Multi-scale orientation estimation using higher order Riesz transforms

Abstract

In this paper, we unify the Riesz transform with the Teager–Kaiser energy operator (TKEO) and monogenic multi-resolution analysis in comparison to conventional gradient and Riesz transform-based approaches. We show that benefits of our approach maintain the following aspects of different known estimators: the stability of mixed (higher) order of derivatives, like given in TKEO, the all-pass filter characteristics featuring the Riesz transform and the scale-based analysis. Furthermore, we demonstrate the ability of the considered technique for extracting structural defects at different scales, estimating orientation or being used for 2D demodulation of amplitude- and phase modulated signals, like interferometric fringe patterns. Additionally, the abilities of orientation estimation of 3D data is demonstrated. From the viewpoint of mathematical analysis, we will emphasize the connection to monogenic higher dimensional signals, Clifford frames, and monogenic multi-resolution signal analysis. Furthermore, we will discuss higher order Riesz transform.