A translation- and scale-invariant adaptive wavelet transform

This paper presents a new approach to deal with the translation- and scale-invariant problem of discrete wavelet transform (DWT). Using a signal-dependent filter, whose impulse response is calculated by the first two moments of the original signal and a scale function of an orthonomal wavelet, we adaptively renormalized a signal. The renomalized signal is then decomposed by using the algorithm of the conventional DWT. The final wavelet transform coefficients, called adaptive wavelet invariant moments (AWIM), are proved to be both translation- and scale-invariant. Furthermore, as an application, we define a new textural feature in the framework of our adaptive wavelet decomposition, show its stability to shift and scaling, and demonstrate its efficiency for the task of scale-invariant texture identification.