Open AccessIsotropic and Steerable Wavelets in N Dimensions. A multiresolution analysis framework.
Author(s) -
Pablo Hernandez-Cerdan
Publication year - 2016
Publication title -
the insight journal
Language(s) - English
Resource type - Journals
ISSN - 2327-770X
DOI - 10.54294/0e1c0748fe24
Subject(s) - wavelet , multiresolution analysis , computer science , pyramid (geometry) , algorithm , wavelet transform , computation , isotropy , filter (signal processing) , analytic signal , artificial intelligence , computer vision , mathematics , signal processing , optics , discrete wavelet transform , geometry , physics , telecommunications , radar
This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides the backbone for state of the art filters for denoising, feature detection or phase analysis in N-dimensions. It focus on reusability, and highly decoupled modules for easy extension and implementation of new filters, and it contains a filter for multiresolution phase analysis, The backbone of the multi-scale analysis is provided by an isotropic band-limited wavelet pyramid, and the detection of directional features is provided by coupling the pyramid with a generalized Riesz transform. The generalized Riesz transform of order N behaves like a smoothed version of the Nth order derivatives of the signal. Also, it is steerable: its components impulse responses can be rotated to any spatial orientation, reducing computation time when detecting directional features. This paper is accompanied with the source code, input data, parameters and output data that the author used for validating the algorithm described in this paper. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.