ready for storage or transmission.

To decompress the data, the encoded data is passed through a decoder, which

applies the inverse of the transform and quantization processes to reconstruct an

approximation of the original data.

Overall, this lossy compression system reduces the size of the input data by

removing redundant and less significant information and representing the data in a

more efficient form. The quality of the reconstructed data will depend on the level of

quantization and the efficiency of the encoding algorithm.

Part a

1)Determine the Huffman code procedure for the following data

2)A source emits letters from an alphabet for this source? Find the average length of
the code and its redundancy

To determine the average length of the code and the redundancy for a source
that emits letters from an alphabet, we would need to know the probability
distribution of the letters in the alphabet. The probability distribution specifies
the probability of each letter occurring in the source.
For example, consider a source that emits letters from the alphabet {a, b, c, d,
e} with the following probability distribution:

Letter Probability
a 0.4
b 0.2
c 0.2
d 0.1

e 0.1

To find the average length of the code for this source, we can use the formula:

Average length = ∑(probability of letter) * (length of code for letter)

For example, if we use a Huffman code to encode the letters, we might assign
the following codes:

Letter Code Probability (Probability) * (Length of code)

a 0 0.4 0.4 * 1 = 0.4
b 10 0.2 0.2 * 2 = 0.4
c 110 0.2 0.2 * 3 = 0.6
d 111 0.1 0.1 * 3 = 0.3

e 1111 0.1 0.1 * 4 = 0.4

Using these codes, the average length of the code would be:

Average length = 0.4 + 0.4 + 0.6 + 0.3 + 0.4 = 2.1

The redundancy of the code is a measure of how much the code deviates
from the theoretical minimum length, which is known as the entropy of the
source. The entropy is defined as:

Entropy = ∑(prob

3)For the image shown below compute the compression ratio that
can be achieved using Huffman coding
4)A source emits three symbols A,B,C with a
probability{0.5,0.25,0.25} respectively. Construct an arithmetic code
to encode the word ‘C A B’

To encode the word "C A B" using arithmetic coding, we can follow these steps:

1. Determine the range of the alphabet: First, we need to determine the range of the
alphabet. Since the alphabet consists of three symbols {A, B, C} with probabilities
{0.5, 0.25, 0.25}, the range of the alphabet can be represented as follows:

A: [0, 0.5)
B: [0.5, 0.75)

C: [0.75, 1.0)

2. Initialize the range: Next, we need to initialize the range to the full range of the
alphabet, which is [0, 1.0).
3. Encode the first symbol: To encode the first symbol "C", we need to narrow the
range to the range of symbol "C", which is [0.75, 1.0). The encoded value is the
midpoint of this range, which is 0.875.
4. Encode the second symbol: To encode the second symbol "A", we need to narrow
the range to the range of symbol "A", which is [0, 0.5). The encoded value is the
midpoint of this range, which is 0.25.
5. Encode the third symbol: To encode the third symbol "B", we need to narrow the
range to the range of symbol "B", which is [0.5, 0.75). The encoded value is the
midpoint of this range, which is 0.625.
6. Output the encoded value: Finally, the encoded value is the midpoint of the final
range, which is 0.625. This is the arithmetic code for the word "C A B".

Overall, the arithmetic code for the word "C A B" is 0.625. This code represents the

probability of the word occurring in the source, based on the probability of each symbol

in the alphabet.

5)Encode the word a1,a2,a3,a4 using arithmetic coding and find tag
for the given probabilities.a1=0.2, a2= 0.2,a3=0.4, a4=0.2
To encode the word "a1, a2, a3, a4" using arithmetic coding, we can follow these

steps:

1. Determine the range of the alphabet: First, we need to determine the range of
the alphabet. Since the alphabet consists of four symbols {a1, a2, a3, a4} with
probabilities {0.2, 0.2, 0.4, 0.2}, the range of the alphabet can be represented
as follows:

a1: [0, 0.2)

a2: [0.2, 0.4)
a3: [0.4, 0.8)

a4: [0.8, 1.0)

2. Initialize the range: Next, we need to initialize the range to the full range of the
alphabet, which is [0, 1.0).
3. Encode the first symbol: To encode the first symbol "a1", we need to narrow
the range to the range of symbol "a1", which is [0, 0.2). The encoded value is
the midpoint of this range, which is 0.1.
4. Encode the second symbol: To encode the second symbol "a2", we need to
narrow the range to the range of symbol "a2", which is [0.2, 0.4). The encoded
value is the midpoint of this range, which is 0.3.
5. Encode the third symbol: To encode the third symbol "a3", we need to narrow
the range to the range of symbol "a3", which is [0.4, 0.8). The encoded value is
the midpoint of this range, which is 0.6.
6. Encode the fourth symbol: To encode the fourth symbol "a4", we need to
narrow the range to the range of symbol "a4", which is [0.8, 1.0). The encoded
value is the midpoint of this range, which is 0.9.
7. Output the encoded value: Finally, the encoded value is the midpoint of the
final range, which is 0.9. This is the arithmetic code for the word "a1, a2, a3,
a4".

Overall, the arithmetic code for the word "a1, a2, a3, a4" is 0.9. This code represents

the probability of the word occurring in the source

6)Perform Huffman algorithm for the following intensity
distribution, for a 64 x 64 image. Obtain the coding efficiency and
compare with that of uniform length code. R0 = 1008, r1 = 320 , r2 =
456 , r3 = 686 ,r4 = 803 .r5 = 105 ,r6 =417 ,r7 = 301

To perform the Huffman algorithm for the given intensity distribution of a 64 x 64 image,

we can follow these steps:

1. Calculate the probability of each intensity level: First, we need to calculate the
probability of each intensity level by dividing the frequency of each level by the
total number of pixels in the image. The total number of pixels in a 64 x 64 image
is 64 * 64 = 4096. Therefore, the probabilities of each intensity level are as
follows:

Intensity Frequency Probability

r0 1008 1008 / 4096 = 0.247
r1 320 320 / 4096 = 0.078
r2 456 456 / 4096 = 0.111
r3 686 686 / 4096 = 0.168
r4 803 803 / 4096 = 0.197
r5 105 105 / 4096 = 0.026
r6 417 417 / 4096 = 0.102

r7 301 301 / 4096 = 0.074

2. Construct the Huffman tree: Next, we need to construct the Huffman tree by
combining the intensity levels with the lowest probabilities until there is only one
node left. The resulting tree will have a set of branches, with each branch
representing a unique intensity level. The length of each branch will be equal to
the depth of the node in the tree, with the root node at depth 0.
3. Assign codes to each intensity level: Finally, we need to assign a code to each
intensity level by traversing the tree and assigning a 0 to a left branch and a 1 to a
right branch. The code for each intensity level will be the concatenation of the
branches from the root to the node representing the intensity level.

For example, the Huffman code for intensity level r3 would be "11", since it is located on

the right branch of the root node and the right branch of the next node. The Huffman
code for intensity level r5 would be "000", since it is located on the left branch of the root

node and the left branch of the next two nodes.

The coding efficiency of the Huffman code can be calculated by dividing the average

length of the code by the entropy of the source, which is the theoretical minimum length

of the code. The entropy of the source can be calculated as follows:

Entropy = ∑(probability of intensity level) * (log2(1 / probability of intensity level))

For the given intensity distribution, the coding efficiency of the Huffman code can be

compared with the coding efficiency of a uniform length code, which assigns the same

number of bits to each intensity level. The coding efficiency of the uniform length code

can be calculated by dividing the number of bits per intensity level by the entropy of the

source.

Overall, the Huffman algorithm is a technique for constructing a prefix code for a set of

symbols with probabilities, with the goal of minimizing the average length of the code.

By constructing a code with shorter average length, the Huffman code can achieve a

higher coding efficiency than a uniform length code, especially if the probabilities of the

symbols are widely distributed.

7)Explain in detail about histogram processing.

Histogram processing is a technique that involves manipulating the distribution of pixel

values in an image to achieve a desired effect. It is often used to adjust the contrast and

brightness of an image, as well as to enhance the detail and clarity of the image.

There are several common techniques used in histogram processing, including:

1. Histogram equalization: This technique redistributes the pixel values in an image

to a uniform distribution, resulting in an increase in contrast and a reduction in
 the overall intensity range of the image. This can be useful for enhancing the
detail in images that are poorly lit or have a low contrast.
2. Histogram stretching: This technique expands the intensity range of an image by
stretching the histogram to fill the full range of available pixel values. This can be
useful for increasing the contrast of an image and making the details more
visible.
3. Histogram matching: This technique adjusts the pixel values of an image to
match the pixel values of a reference image. This can be useful for normalizing
the intensity values of different images to a common scale.
4. Histogram smoothing: This technique reduces the noise and variations in the
pixel values of an image by smoothing the histogram. This can be useful for
reducing the visual artifacts in an image and improving the overall appearance.

Overall, histogram processing is an important technique in image processing and can be

used to improve the visual quality and clarity of an image.

8)Obtain Huffman coding for the source symbols S={S0 ,S1, S2, S3,S4}
and the corresponding probabilities P= {0.4 ,0.2,0.2,0.1,0.1}

To obtain the Huffman coding for the source symbols S={S0, S1, S2, S3, S4} and the

corresponding probabilities P={0.4, 0.2, 0.2, 0.1, 0.1}, we can follow these steps:

1. Construct the Huffman tree: First, we need to construct the Huffman tree by
combining the symbols with the lowest probabilities until there is only one node
left. The resulting tree will have a set of branches, with each branch representing
a unique symbol. The length of each branch will be equal to the depth of the node
in the tree, with the root node at depth 0.
2. Assign codes to each symbol: Next, we need to assign a code to each symbol by
traversing the tree and assigning a 0 to a left branch and a 1 to a right branch.
The code for each symbol will be the concatenation of the branches from the root
to the node representing the symbol.

For example, the Huffman code for symbol S3 would be "11", since it is located on the

right branch of the root node and the right branch of the next node. The Huffman code

for symbol S4 would be "000", since it is located on the left branch of the root node and

the left branch of the next two nodes.

The resulting Huffman codes for the symbols S={S0, S1, S2, S3, S4} with probabilities

P={0.4, 0.2, 0.2, 0.1, 0.1} would be:

Symbol Probability Huffman code

S0 0.4 0
S1 0.2 10
S2 0.2 11
S3 0.1 110

S4 0.1 111

Overall, the Huffman coding is a technique for constructing a prefix code for a set of

symbols with probabilities, with the goal of minimizing the average length of the code.

By constructing a code with shorter average length, the Huffman code can achieve a

higher coding efficiency than a uniform length code, especially if the probabilities of the

symbols are widely distributed.

9)Explain the steps in histogram equalization.

Histogram equalization is a technique used to redistribute the pixel values in an image to

a uniform distribution, resulting in an increase in contrast and a reduction in the overall

intensity range of the image. It is often used to enhance the detail in images that are

poorly lit or have a low contrast.

The steps involved in histogram equalization are:

1. Calculate the histogram: First, we need to calculate the histogram of the image,
which is a plot of the number of pixels at each intensity level. The histogram can
be used to visualize the distribution of pixel values in the image.
2. Normalize the histogram: Next, we need to normalize the histogram by dividing
the number of pixels at each intensity level by the total number of pixels in the
image. This step converts the histogram into a probability distribution, with the
probability of each intensity level representing the fraction of pixels at that
intensity level.
3. Accumulate the normalized histogram: Next, we need to accumulate the
normalized histogram by adding up the probabilities of each intensity level. This
 step converts the probability distribution into a cumulative distribution function
(CDF), with the CDF representing the accumulated probability of each intensity
level.
4. Map the CDF to the full intensity range: Finally, we need to map the CDF to the full
intensity range of the image by scaling the CDF to the desired intensity range.
This step redistributes the pixel values to a uniform distribution, resulting in an
increase in contrast and a reduction in the overall intensity range of the image.

Overall, histogram equalization is a simple but effective technique for enhancing the

contrast and detail of an image. It is often used as a preprocessing step in image

analysis and computer vision applications.

10)Why JPEG is better than a Raw free? Summarize the merits and
de-merits.

JPEG (Joint Photographic Experts Group) is a widely used image compression

standard that is designed to compress digital images with a high degree of

efficiency. It is often used for storing and transmitting images on the internet, as well

as for storing images on digital cameras, smartphones, and other devices.

There are several reasons why JPEG is often considered to be better than a Raw

image format:

1. Compression efficiency: JPEG uses a lossy compression algorithm that

removes certain details from the image in order to reduce the file size. While
this can result in some loss of quality, the resulting images are typically
smaller than Raw images, making them faster to transmit and easier to store.
2. Compatibility: JPEG is a widely supported image format that can be opened
and edited by a wide range of software applications, including image editing
software, web browsers, and more. This makes it easier to share and view
JPEG images compared to Raw images, which may require specialized
software to open and edit.
3. Ease of use: JPEG images are typically easier to work with than Raw images,
as they do not require as much post-processing and editing. This can be
 especially useful for users who are new to photography or who do not have
advanced editing skills.

However, there are also some drawbacks to using JPEG compared to Raw:

1. Quality: JPEG images are lossy, which means that they suffer from some loss
of quality compared to Raw images. This can be especially noticeable in
images with a lot of detail or high contrast, as these details may be lost or
distorted during the compression process.
2. Dynamic range: JPEG images typically have a lower dynamic range compared
to Raw images, which means that they may not be able to capture as much
detail in the highlights and shadows. This can be a problem in high-contrast
scenes or when shooting in difficult lighting conditions.

Overall, JPEG is a popular and efficient image format that is well-suited for a wide

range of applications. However, it is not always the best choice for all situations, and

users may prefer to use Raw images in some cases in order to achieve the highest

possible image quality.