Multiscale Product for Edge Detection

Many methods have been proposed to extract the most relevant areas of an image. This article explores the method of edge detection by the multiscale product （MP） of the wavelet transform. The wavelet used in this work is the first derivative of a bidimensional Gaussian function. InitiaRy, we construct the wavelet, then we present the MP approach which is applied to binary and grey levels images. This method is compared with other methods without noise and in the presence of noise. The experiment results show fhht the MP method for edge detection outPerforms conventional methods even in noisy environments.

A generic approach to the dynamical interpretation of ocean-atmosphere processes

This paper summarizes the recent development of a portable self-contained system to unravel the intricate multiscale dynamical processes from real oceanic flows, which are in nature highly nonlinear and intermittent in space and time. Of particular focus are the interactions among largescale, mesoscale, and submesoscale processes.We firsu introduce the concept of scale window, and an orthogonal subspace decomposition technigue called multiscale window transform (MWT). Established on MWT is a rigorous formalism of multiscale transport, perfect transfer, and multiscale conversion, which makes a new methodology, multiscale energy and vorticity analysis (MS-EVA). A direct application of the MS-EVA is the development of a novel localized instability analysis, generalizing the classical notion of hydrodynamic instability to finite amplitude processes on irregularly variable domains. The theory is consistent with the analytical solutions of Eady's model and Kuo's model, the benchmark models of baroclinic instability and barotropic instability; it is further validated with a vortex shedding control problem. We have put it to application with a variety of complicated real ocean problems, which would be otherwise very difficult, if not impossible, to tackle. Briefly shown in this paper include the dynamical studies of a highly variable open ocean front, and a complex coastal ocean circulation. In the former, it is found that underlying the frontal meandering is a convective instability followed by an absolute instability, and correspondingly a rapid spatially amplifying mode locked into a temporally growing mode; in the latter, we see a real ocean example of how upwelling can be driven by winds through nonlinear instability, and how winds may excite the ocean via an avenue which is distinctly different from the classical paradigms. This system is mathematically rigorous, physically robust, and practically straightforward.

Drastic change in dynamics as Typhoon Lekima experiences an eyewall replacement cycle

Why does the 1909 typhoon,Lekima,become so destructive after making landfall in China?Using a newly developed mathematical apparatus,the multiscale window transform(MWT),and the MWT-based localized mutliscale energetics analysis and theory of canonical transfer,this study is intended to give a partial answer from a dynamical point of view.The ECMWF reanalysis fields are first reconstructed onto the background window,the TC-scale window,and the convection-scale window.A localized energetics analysis is then performed,which reveals to us distinctly different scenarios before and after August 8–9,2019,when an eyewall replacement cycle takes place.Before that,the energy supply in the upper layer is mainly via a strong upper layer-limited baroclinic instability;the available potential energy thus-gained is then converted into the TC-scale kinetic energy,with a portion to fuel Lekima’s upper part,another portion carried downward via pressure work flux to maintain the cyclone’s lower part.After the eyewall replacement cycle,a drastic change in dynamics occurs.First,the pressure work is greatly increased in magnitude.A positive baroclinic transfer almost spreads throughout the troposphere,and so does barotropic transfer;in other words,the whole air column is now both barotropically and baroclinically unstable.These newly occurred instabilities help compensate the increasing consumption of the TC-scale kinetic energy,and hence help counteract the dissipation of Lekima after making landfalls.