A Structurally Coherent Spatial Phase Estimate

TL;DR

This paper introduces a new multiscale phase estimation method using the structure multivector (SMV) model and steerable wavelets, improving robustness and coherence in noisy 2D image phase analysis.

Contribution

It extends steerable wavelet frames to incorporate SMV features and proposes a novel quality map for structurally coherent phase estimation in noisy images.

Findings

Performs well at low SNR (≤ 1)

Outperforms traditional methods in synthetic phase tasks

Enhances fingerprint registration accuracy

Abstract

The monogenic signal (MS) was introduced by Felsberg and Sommer, and independently by Larkin under the name vortex operator. It is a two-dimensional (2D) analog of the well-known analytic signal, and allows for direct amplitude and phase demodulation of (amplitude and phase) modulated images so long as the signal is intrinsically one-dimensional (i1D). Felsberg's PhD dissertation also introduced the structure multivector (SMV), a model allowing for intrinsically 2D (i2D) structure. While the monogenic signal has become a well-known tool in the image processing community, the SMV is little used, although even in the case of i1D signals it provides a more robust orientation estimation than the MS. We argue the SMV is more suitable in standard i1D image feature extraction due to the this improvement, and extend the steerable wavelet frames of Held et al. to accommodate the additional features of the SMV. We then propose a novel quality map based on local orientation variance which values structurally coherent patches. This yields a multiscale phase estimate which performs well even when signal to noise ratio (SNR) is $\le$ 1. The performance is evaluated on several synthetic phase estimation tasks as well as on a fine-scale fingerprint registration task related to the 2D phase demodulation problem.