4 October 2000 Modeling and analysis of cosmetic treatment effects on human skin
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Abstract
In view of treatment effects of cosmetics, quality management becomes more and more important. Due to the efficiency reasons it is desirable to quantify these effects and predict them as a function of time. For this, a mathematical model of the skin's surface (epidermis) is needed. Such a model cannot be worked out purely analytically. It can only be derived with the help of measurement data. The signals of interest as output of different measurement devices consist of two parts: noise of high (spatial) frequencies (stochastic signal) and periodic functions (deterministic signal) of low (spatial) frequencies. Both parts can be separated by correlation analysis. The paper introduces in addition to the Fourier Transform (FT) with the Wavelet Transform (WT), a brand new, highly sophisticated method with excellent properties for both modeling the skin's surface as well as evaluating treatment effects. Its main physical advantage is (in comparison to the FT) that local irregularities in the measurement signal (e.g. by scars) remain at their place and are not represented as mean square values as it is the case when applying the FT. The method has just now been installed in industry and will there be used in connection with a new in vivo measurement device for quality control of cosmetic products. As texture parameter for an integral description of the human skin the fractal dimension D is used which is appropriate for classification of different skin regions and treatment effects as well.
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Reinhart A. Lunderstaedt, Hermann Hopermann, Thomas Hillemann, "Modeling and analysis of cosmetic treatment effects on human skin", Proc. SPIE 4121, Mathematical Modeling, Estimation, and Imaging, (4 October 2000); doi: 10.1117/12.402431; https://doi.org/10.1117/12.402431
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