@conference {14208,
	title = {Combining powerful local and global statistics for texture description},
	booktitle = {IEEE Conference on Computer Vision and Pattern Recognition, 2009. CVPR 2009},
	year = {2009},
	month = {2009/06/20/25},
	pages = {573 - 580},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {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.},
	keywords = {Computer science, discretized measurements, fractal geometry, Fractals, geometric transformations, global statistics, Histograms, illumination transformations, image classification, image resolution, Image texture, lighting, local measurements SIFT features, local statistics, MATHEMATICS, multifractal spectrum, multiscale representation, Power engineering and energy, Power engineering computing, Robustness, Solids, Statistics, texture description, UMD high-resolution dataset, wavelet frame system, Wavelet transforms},
	isbn = {978-1-4244-3992-8},
	doi = {10.1109/CVPR.2009.5206741},
	author = {Yong Xu and Si-Bin Huang and Hui Ji and Ferm{\"u}ller, Cornelia}
}
@conference {14187,
	title = {A Projective Invariant for Textures},
	booktitle = {2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition},
	volume = {2},
	year = {2006},
	month = {2006///},
	pages = {1932 - 1939},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {Image texture analysis has received a lot of attention in the past years. Researchers have developed many texture signatures based on texture measurements, for the purpose of uniquely characterizing the texture. Existing texture signatures, in general, are not invariant to 3D transforms such as view-point changes and non-rigid deformations of the texture surface, which is a serious limitation for many applications. In this paper, we introduce a new texture signature, called the multifractal spectrum (MFS). It provides an efficient framework combining global spatial invariance and local robust measurements. The MFS is invariant under the bi-Lipschitz map, which includes view-point changes and non-rigid deformations of the texture surface, as well as local affine illumination changes. Experiments demonstrate that the MFS captures the essential structure of textures with quite low dimension.},
	keywords = {Computer science, Computer vision, Educational institutions, Fractals, Geometry, Image texture, Level set, lighting, Robustness, Surface texture},
	isbn = {0-7695-2597-0},
	doi = {10.1109/CVPR.2006.38},
	author = {Yong Xu and Hui Ji and Ferm{\"u}ller, Cornelia}
}
