Total Least Square Optimal Analytic Signal by Structure Tensor for N-D images
This work addresses the need for robust local frequency analysis in image processing, particularly for applications like optics and fingerprint recognition, though it appears incremental as it builds on existing methods like the Structure Tensor and Gabor filters.
The authors tackled the problem of estimating orientation, scale, phase, and amplitude in N-D images by developing an analytic signal using the Structure Tensor for Total Least Squares optimal vectors, resulting in continuous and isotropic representations with demonstrated applications in fringe pattern processing and fingerprint measurements. They reported comparisons to baseline alternatives using images with known ground truths.
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.