Vector Space Image Model (VSIM) for Content-Based ... - CiteSeerX

Vector Space Image Model (VSIM) for Content-Based Image Retrieval Santosh Kulkarni Bala Srinivasan School of Computer Science and Software Engineering, Monash University, Australia M V. Ramakrishna Department of Computer Science Royal Melbourne Institute of Technology, Australia Abstract

A new method for content-based image retrieval is being presented. This method uses a vector-space model to represent images in a multidimensional space. This model allows the use of multiple attributes in the retrieval process and also identi es the most selective values for each attribute. Therefore by ignoring the less signi cant values the user can reduce the dimensionality of the feature set and simplify the vector model. It also allows the user to choose any similarity measure depending on the application. The user can also assign weights to the dierent attributes depending on the retrieval mechanism intended. These characteristics of the retrieval method increase the retrieval eciency and makes the model very exible as it can be used universally for retrieving images from different domains.

Keywords: Content-Based Image Retrieval, Multimedia Information Database Systems

1 Introduction The digital revolution has resulted in an increase in the number and size of multimedia information systems. For these systems to be useful in practice, it is necessary to provide ecient access to the objects stored in such systems. Images are the most frequently accessed multimedia objects, and hence ecient image retrieval systems to provide access to image data have gained considerable attention from commercial and academic community. One of the major goal in image databases is to provide retrieval based on contents of the images (such as \retrieve images of mountains"). Many proto-type (and commercial) contentbased retrieval systems have been developed in recent years. These systems are based on the use of image attributes such as colour, texture and shape. The features are extracted from the images (usually at the time of populating the database) and indexed using an appropriate indexing structure such as Rtrees. A search vector is formed corresponding to the query image and is used to search the indexed structure for the most similar matching images. The matching images are retrieved and output in the ranked order of similarity. 1

Most systems use multiple attributes such as colour, texture, shape to retrieve images. For indexing and retrieval, each attribute is treated as a separate entity with the query processor having the responsibility of combining the result of the individual (indexing) subsystems using some algebra [12]. The only rationale for this approach is its simplicity and intituively it appears that this task of combining should be done at a lower level/earlier. Our approach is not constrained by this necessity of simplicity. In this paper, we propose a new approach to this problem of nding most similar images from the database of images. It is a vector-based approach, and the model is motivated by the latent semantic indexing model proposed for text retrieval in [5]. The idea behind this approach is as follows. Unlike a traditional database system, the retrieval in image databases is based on similarity of features, and not the actual image itself. The problem therefore is how to identify the dominant features which provide maximum discrimination among the images in the database. We exploit a property of SVD decomposition of matrices to identify the most discriminating features. In [11], interactive relevance feedback technique has been used to determine the weight factors that identi es the most relevant attributes of the features from the point of view of human perception. This being a interactive process has obvious limitations. The approach we are investigating in this paper provides a mathematical framework for this task. The rest of the paper is organised as follows. The next section explains the construction and working of the model including the necessary mathematical formulation. The retrieval process for a given query image is also discussed. In section 3, we describe a prototype system using the proposed approach. Experimental results and comparison with other image retrieval systems are also presented. The last section provides directions for future research and conclusions.

2 Vector Space Representation of Images

Given any m  n matrix X having a rank p, we can decompose into three matrices U , , V , such that,

X = U V 

(1)

Here  is a p  p positive diagonal matrix(the diagonal elements are all positive and the rest of the elements are zero). U and V are isometric matrices of order m  p and n  p respectively. V  indicates the adjoint of the matrix V . This decomposition is known as Singular Value Decomposition (SVD) and nds a wide application. There are standard algorithms to obtain SVD of a given matrix. In particular, if every element of X is a real number then V is also real. This means that the transpose of V , V T is same as the adjoint matrix V  . The rst p columns of the matrices U and V are called the left and right singular vectors respectively. SVD is closely related to the standard eigenvalue-eigenvector or spectral decomposition of a square matrix, Y , into V LV , where V is orthonormal and L is diagonal [5]. In fact the matrices U and V of the SVD decomposed matrix X , represent the eigen vectors for XX and X X respectively. 0

0

2

0

Attributes

Images X

= txd

D’

S0

T0

mxm

mxd

txm

Singular value decomposition of the image matrix X: T0 has orthogonal, unit length columns D0 has orthogonal, unit length columns S0 is the diagonal matrix t is the number of rows of X d is the number of columns of X m is the rank of X (