Regularity of the free boundary for the two-phase Bernoulli problem

We prove a regularity theorem for the free boundary of minimizers of the two-phase Bernoulli problem, completing the analysis started by Alt, Caffarelli and Friedman in the 80s. As a consequence, we also show regularity of minimizers of the multiphase spectral optimization problem for the principal eigenvalue of the Dirichlet Laplacian.

Spectral Optimization of Airborne Multispectral Camera for Land Cover Classification: Automatic Feature Selection and Spectral Band Clustering

Hyperspectral imagery consists of hundreds of contiguous spectral bands. However, most of them are redundant. Thus a subset of well-chosen bands is generally sufficient for a specific problem, enabling to design adapted superspectral sensors dedicated to specific land cover classification. Related both to feature selection and extraction, spectral optimization identifies the most relevant band subset for specific applications, involving a band subset relevance score as well as a method to optimize it. This study first focuses on the choice of such relevance score. Several criteria are compared through both quantitative and qualitative analyses. To have a fair comparison, all tested criteria are compared to classic hyperspectral data sets using the same optimization heuristics: an incremental one to assess the impact of the number of selected bands and a stochastic one to obtain several possible good band subsets and to derive band importance measures out of intermediate good band subsets. Last, a specific approach is proposed to cope with the optimization of bandwidth. It consists in building a hierarchy of groups of adjacent bands, according to a score to decide which adjacent bands must be merged, before band selection is performed at the different levels of this hierarchy.

Spectral Optimization of White LED Based on Mesopic Luminance and Color Gamut Volume for Dim Lighting Conditions

The study aims to propose an approach of white LED spectral optimization based on mesopic luminance and color gamut volume for dim lighting conditions. Three optimal white LED spectra with relatively higher mesopic luminance and color gamut volume, the highest mesopic luminance, and the largest gamut volume are recommended for reducing energy consumption and enhancing color perception and recognition of human eyes. The theoretical simulation shows that the spectra with higher correlated color temperatures (CCT) and S/P-ratio increase the mesopic luminance and also extend the range of color gamut with the decreasing of lighting level. An evaluation model is developed to faster predict mesopic luminance, color gamut volume, and S/P ratio for lighting applications.