The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
The steerable pyramid: a flexible architecture for multi-scale derivative computation
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 3)-Volume 3 - Volume 3
Isotropic polyharmonic B-splines: scaling functions and wavelets
IEEE Transactions on Image Processing
The Pairing of a Wavelet Basis With a Mildly Redundant Analysis via Subband Regression
IEEE Transactions on Image Processing
Complex Wavelet Bases, Steerability, and the Marr-Like Pyramid
IEEE Transactions on Image Processing
Analytical footprints: compact representation of elementary singularities in wavelet bases
IEEE Transactions on Signal Processing
Directional Multiscale Amplitude and Phase Decomposition by the Monogenic Curvelet Transform
SIAM Journal on Imaging Sciences
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We introduce an Nth-order extension of the Riesz transform in d dimensions. We prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, innerproduct preservation, and steerability. The pleasing consequence is that the transform maps any primary wavelet frame (or basis) of L2(Rd) into another "steerable" wavelet frame, while preserving the frame bounds. The concept provides a rigorous functional counterpart to Simoncelli's steerable pyramid whose construction was entirely based on digital filter design. The proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions; it also yields a perfect reconstruction filter-bank algorithm. We illustrate the method using a Mexican-hatlike polyharmonic spline wavelet transform as our primary frame.