Isotropic and Steerable Wavelets in N Dimensions. A multiresolution analysis framework for ITK

TL;DR

This paper introduces a multiresolution analysis framework using isotropic and steerable wavelets in N-dimensions, enabling advanced denoising, feature detection, and phase analysis with high reusability and efficiency.

Contribution

It presents a flexible, decoupled implementation of isotropic and steerable wavelets in N-dimensions, including a multiresolution phase analysis filter and a steerable Riesz transform for directional feature detection.

Findings

Provides a multiresolution phase analysis filter.

Implements a steerable Riesz transform for directional features.

Enables efficient detection of features in N-dimensional data.

Abstract

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.