Combining powerful local and global statistics for texture description

A texture descriptor is proposed, which combines local highly discriminative features with the global statistics of fractal geometry to achieve high descriptive power, but also invariance to geometric and illumination transformations. As local measurements SIFT features are estimated densely at multiple window sizes and discretized. On each of the discretized measurements the fractal dimension is computed to obtain the so-called multifractal spectrum, which is invariant to geometric transformations and illumination changes. Finally to achieve robustness to scale changes, a multi-scale representation of the multifractal spectrum is developed using a framelet system, that is, a redundant tight wavelet frame system. Experiments on classification demonstrate that the descriptor outperforms existing methods on the UIUC as well as the UMD high-resolution dataset.