References
Soulard, Carré & Fernandez,
Vector extension of monogenic wavelets... IEEE TIP 2013
This first paper proposes to use a
structure tensor based Riesz transform
jointly with a color axis concept.
The color phase is defined as the angle between
the Euclidean norms of vector-valued primary and Riesz parts.
The experimental part shows
partial reconstruction with quantization artifacts
and invariance properties.
Soulard & Carré,
Elliptical Monogenic Wavelets... IEEE TSP 2015
This paper defines the elliptical monogenic model,
a more advanced color extension than the one previously proposed.
The article contains the justification of
the monogenic reconstruction by summation of the filterbank outputs,
as well as an innovative Radon-based filterbank.
The experimental part shows amplitude-based wavelet shrinkage,
showing promising with respect to channelwise processing,
and the "pure-directional reconstruction" method,
able to produce modulated color wavelets.
A local 2d frequency estimation algorithm is also proposed.
Soulard & Carré,
...Monogenic maxima... IEEE TPAMI 2017
This paper proposes a color extension of the wavelet maxima representation
from Mallat & Zhong, with the elliptical monogenic wavelets.
A new isotropic filterbank is proposed (FFT-based undecimated Gaussian filterings).
Amplitude maxima are detected from a sharpness measure and
elliptical features are associated with them.
The local frequency is processed and used.
The reconstruction from maxima is tackled through the "color Marr conjecture".
Approximate reconstruction is achieved by feature interpolation.
This uses 2d segmentation around maxima, as well as
amplitude and phase models for lines, edges and radial shapes.
The experimental part shows that increasing the number of maxima
performs progressive image reconstruction.
A preliminary denoising method is proposed.
