Higher-Order Riesz Transforms And Steerable Wavelet Frames

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, inner-product preservation, and steerability. The pleasing consequence is that the transform maps any primary wavelet frame (or basis) of L-2(R-d) 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-hat-like polyharmonic spline wavelet transform as our primary frame.

Published in:
2009 16Th Ieee International Conference On Image Processing, Vols 1-6, 3757-3760
Presented at:
16th IEEE International Conference on Image Processing, Cairo, EGYPT, Nov 07-10, 2009
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa

 Record created 2010-11-30, last modified 2018-03-18

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