Rotation-invariant texture retrieval via signature alignment based on steerable sub-Gaussian modeling.

This paper addresses the construction of a novel efficient rotation-invariant texture retrieval method that is based on the alignment in angle of signatures obtained via a steerable sub-Gaussian model. In our proposed scheme, we first construct a steerable multivariate sub-Gaussian model, where the fractional lower-order moments of a given image are associated with those of its rotated versions. The feature extraction step consists of estimating the so-called covariations between the orientation subbands of the corresponding steerable pyramid at the same or at adjacent decomposition levels and building an appropriate signature that can be rotated directly without the need of rotating the image and recalculating the signature.

Space-frequency quantization for image compression with directionlets.

The standard separable 2-D wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to efficiently capture 1-D discontinuities, like edges or contours. These features, being elongated and characterized by geometrical regularity along different directions, intersect and generate many large magnitude wavelet coefficients.

Rotation-invariant texture retrieval with Gaussianized steerable pyramids.

This paper presents a novel rotation-invariant image retrieval scheme based on a transformation of the texture information via a steerable pyramid. First, we fit the distribution of the subband coefficients using a joint alpha-stable sub-Gaussian model to capture their non-Gaussian behavior. Then, we apply a normalization process in order to Gaussianize the coefficients.

Directionlets: anisotropic multidirectional representation with separable filtering.

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required.