Indexing image databases using wavelet and discrete fourier transform

Abstract

Image database processing depends on the efficiency with which the images are stored and retrieved. We present a new hybrid technique, which uses the compression power of Wavelet Transform and the rotation, scaling, translation & reflection (RSTN) invariance of Fourier Transform Spectrum. This hybrid technique is faster and more robust than the separate use of Discrete Fourier Transform and holistic Wavelet Transform for designing image indexes. The experimental results on the accuracy and computation time performance of the hybrid indexing algorithm are presented. Introduction Image database processing depends on the efficiency with which the images are stored and retrieved in response to the image query. The image databases are very large as compared to textual databases. There are several transforms such as Discrete Cosine Transform, Discrete Fourier Transform, Wavelet Transform etc. After a transform is applied to an image, a few of the significant transform coefficients are used to represent the original image. These elements are represented as a vector which is called the feature vector which serves as the index or signature of the image during search and retrieval. In the context of our discussion of raster image databases, the index of an image is a vector. The index is useful for image database query resolution. Since the size of index is small as compared to size of the image, it is quicker to process indexes. An image index saves space because it needs much less space than the image itself. Due to complexity of image content, image size, and the number of images used in various applications, it is an open area of research for devising efficient archival and retrieval Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies axe not made or distributed for profit or commercial advantage a n d that copies bear this notice and the full citation on the firs~ page. To copy othenvise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. SAC 2001, I_as Vegas, NV © 2001 ACM 1-58113-287-5/01/02...$5.00 of images. We develop an indexing algorithm such that similarity of images is determined from similarity of image indexes. The term 'index' and 'signature' are synonymously used in this paper. The size of the index is the number of elements in the feature vector. The proposed new Hybrid technique uses the compression power of Wavelet Transform and the rotation, scaling, translation & reflection (RSTN) invariance of Discrete Fourier Transform Spectrum. The hybrid technique is uniform with respect to the RSTN-transformations. The paper is organized as follows: (1) The relation between image indexing and Wavelet Transform is discussed. The Wavelet Transform is briefly described in both ID and 2D. (2) Three similarity metrics are described tbr resolving image queries using indexes. (3) For the raw RSTN-transtbrmed images and their Wavelet transforms, the relative deviations between the corresponding images are given. (4) Discrete Fourier Transform in both 1D and 2D is described along with projection method for the DFr Power Spectrums. The performance of Wavelet Transform and DFT are compared. (5) Finally the Hybrid approach to indexing and its comparison with the previous two approaches is given. (6) Experimental results on computation time and accuracy of the indexing algorithms using cross validation testing technique are given. This paper ends with conclusions and bibliography. Wavelet Transform And Image Indexing Wavelets are a useful tool ibr compressing images but the shortcoming is that Wavelet transform is not invariant with respect to affine transformations such as Rotation, Scaling, Translation and Reflection (RSTN). For example, when a 2"x2" image is Wavelet decomposed to d levels, the approximate part n<l n d (size m = 2 x 2 " ) is used to represent the original image with an image. If the size of approximate part is within the size of the image index, then the Bvo dimensional approximate part is converted into one dimensional vector which is used as the index or the signature of the original image. There are several Wavelets, Haar Wavelet is the simplest and oldest of the Wavelets [Haar 1910]. For an introduction to Wavelets, the reader may refer to A Wavelet tour [Mallet 1998] and Wavelet Primer [Burrus et al. 1998]. Briefly, all Wavelet transforms require a scaling and a wavelet function. For Haar wavelet transform, these functions are described below. If Zt0,1)(x) is the characteristic function of [0,1) then the scaling function is given by ~)(x) = Z[0,1) and wavelet function is given by V(x) = Z[o,I/2) " ZB/2,1). [see Figure I]

DOI: 10.1145/372202.372395

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@inproceedings{Sabharwal2001IndexingID, title={Indexing image databases using wavelet and discrete fourier transform}, author={Chaman L. Sabharwal and S. R. Subramanya}, booktitle={SAC}, year={2001} }