a19 Image Compression Using Pca Technique

qwertyuiopasdfghjklzxcvbnmqwerty

uiopasdfghjklzxcvbnmqwertyuiopasd

fghjklzxcvbnmqwertyuiopasdfghjklzx

cvbnmqwertyuiopasdfghjklzxcvbnmq

wertyuiopasdfghjklzxcvbnmqwertyui

opasdfghjklzxcvbnmqwertyuiopasdfg

hjklzxcvbnmqwertyuiopasdfghjklzxc

vbnmqwertyuiopasdfghjklzxcvbnmq



hjklzxcvbnmqwertyuiopasdfghjklzxc

vbnmqwertyuiopasdfghjklzxcvbnmq



hjklzxcvbnmrtyuiopasdfghjklzxcvbn

mqwertyuiopasdfghjklzxcvbnmqwert

yuiopasdfghjklzxcvbnmqwertyuiopas

dfghjklzxcvbnmqwertyuiopasdfghjklz

IMAGE COMPRESSION USING PCA

TECHNIQUE

www.BEProjectReport.com

VISIT US, CHOOSE THE PROJECT YOU LIKE AND CLICK THE DOWNLOAD BUTTON

IMAGE COMPRESSION USING PCA TECHNIQUE


CHAPTER 1

INTRODUCTION

This tutorial is designed to give the reader an understanding of Principal Components

Analysis (PCA). PCA is a useful statistical technique that has found application in fields such as face

recognition and image compression, and is a common technique for finding patterns in data of high

dimension Before getting to a description of PCA, this tutorial first introduces mathematical concepts

that will be used in PCA. It covers standard deviation, covariance, eigen vectors this tutorial is

designed to give the reader an understanding of Principal Components and eigen values. This

background knowledge is meant to make the PCA section very straightforward, but can be skipped if

the concepts are already familiar. There are examples all the way through this tutorial that are meant

to illustrate the concepts being discussed. If further information is required,

Image compression plays an important role in communication and medical applications. The

main aim of image compression is to remove the redundancy from image data in such a way that it

allows the same image reconstruction at the receiver end. There are mainly two types of image

compression techniques, lossy and lossless. In medical applications like X-ray and EGS images, the

images are compressed by lossless compression methods because each bit of information is

important. On other hand, digital or video images are compressed by lossy compression techniques.

For such type of compression, transform coding techniques like cosine transform, wavelet transform

are very effective techniques, which give better results but it process the data in serial manner and

hence requires more time for processing .The artificial neural network is a recent tool in image

compression as it processes the data in parallel and hence requires less time and therefore, it is

superior over any other technique. Thus, the bottleneck type artificial neural network generally used

to solve an image compression problem discussed in .It is important to transform an image data

efficiently, which is to be compressed by neural network. The data can be transformed by techniques

like Principal Component Analysis (PCA), which is based on factorization techniques developed in

linear algebra. Authors proposed the Bipolar Coding and Levenberg-Marquardt (LM) algorithm

with back propagation neural network for image compression.

An image is essentially a 2-D signal processed by the human visual system. The signals

representing images are usually in analog form. However, for processing, storage and

Transmission by computer applications, they are converted from analog to digital form.

A digital image is basically a 2- Dimensional array of pixels. Images from the significant part of

data, particularly in remote sensing, biomedical and video conferencing applications. The use of and

dependence on information and computers continue to grow, so too does our need for efficient ways

of storing and transmitting large amounts of data.

Images are very important documents nowadays; to work with them in some applications

they need to be compressed, more or less depending on the purpose of the application. There are

some algorithms that perform this compression in different ways; some are lossless and keep the



same information as the original image, some others loss information when compressing the image.

Some of these compression methods are designed for specific kinds of images, so they will not be so

good for other kinds of images.

IMAGE COMPRESSION

Image compression addresses the problem of reducing the amount of data required to

represent a digital image. It is a process intended to yield a compact representation of an image,

thereby reducing the image storage/transmission requirements.

Compression is achieved by the removal of one or more of the three basic data redundancies:

1. Coding Redundancy

2. Interpixel Redundancy

3. Psycho visual Redundancy

Coding redundancy is present when less than optimal code words are used. Interpixel

redundancy results from correlations between the pixels of an image. Psycho visual redundancy is

due to data that is ignored by the human visual system (i.e. visually non essential information).

Image compression techniques reduce the number of bits required to represent an image by taking

advantage of these redundancies. An inverse process called decompression (decoding) is applied to

the compressed data to get the reconstructed image. The objective of compression is to reduce the

number of bits as much as possible, while keeping the resolution and the visual quality of the

reconstructed image as close to the original image as possible.

Image compression systems are composed of two distinct structural blocks :

an encoder and a decoder.



Image f(x, y) is fed into the encoder, which creates a set of symbols form the input data and uses

them to represent the image. If we let n1 and n2 denote the number of information carrying units

(Usually bits) in the original and encoded images respectively, the compression that is achieved can

be quantified numerically via the compression ratio,

CR = n1 /n2

As shown in the figure, the encoder is responsible for reducing the coding, Interpixel and psycho

visual redundancies of input image. In first stage, the mapper transforms the input image into a

format designed to reduce Interpixel redundancies. The second stage, qunatizer block reduces the

accuracy of mapper’s output in accordance with a predefined criterion. In third and final stage, a

symbol decoder creates a code for quantizer output and maps the output in accordance with the code.

These blocks perform, in reverse order, the inverse operations of the encoder’s symbol coder and

mapper block. As quantization is irreversible, an inverse quantization is not included.

IMAGE COMPRESSION TECHNIQUES

The image compression techniques are broadly classified into three categories depending

whether or not an exact replica of the original image could be reconstructed using the compressed

image. These are:

1. Lossless technique

2. Lossy technique

3. PCA

Lossless compression technique

In lossless compression techniques, the original image can be perfectly recovered from the

compressed (encoded) image. These are also called noiseless since they do not add noise to

the signal (image).It is also known as entropy coding since it use statistics/decomposition techniques

to eliminate/minimize redundancy. Lossless compression is used only for a few

applications with stringent requirements such as medical imaging. Following techniques are included

in lossless compression:

a. Run length encoding

b. Huffman encoding

c. LZW coding

d. Area coding

Lossy compression technique

Lossy schemes provide much higher compression ratios than lossless schemes.

Lossy schemes are widely used since the quality of the reconstructed images is adequate for most

applications .By this scheme, the decompressed image is not identical to the original image, but

reasonably close to it



As shown above the outline of lossy compression techniques .In this

Prediction – transformation – decomposition process is completely reversible.The quantization

process results in loss of information. The entropy coding after the quantization step, however, is

lossless. The decoding is a reverse process. Firstly, entropy decoding is applied to compressed data

to get the quantized data. Secondly, dequantization is applied to it &finally the inverse

transformation to get the reconstructed image. Major performance considerations of a lossy

compression scheme include:

1. Compression ratio

2. Signal - to – noise ratio

3. Speed of encoding & decoding.

Lossy compression techniques includes following schemes:

a. Transformation coding

b. Vector quantization

c. Fractal coding

d. Block Truncation Coding

e. Sub band coding



CHAPTER 2

PCA (PRINCIPAL COMPONENTA NALYSIS)

If we have 20 images each with N2 vectors and 20 dimensions. Now, PCA can be

implemented on this set of data. 20 Eigen vectors will be obtained because each vector is 20 –

dimensional. To compress the data, choose the data using only 15 Eigen vectors. This gives a final

data set with only 15 dimensions, which has saved ¼ of the space. However, when the original data

is reproduced, the images have lost some of the information. This compression is said to be lossy

because the decompressed image is not exactly the same as the original.

In statistics, PCA is a technique for simplifying a dataset by reducing multidimensional

datasets to lower dimensions for analysis. PCA is a standard technique commonly used for data

reduction in statistical pattern recognition and signal processing. PCA has been called one of the

most valuable results from applied linear algebra. It is used abundantly in all forms of analysis from

neuroscience to computer graphics, because it is a simple non- parametric method of extracting

relevant information from confusing datasets. PCA is also called the KARHUNEN-LOEVE

Transform (KLT, named after Kari Karhunen & Michel Loeve) or the HOTELLING Transform. Its

general objectives are:

1. Data reduction

2. Interpretation

There are basically two approaches for performing PCA.

They are classical statistical method and artificial neural network method.

Principal Component Analysis Technique

Figure neural network

The images obtained from the satellite are noisy and require large memory space. To compress

such type of images, PCA based neural network model is used. However, adaptive neural network



with PCA can also be used but it compresses the image in very less percentage .Principal Component

Analysis technique is called as Karhunen Loeve transform, Hotelling transform or proper orthogonal

transformation. It is a factorization technique which is generally used in mathematical applications.

PCA technique collects the data and transforms it to the new data which results in same statistical

properties. The data transformation is performed in such a way that its originality remains at the end

of transformation.

The image data can be represented by a set of m vectors: A= (a1,a2,a3......ai......aM)

Where, ai represent n features. The vector is depending on image application.

For example, in image compression each vector represents a major component of each vector

features like color and size. The features of an image can be combined by considering the feature of

each vector.

Thus, data set A represents the features column vector k as:

………………………………………(1)

This approach requires for the computation of the input data convergence matrix A and extraction

of the eigen values and eigen vectors. The feature column vectors can be grouped in a matrix form

for easy processing. That is, C

…………………..(2)

Where the values of a and k are varying from 1 to n.

For compression of data, the component which has less importance has to be eliminated from the

matrix. Therefore, the less important data is replaced by zero value. The new vectors which give the

better classification properties can be form the feature column vectors, ak. PCA method confirms

that the important data which account maximum variation in the covariance matrix to be considered.

The Linear dependence between two random variables can be defined by the covariance measures.

Therefore, by computing the covariance, the relationship between two data sets can be established.

If, Ai={a1i,a2i,a3i,……..ani } then the covariance is defined by equation:



……………………(3)

It is important to note that the covariance measures a linear relationship between the two values of

sets. PCA method gives the simple solution in many applications like linear modeling, data

compression, image compression, image restoration and pattern recognition etc.

The image data can also be compressed using the concept of data transformation using PCA. The

PCA algorithm for data transformation and data compression is summarized in the following

Step 1: Obtain the feature column vector matrix from the given image data.

Step 2: Obtain the covariance matrix a.

Step 3: Using characteristic equation (λi-Ea) =0 Obtain the Eigen values. These Eigen values forms

the matrix Ey.

Step 4: Also, calculate the eigenvectors matrix by considering the eigen values.

Step 5: Obtain the Transformation

By considering the eigenvectors as their columns. T

w

Step 6: Obtain the features vector matrix by

Step 7: For compression of an image, the dimensionality of the new feature vector is reduce by

setting small Eigen values l to zeros.

The dimensionality of input feature vector is changed by considering the small eigen values as

zeros. The accuracy of the obtained results depends upon the selected threshold value of an eigen

value. If the threshold value of Eigen value is high, then the dimension of feature eigen

vector is reduced more and hence the high compression can be achieved. This method considers

only the data which has the maximum variation. Thus, PCA gives the simple solution to achieve

high data compression; image compression and eigen face recognition. But, at high threshold

eigen value, the loss of image data is very large. To overcome this drawback in PCA, authors

suggested a bottleneck type neural network which is used to change the dimension of feature

eigenvector matrix efficiently as well as reconstruction of an original image data. The architecture

of such bottleneck type feed forward back propagation neural network for compression

application is shown in Figure



PCA Classical Statistical Method

It involves finding eigen values and corresponding eigen vectors of the data set using covariance

matrix. The corresponding eigen values of the matrix gives an indication of amount of information

the respective principal components represent. The methodology for calculating principal component

is given by the following algorithm. Let X1, X2…Xm are the sub images of dimension N. The

corresponding algorithm is described as follows:

1. Computation of the global mean (X) from sub images.

X⎯ = 1 / M Σ Xi

2. Subtraction of the mean from each sub image to generate the mean removed image.

Øi = Xi - X⎯

3. Formation of the matrix using mean removed sub image of ( M X N ) dimension

A = [Ø 1 Ø2 … ……ØM]

4. Computation of the sample covariance matrix (C) of dimension (N X N)

5. Computation of the Eigen values of the covariance matrix.

Computation of Eigen values is performed by jaccobian iteration method.

C : λ1 > λ2 > ……… >λN

6. Computation of the eigen vectors for the eigen values

C: u1, u2…uN

7. Dimensionality reduction step.

Keep only the Eigen vectors corresponding to K largest eigen values. These Eigen values are

called as “principal components”.

The above said steps are needed to generate the principal components of the image.

Corresponding eigen vectors are uncorrelated and have the greater variance. In order to avoid the

components that have an undue influence on the analysis, the components are usually coded with

mean as zero and variance as one. This standardization of the measurement ensures that they all

have equal weight in the analysis.

PCA Neural Network

Artificial neural network are model that attempt to achieve performance via dense inter

connection of simple computational elements. The most important property of a neural network is

the ability to learn from its environment. PCA is a powerful linear block transform coding in which,

an image is subdivided into non-overlapping blocks of N×N pixels which can be considered as N-

Dimensional vectors with N = n × n. A linear Transformation, which can be written as an M ×N –

dimensional matrix W with M ≤ N, is performed on each block with the

M rows of W, wi being the basis vectors of the transformation. An adaptive principal component

extraction (APEX) is used to decorrelate the principal components. The main difference between this

APEX architecture and the existing PCA networks lies in the additional lateral connections at the

outputs of the network.



Artificial Neural Network Architecture

A neural network architecture as shown in Figure 1 is used for solving the image compression

problem. In this type of architecture, input from the large number of input neurons is fed to a less

number of neurons in hidden layer, which is further fed to large number of neurons in Output layer

of the network. Such type of network is referred as bottleneck feed forward neural network

I

One of the most important types of feed forward network is the multilayer back propagation neural

network the neural network architecture for image compression is having 64 input neurons, 16

hidden neurons and 64 output neurons according to the requirements. The input layer encodes the

inputs of neurons and transmits the encoded information to the hidden layer neurons. The output

layer receives the hidden layer information and decodes the information at the output. The outputs

of hidden layer are real valued and require large number of bits to transmit the data. The transmitter

encodes and then transmits the output of the hidden layer 16 values as com- pared to the 64 values of

the original image. The receiver receives and decodes the 16 hidden neurons output and generates the

64 outputs at the output layer. The techniques like Principal Component Analysis (PCA) and

proposed Bipolar Coding with Linear transformations are required to incorporate with neural

network to manage the input and output image data. PCA technique transforms an image data into

small valued data which can be easily handled by neural network.



Other properties:

The best image quality at a given bit-rate (or compression rate) is the main goal of image

compression, however, there are other important properties of image compression schemes:

Scalability generally refers to a quality reduction achieved by manipulation of the bitstreams or file

(without decompression and re-compression). Other names for scalability are progressive coding or

embedded bitstreams. Despite its contrary nature, scalability also may be found in lossless codecs,

usually in form of coarse-to-fine pixel scans. Scalability is especially useful for previewing images

while downloading them (e.g., in a web browser) or for providing variable quality access to e.g.,

databases.

There are several types of scalability:

Quality progressive or layer progressive: The bit stream successively refines the reconstructed

image.

Resolution progressive: First encode a lower image resolution; then encode the difference to higher

resolutions.

Component progressive: First encode grey; then color.

Region of interest coding. Certain parts of the image are encoded with higher quality than others.

This may be combined with scalability (encode these parts first, others later).

Meta information. Compressed data may contain information about the image which may be used

to categorize, search, or browse images. Such information may include color and texture statistics,

small preview images, and author or copyright information.

Processing power. Compression algorithms require different amounts of processing power to

encode and decode. Some high compression algorithms require high processing power.

The quality of a compression method often is measured by the Peak signal-to-noise ratio. It

measures the amount of noise introduced through a lossy compression of the image, however, the

subjective judgment of the viewer also is regarded as an important measure, perhaps, being the most

important measure.



CHAPTER 3

ADVANTAGES AND APPLICATIONS

ADVANTAGES:

• It provides a potential cost savings associated with sending less data over switched telephone

network where cost of call is really usually based upon its duration.

• It not only reduces storage requirements but also overall execution time.

• It also reduces the probability of transmission errors since fewer bits are transferred.

• It also provides a level of security against illicit Monitoring.

APPLICATIONS OF PCA:

• Representation

When using these sort of matrix techniques in computer vision, representation of images should

be considered. A square, N by N image can be expressed as an N2 –

Dimensional vector.

X = ( x1 x2 x3 …………………xn)

Where the rows of pixels in the image are placed one after the other to form a one dimensional

image. E.g. the first N Elements x1 – xn will be the first row of the image, the next N Elements are

the next row, and so on. The values in the vector Are the intensity values of the image, possibly a

single grayscale value



CHAPTER 4

CONCLUSION

This paper presents various types of image compression techniques. There are basically two

types of compression techniques. One is Lossless Compression and other is Lossy Compression

Technique. Comparing the performance of compression technique is difficult unless identical data

sets and performance measures are used. Some of these techniques are obtained good for certain

applications like security technologies. Some techniques perform well for certain classes of data and

poorly for others. PCA (Principal Component Analysis) also found its applications as image

compression. PCA can be implemented in two forms i.e. either statistical approach or neural network

approach. The PCA Neural Network provides new way of generating Codebook based on statistical

feature of PCA transformational coefficients. It leads to less storage of memory and reduction of

calculation.



BIBLIOGRAPHY

1. Subramanian A, “Image Compression Technique,” Potentials IEEE, Vol. 20, Issue 1, pp 19-23,

Feb-March 2001,

2. David Jeff Jackson & Sidney Joel Hannah, “Comparative Analysis of image Compression

Techniques,” System Theory 1993, Proceedings SSST ’93, 25th Southeastern Symposium,pp 513-

517, 7 –9 March 1993.

3. Hong Zhang, Xiaofei Zhang & Shun Cao, “ Analysis & Evaluation of Some Image Compression

Techniques,” High Performance Computing in AsiaPacific Region, 2000 Proceedings, 4th Int.

Conference, vol. 2, pp 799-803,14-17 May, 2000

4. Ming Yang & Nikolaos Bourbakis ,“An Overview of Lossless Digital Image Compression

Techniques,” Circuits & Systems, 2005 48th Midwest Symposium ,vol. 2 IEEE ,pp 1099-1102,7 –

10 Aug, 2005

5. Milos Klima, Karel Fliegel, “Image Compression Techniques in the field of security Technology:

Examples and Discussion,”Security Technology, 2004, 38th Annual 2004 Intn. Carnahan

Conference, pp 278- 284,11-14 Oct., 2004

6. Ismail Avcibas, Nasir Memon, Bulent Sankur, Khalid Sayood, “ A Progressive Lossless / Near

Lossless Image Compression Algorithm,”IEEE Signal Processing Letters, vol. 9, No. 10, pp 312-

314, October 2002.

7. Dr. Charles F. Hall, “A Hybrid Image Compression Technique,” Acoustics Speech & Signal

Processing, IEEE International Conference on ICASSP’ 85, Vol. 10, pp 149- 152, Apr, 1985

8. Wen Shiung Chen, en- HuiYang & Zhen Zhang, “ A New Efficient Image Compression

Technique with Index- Matching Vector Quantization,” Consumer Electronics, IEEE Transactions,

Vol. 43, Issue 2, pp 173- 182, May 1997.

9. David H. Kil and Fances Bongjoo Shin, “Reduced Dimension Image Compression and its

Applications,”Image Processing, 1995, Proceedings, International Conference,Vol. 3 , pp 500-503,

23-26 Oct.,1995

10. C.K. Li and H.Yuen, “A High Performance Image Compression Technique For Multimedia

Applications,” IEEE Transactions on Consumer Electronics, Vol. 42, no. 2, pp 239-243, 2 May 1996.

a19 Image Compression Using Pca Technique

Documents

Transcript of a19 Image Compression Using Pca Technique