Adaptive non-separable wavelet transform via lifting and its application to Content-Based Image Retrieval
Résumé
We present in this article a novel way to adapt a multidimensional wavelet filter bank, based on the non-separable lifting scheme framework, to any specific problem. It allows the design of filter banks with a desired number of degrees of freedom, while controlling the number of vanishing moments of the primal wavelet (~N moments) and of the dual wavelet (N moments). The prediction and update filters, in the lifting scheme based filter banks, are defined as Neville filters of order ~N and N, respectively. But, in order to introduce some degrees of freedom in the design, these filters are not defined as the simplest Neville filters. The proposed method is convenient: the same algorithm is used whatever the dimensionality of the signal, and whatever the lattice used. The method is applied to Content-Based Image Retrieval (CBIR): an image signature is derived from this new adaptive non-separable wavelet transform. The method is evaluated on four image databases and compared to a similar CBIR system, based on an adaptive separable wavelet transform. The mean precision at five of the non-separable wavelet based system is notably higher on three out of the four databases, and comparable on the other one. The proposed method also compares favorably with the dual-tree complex wavelet transform, an overcomplete non-separable wavelet transform.
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