Steerlets: a novel approach to rigid-motion covariant multiscale transforms

Robert Azencott; Bernhard G. Bodmann; Manos Papadakis

doi:10.1117/12.825704

4 September 2009 Steerlets: a novel approach to rigid-motion covariant multiscale transforms

Robert Azencott, Bernhard G. Bodmann, Manos Papadakis

Proceedings Volume 7446, Wavelets XIII; 74460A (2009) https://doi.org/10.1117/12.825704
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

We present steerlets, a new class of wavelets which allow us to define wavelet transforms that are covariant with respect to rigid motions in d dimensions. The construction of steerlets is derived from an Isotropic Multiresolution Analysis, a variant of a Multiresolution Analysis whose core subspace is closed under translations by integers and under all rotations. Steerlets admit a wide variety of design characteristics ranging from isotropy, that is the full insensitivity to orientations, to directional and orientational selectivity for local oscillations and singularities. The associated 2D or 3D-steerlet transforms are fast MRA-type of transforms suitable for processing of discrete data. The subband decompositions obtained with 2D or 3D-steerlets behave covariantly under the action of the respective rotation group on an image, so that each rotated steerlet is the linear combination of other steerlets in the same subband.

Citation Download Citation

Robert Azencott, Bernhard G. Bodmann, and Manos Papadakis "Steerlets: a novel approach to rigid-motion covariant multiscale transforms", Proc. SPIE 7446, Wavelets XIII, 74460A (4 September 2009); https://doi.org/10.1117/12.825704

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