Edge detection of potential-field sources using scale-space monogenic signal: Fundamental principles

Abstract

We have developed a new phase-based filter to enhance the edges of geologic sources from potential-field data using the local phase in the Poisson scale-space monogenic signal. The Poisson scale-space representation of a potential-field data is equivalent to performing an upward continuation of the data. We created a band-pass filter by taking the differences between two Poisson scale-space representations of the data. The local phase was defined as the arctangent of the ratio of the magnitude of the x-and y-components of the first-order Riesz transform of the filtered data to these data. These components were computed in the wavenumber domain and then transformed back into the space domain by the inverse Fourier transform. In the wavenumber domain, we found that these components are the multiplication of the Fourier transform of the filtered data by a Fourier-domain kernel, which in turn is the multiplication of the first-order horizontal derivative filter by the first-order vertical integral filter. This operation is stable, making the local phase of the monogenic signal quite insensitive to noise. We proved that if the data were the vertical component f z of a conservative field F, the x-and y-components of the first-order Riesz transform of f z were the horizontal components f x and f y of F. Hence, the local amplitude of the monogenic signal of f z is the 3D analytic signal amplitude of the scalar potential of F and the local phase resembles the tilt angle (TILT). Tests on synthetic total-field anomalies and a real aeromagnetic anomaly over the Pará-Maranhão Basin, Brazil, showed that the local phase in the scale-space monogenic signal had better performance than the TILT in delineating the geologic contacts that were not seen in the original data.

Investigation of the linear structures of the Menderes Massif (Western Anatolia) using the moving average differences ‘mad’ boundary analysis method

“…Recognition of the amplitude changes within anomalies becomes harder as the depth of the source increases, which makes amplitude‐dependent methods (such as HGM, AS and TM, that is the ratio of the HGM and AS) ineffective for such source boundaries (Arısoy and Dikmen, 2015; Hidalgo‐Gato and Barbosa, 2015). The methods correlating the horizontal and vertical derivatives (such as TA) are more effective when the sources with different depths are in the same area, whereas they are weak when the sources are vertically piled, resulting in superposed effects in gravity anomalies.…”

Korištenje Varimax Norm metode za poboljšanje i prepoznavanje rubnih podataka polja potencijala

“…Lots of methods for edge detection and enhancement are widely applied to potential field data( gravity and magnetic data) to distinguish between geological bodies with different densities and magnetic properties detailedly indicate subsurface faults, plutons, contacts, and other tectonic features (Alamdar et al, 2009;Sun et al, 2016). Among all the edge-detection methods, derivative-based filters have primarily and successfully been used to enhance short-wavelength anomalies produced by small and shallow sources; moreover, these methods are simple to implement and are not computationally demanding (Hidalgo-Gato and Barbosa, 2015;Oliveira et al, 2017). The horizontal derivative enhances edges, whereas the vertical derivative narrows the width of anomalies (Cooper and Cowan, 2004).…”

A Comparative Study on the Method of Extracting Edge and Contour Information of Multifunctional Digital Ship Image

“…The edge and contour information of multifunctional digital ship image refers to the part of that the local brightness changes significantly [6], it exists between the target image and another target image [7], the target image and background image, the regional image and another regional image [8][9]. At present, the edge feature extraction technology of multifunctional digital ship image has been widely used in the field such as target tracking, fingerprint recognition, laser remote sensing image segmentation and many others.…”