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.

Date Published: 4 September 2009
PDF: 10 pages
Proc. SPIE 7446, Wavelets XIII, 74460A (4 September 2009); doi: 10.1117/12.825704

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)