Estimation of illuminants from color signals of illuminated objects

Color constancy is the ability of the human visual systems to discount the effect of the illumination and to assign approximate constant color descriptions to objects. This ability has long been studied and widely applied to many areas such as color reproduction and machine vision, especially with the development of digital color processing. This thesis work makes some improvements in illuminant estimation and computational color constancy based on the study and testing of existing algorithms. During recent years, it has been noticed that illuminant estimation based on gamut comparison is efficient and simple to implement. Although numerous investigations have been done in this field, there are still some deficiencies. A large part of this thesis has been work in the area of illuminant estimation through gamut comparison. Noting the importance of color lightness in gamut comparison, and also in order to simplify three-dimensional gamut calculation, a new illuminant estimation method is proposed through gamut comparison at separated lightness levels. Maximum color separation is a color constancy method which is based on the assumption that colors in a scene will obtain the largest gamut area under white illumination. The method was further derived and improved in this thesis to make it applicable and efficient. In addition, some intrinsic questions in gamut comparison methods, for example the relationship between the color space and the application of gamut or probability distribution, were investigated. Color constancy methods through spectral recovery have the limitation that there is no effective way to confine the range of object spectral reflectance. In this thesis, a new constraint on spectral reflectance based on the relative ratios of the parameters from principal component analysis (PCA) decomposition is proposed. The proposed constraint was applied to illuminant detection methods as a metric on the recovered spectral reflectance. Because of the importance of the sensor sensitivities and their wide variation, the influence from the sensor sensitivities on different kinds of illuminant estimation methods was also studied. Estimation method stability to wrong sensor information was tested, suggesting the possible solution to illuminant estimation on images with unknown sources. In addition, with the development of multi-channel imaging, some research on illuminant estimation for multi-channel images both on the correlated color temperature (CCT) estimation and the illuminant spectral recovery was performed in this thesis. All the improvement and new proposed methods in this thesis are tested and compared with those existing methods with best performance, both on synthetic data and real images. The comparison verified the high efficiency and implementation simplicity of the proposed methods

Fast time-stepping discontinuous Galerkin method for the subdiffusion equation

The nonlocality of the fractional operator causes numerical difficulties for long time computation of the time-fractional evolution equations. This paper develops a high-order fast time-stepping discontinuous Galerkin finite element method for the time-fractional diffusion equations, which saves storage and computational time. The optimal error estimate $O(N^{-p-1} + h^{m+1} + \varepsilon N^{r\alpha})$ of the current time-stepping discontinuous Galerkin method is rigorous proved, where $N$ denotes the number of time intervals, $p$ is the degree of polynomial approximation on each time subinterval, $h$ is the maximum space step, $r\ge1$, $m$ is the order of finite element space, and $\varepsilon>0$ can be arbitrarily small. Numerical simulations verify the theoretical analysis.Comment: 21 pages, 1 figure,4 table

A Fractional Anomalous Diffusion Model and Numerical Simulation for Sodium Ion Transport in the Intestinal Wall

The authors present a fractional anomalous diffusion model to describe the uptake of sodium ions across the epithelium of gastrointestinal mucosa and their subsequent diffusion in the underlying blood capillaries using fractional Fick’s law. A heterogeneous two-phase model of the gastrointestinal mucosa is considered, consisting of a continuous extracellular phase and a dispersed cellular phase. The main mode of uptake is considered to be a fractional anomalous diffusion under concentration gradient and potential gradient. Appropriate partial differential equations describing the variation with time of concentrations of sodium ions in both the two phases across the intestinal wall are obtained using Riemann-Liouville space-fractional derivative and are solved by finite difference methods. The concentrations of sodium ions in the interstitial space and in the cells have been studied as a function of time, and the mean concentration of sodium ions available for absorption by the blood capillaries has also been studied. Finally, numerical results are presented graphically for various values of different parameters. This study demonstrates that fractional anomalous diffusion model is appropriate for describing the uptake of sodium ions across the epithelium of gastrointestinal mucosa