Journal of Approximation Theory
The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Radial Basis Functions
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
On the Choice of Band-Pass Quadrature Filters
Journal of Mathematical Imaging and Vision
Signal modeling for two-dimensional image structures
Journal of Visual Communication and Image Representation
Construction of Hilbert transform pairs of wavelet bases and Gabor-like transforms
IEEE Transactions on Signal Processing
α scale spaces on a bounded domain
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Steerable wavelet frames based on the Riesz transform
IEEE Transactions on Image Processing
IEEE Transactions on Signal Processing
The design of approximate Hilbert transform pairs of wavelet bases
IEEE Transactions on Signal Processing
Multiple Multidimensional Morse Wavelets
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Hypercomplex signals-a novel extension of the analytic signal tothe multidimensional case
IEEE Transactions on Signal Processing
Isotropic polyharmonic B-splines: scaling functions and wavelets
IEEE Transactions on Image Processing
Coherent Multiscale Image Processing Using Dual-Tree Quaternion 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
Wavelet steerability and the higher-order Riesz transform
IEEE Transactions on Image Processing
Steerable wavelet frames based on the Riesz transform
IEEE Transactions on Image Processing
Analytical footprints: compact representation of elementary singularities in wavelet bases
IEEE Transactions on Signal Processing
Coherence probe microscopy imaging and analysis for fiber-reinforced polymers
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Directional Multiscale Amplitude and Phase Decomposition by the Monogenic Curvelet Transform
SIAM Journal on Imaging Sciences
Hi-index | 0.02 |
The monogenic signal is the natural 2-D counterpart of the 1-D analytic signal. We propose to transpose the concept to the wavelet domain by considering a complexified version of the Riesz transform which has the remarkable property of mapping a real-valued (primary) wavelet basis of L2(R2) into a complex one. The Riesz operator is also steerable in the sense that it give access to the Hilbert transform of the signal along any orientation. Having set those foundations, we specify a primary polyharmonic spline wavelet basis of L2(R2) that involves a single Mexican hat-like mother wavelet (Laplacian of a B-spline). The important point is that our primary wavelets are quasi-isotropic: they behave like multiscale versions of the fractional Laplace operator from which they are derived, which ensures steerability. We propose to pair these real-valued basis functions with their complex Riesz counterparts to specify a multiresolution monogenic signal analysis. This yields a representation where each wavelet index is associated with a local orientation, an amplitude and a phase. We give a corresponding wavelet-domain method for estimating the underlying instantaneous frequency.We also provide a mechanism for improving the shift and rotation-invariance of the wavelet decomposition and show how to implement the transform efficiently using perfect-reconstruction filterbanks. We illustrate the specific feature-extraction capabilities of the representation and present novel examples of wavelet-domain processing; in particular, a robust, tensor-based analysis of directional image patterns, the demodulation of interferograms, and the reconstruction of digital holograms.