Total Least Square Optimal Analytic Signal by Structure Tensor for N-D images

TL;DR

This paper introduces a novel N-D analytic signal construction using the Structure Tensor for optimal orientation and scale estimation, enabling enhanced feature detection and analysis in multidimensional images.

Contribution

It presents a new method for generating N-D analytic signals based on the Structure Tensor, providing continuous, isotropic phase and orientation information with applications in singularity detection.

Findings

Effective in detecting singularities in 2-D images

Outperforms baseline methods in orientation and scale estimation

Applicable to various N-D imaging modalities

Abstract

We produce the analytic signal by using the Structure Tensor, which provides Total Least Squares optimal vectors for estimating orientation and scale locally. Together, these vectors represent N-D frequency components that determine adaptive, complex probing filters. The N-D analytic signal is obtained through scalar products of adaptive filters with image neighborhoods. It comprises orientation, scale, phase, and amplitude information of the neighborhood. The ST analytic signal $ f_A $ is continuous and isotropic, and its extension to N-D is straightforward. The phase gradient can be represented as a vector (instantaneous frequency) or as a tensor. Both are continuous and isotropic, while the tensor additionally preserves continuity of orientation and retains the same information as the vector representation. The tensor representation can also be used to detect singularities. Detection with known phase portraits has been demonstrated in 2-D with relevance to fringe pattern processing in wave physics, including optics and fingerprint measurements. To construct adaptive filters we have used Gabor filter family members as probing functions, but other function families can also be used to sample the spectrum, e.g., quadrature filters. A comparison to three baseline alternatives-in representation (Monogenic signal), enhancement (Monogenic signal combined with a spline-wavelet pyramid), and singularity detection (mindtct, a fingerprint minutia detector widely used in numerous studies)-is also reported using images with precisely known ground truths for location, orientation, singularity type (where applicable), and wave period.