InsightSoftwareConsortium / ITKIsotropicWavelets

External Module for ITK, implementing Isotropic Wavelets and Riesz Filter for multiscale phase analysis.
Apache License 2.0
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Steerability: Add RieszRotationMatrix #32

Closed phcerdan closed 7 years ago

phcerdan commented 7 years ago

Add S_r, rotation matrix, that steers the generalized riesz function.

Get a steerable matrix for the Riesz transform: Sr from a rotation matrix R in the spatial domain, and the order of the Riesz transform (T) T f( R*x ) = T{S_r} f(x)

S_r is a MxM matrix, where M = p(N,d) is the number of components of a riesz transform of order N and dimension d. M := p(N,d) = \frac{(N+d-1)!}{(d-1)! N!}

The rotation matrix is a dxd matrix.