In this paper, the authors propose a new wavelet-based representation formula. They verify and justify, through computation, that the formula-generating feature vectors are invariant with respect to rotation. It is shown experimentally that the algorithm works well for content-based image retrieval (CBIR) applications.
The proposed rotation invariant retrieval algorithm is suitable for both texture and nontexture images, and avoids missing any relevant images, but may retrieve some other images that are not very relevant. The paper primarily focuses on developing a procedure for rotation independent feature extraction, and also focuses on the application of this procedure to CBIR. The authors observe that radially symmetric wavelet bases can generate future vectors that are invariant with respect to rotation. The construction procedure of the formula ensures some kind of radial symmetry in the representation. The authors make use of multiresolution and radial symmetry features in the representation to capture image signatures in the form of combined feature vectors for rotation invariant CBIR. Signature vectors are sequences of numbers. Therefore, it is natural to employ well-known techniques of similarity search in a sequence database. The main aim is to retrieve all relevant images at the same time, minimizing irrelevant images during pruning.
For the wavelet-based decomposition formula, let &psgr; be the compactly supported, sufficiently smooth, real, and orthonormal wavelet associated with a multiresolution framework. &phgr; is the scaling function and m0 is the low pass filter satisfying the following equations:
After some steps of calculation and definition, the authors get:
where the function &PHgr;j is the autocorrelation function of &phgr;j, and &PHgr;j denotes the autocorrelation function of &psgr;j, with analogous notations. A sufficiently regular function, f, is defined on ℜ, and the Fourier transform is defined by
The authors also present simulation results.
