Riesz Transforms for the Isotropic Estimation of the Local Phase of Moir e Interferograms

. The estimation of the local phase and local amplitude of 1-D signals can be realized by the construction of the analytic signal. This includes the evaluation of the signal's Hilbert transform, which performs a phase shift. In the past, different definitions of the analytic signal of multidimensional signals have been proposed, all of which are based on different combinations of partial and total Hilbert transforms. None of these approaches is isotropic. We propose the use of Riesz transforms which are known to mathematicians as appropriate generalizations of the Hilbert transform to n-D. This approach allows the isotropic estimation of the intrinsically 1-D local image phase. Applications to Moire interferograms are shown.

A new extension of linear signal processing for estimating local properties and detecting features

The analytic signal is one of the most capable approaches in one-dimensional signal processing. Two-dimensional signal theory suffers from the absence of an isotropic extension of the analytic signal. Accepting the fact that there is no odd filter with isotropic energy in higher dimensions, one tried to circumvent this drawback using the one-dimensional quadrature filters with respect to several preference directions. Disadvantages of these methods are an increased complexity, the loss of linearity and a lot of different heuristic approaches. In this paper we present a filter that is isotropic and odd, which means that the whole theory of local phase and amplitude can directly be applied to images. Additionally, a third local property is obtained which is the local orientation. The advantages of our approach are demonstrated by a stable orientation detection algorithm and an adaption of the phase congruency method which yields a superior edge detector with very low complexity