Multifractal Theory And Some Applications

Multifractality is a new branch of nonlinear science and has been used in the other fields of science more and more widely. In this paper, we study the simulated palmprint image(the application in two-dim) and the temperature time series(the application in one-dim) with the help of related multifractal theory and method. Firstly, for the irregular palmprint veins, with using the standard partition function-based multifractal formalism and box-counting method, we show that the palmprints possess multifractal property and extract palmprints' multifractal characteristics. These characteristics that include the width spread and maximum of multifractal spectrum, and a parameter which describes the asymmetry of the spectrum curve are proposed as the distinguishing palmprint features that provide a foundation for further pattern matching. With using multifractal approach, it might shed some light on the theory of biometric recognition. Secondly, with using the standard partition function-based multifractal formalism and multifractal detrended fluctuation analysis, we analyse the temperature time series from 1973 to 2004 in BeiJing and show that the time series possess multifractal property. This will provide a new idea and method for researching in meteorology.