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A new class of features for wavelet-based texture classification is introduced using a new feature-weighting scheme adapted to non-Euclidean similarity measures. The feature extraction is based on the histogram of the local second moment estimates of the wavelet transform. It is shown that the bins' centers of such histograms should be scaled logarithmically rather than linearly. The distance between two texture features is measured using the x2 similarity measure, weighted according to the feature's degree of dispersion within the training dataset. Classification experiments of the proposed approach using an orthonormal wavelet transform show improved classification results compared to presently available methods.