Need for image data management

For efficient storage and retrieval of images in large databases.

While it is perfectly feasible to identify a desired image from a small collection simply by browsing, more effective techniques are needed with collections containing thousands of items which need some form of access by image content.

What is CBIR? Process of retrieving desired images from a

large collection on the basis of features (such as colour, texture and shape) that can be automatically extracted from the images themselves.

Also known as query by image content (QBIC) and content-based visual information retrieval (CBVIR)

Contd…..“Content-based” means that the search will analyze the actual contents of the image. Indexing is often used as identifying features within an image.Indexing data structures: structures to speed up the retrieval of features within image collections.

Practical applications of CBIR Crime prevention The military Architectural and engineering design Fashion and interior design Journalism and advertising Medical diagnosis Geographical information and remote sensing systems Cultural heritage Education and training Home entertainment Web searching.

Content comparisons

Color : The size of the feature vector depends on the size of the image.

Texture: Texture based features do not describe much about variance and rotation.

So we have considered shape features

Feature extraction using Exact Legendre moment computation image moments :particular weighted

averages of the image pixels' intensities

or functions of those moments chosen to have some attractive property or interpretation.

Main advantage :ability to provide invariant measures of shape.

Image moments are basically classified into a) non-orthogonal moments andb) orthogonal moments.

Orthogonal moments: representation of image with minimum amount of information redundancy

CLASSIFICATION OF IMAGE MOMENTS

Legendre moments

Belong to the class of orthogonal moments

used to attain a near zero value of redundancy measure in a set of moment functions

correspond to independent characteristics of the image.

The definition of Legendre moments has a form of projection of the image intensity function onto the Legendre polynomials.

Legendre moments of order (p + q) for an image with intensity function f (x, y) are defined as

Contd….

Contd…….

where P(x) is the pth-order Legendre polynomial defined as

where x [−1, 1], and the Legendre polynomial Pp(x) obeys the following recursive relation:

with P0(x) = 1, P1(x) = x and p>1.

A digital image of size M ×N is an array of pixels. Centers of these pixels are the points (xi,yj ), where the image intensity function is defined only for this discrete set of points fixed at constant values

Δxi = 2/M, and Δyj = 2/N in x and y directions repectively.

Exact Legendre moments

The integrals in Legendre moments are evaluated exactly using summations to reduce the approximation error.

The computation time and computational complexity are reduced by applying fast algorithm.

Contd….

The set of Legendre moments can be computed exactly by

Where,

Contd…

Exact Legendre moments are computed using fast algorithm as follows:

Where,

Yiq is the qth order moment of row i.

Classification of data classes using support vector machine (SVM)

SVMs are a set of related supervised learning methods used for classification .

Viewing input data as two sets of vectors in an n-dimensional space, an SVM will construct a separating hyperplane in that space, one which maximizes the margin between the two data sets.

Contd…..Margin: two parallel hyperplanes are constructed, one on each side of the separating hyperplane, which are "pushed up against" the two data sets.

Larger the margin, better the generalization error of the classifier.

Objectives

The objectives of SVM are: To define a optimal hyper plane with

maximum margin. To map data into high dimensional space to

make it easier for linear classification.

A p − 1-dimensional hyper plane separating p-dimensional data points. The points of one class are divided from the other class using this hyper plane

Linear classifiers

Which Separating Hyperplane to Use?

22

Maximizing the Margin Var1

Var2

Margin Width

Margin Width

23

Support Vectors

Margin Width

Support Vectors

24`

Setting Up the Optimization Problem

kbxw

kbxw

0 bxw kk

w

The width of the margin is:

2 kw

Now we have to maximize the margin. K=1=>

2max

. . ( ) 1, of class 1( ) 1, of class 2

w

s t w x b xw x b x

quadratic programming (QP) optimization problem.

We have to minimize the value of Subjected to certain constraints

This is the primal form

It is expressed in dual form to make it easier to optimize

Here we obtain non zero Lagrange multipliers. These are called support vectors.

Calculating HyperplaneUsing support vectors the value of W is calculated

Finally the value of b is obtained by the equation

b= w.x-1

Algorithm

1. Read all the images from the database. 2. The Exact Legendre moments of each

image is calculated. 3.Each class is trained with every other class

independently using SVM. 4. The first class of images is trained with all

the other 19 classes using SVM and 19 different hyper planes are constructed.

5. The first step in training process involves labeling of the training images. The class that is considered positive for training is labeled Y= +1 and all other images are labeled Y=-1.

6. A optimized hyper plane is constructed that divides the positive images from other classes using SVM.

7. The Hessian matrix is calculated for the set of training vectors.

H=∑Xi.Xj.ci.cj. where X is the set of feature vectors.

8. the dual optimization form of the equation is calculated

9. Using ‘quadprog’ function in Matlab the optimization of equation is done.

10.there is one weight for every training point where the points with O< a, < C are called support vectors. Using these support vectors the value of W is calculated.

11. The value of bias is obtained from the equation,

b= w.x-1, where x is a training image

……….so on

Each class is trained with every other class and a hyper plane is constructed.

12.The feature vectors of a query image are taken and are substituted in all the planes.

13. The values of the planes are observed. The image is classified into that class which has the maximum number of planes satisfied.

1

2

34

5

Classification of Images

Experimental work and results We have taken coil database consisting of 20

different classes of images each class consisting of 72 images.

The different classes of images that were taken in the database are as shown below:

Contd…

The results show that there has been a linear growth in the classification percentage with the number of training images increased.

The feature vectors of the images are increased by taking higher orders of Legendre moments.

The retrieval rate is found to be 96.592% with 18 images taken for training and legendre moments upto the order of 5.

Number of training images

Classification percentage %

(retrieval efficiency)

Computational time (sec)

6 81.458 11.6

9 92.083 19.9

12 92.917 29.1

14 96.25 35.4

16 94.653 44.0

18 96.592 49.5

24 98.542 82.2

FEATURES TAKEN UPTO ORDER FIVE

Order of Legendre moments (feature vectors)

Classifying percentage(%)

3(10) 80.486

4(15) 91.806

5(21) 92.917

6(28) 93.333

7(36) 94.514

8(45) 94.544

9(55) 94.167

Enter the query Image:

Future scope

Exact Legendre moments of higher order can be considered.

Focus on CBIR systems that can make use of relevance feedback, where the user progressively refines the search results by marking images in the results as "relevant", "not relevant", or "neutral" to the search query, then repeating the search with the new information may be done in future.

Non-linear classification of database can be implemented using Kernel functions.