Estimating the crop leaf area index using hyperspectral remote sensing

The leaf area index（LAI） is an important vegetation parameter,which is used widely in many applications.Remote sensing techniques are known to be effective but inexpensive methods for estimating the LAI of crop canopies.During the last two decades,hyperspectral remote sensing has been employed increasingly for crop LAI estimation,which requires unique technical procedures compared with conventional multispectral data,such as denoising and dimension reduction.Thus,we provide a comprehensive and intensive overview of crop LAI estimation based on hyperspectral remote sensing techniques.First,we compare hyperspectral data and multispectral data by highlighting their potential and limitations in LAI estimation.Second,we categorize the approaches used for crop LAI estimation based on hyperspectral data into three types：approaches based on statistical models,physical models（i.e.,canopy reflectance models）,and hybrid inversions.We summarize and evaluate the theoretical basis and different methods employed by these approaches（e.g.,the characteristic parameters of LAI,regression methods for constructing statistical predictive models,commonly applied physical models,and inversion strategies for physical models）.Thus,numerous models and inversion strategies are organized in a clear conceptual framework.Moreover,we highlight the technical difficulties that may hinder crop LAI estimation,such as the ＂curse of dimensionality＂ and the ill-posed problem.Finally,we discuss the prospects for future research based on the previous studies described in this review.

Zagreb indices of graphs

The first Zagreb index M1 （G） is equal to the sum of squares of the degrees of the vertices, and the second Zagreb index M2 （G） is equal to the sum of the products of the degrees of pairs of adjacent vertices of the underlying molecular graph G. In this paper, we obtain lower and upper bounds on the first Zagreb index MI（G） of G in terms of the number of vertices （n）, number of edges （m）, maximum vertex degree （△）, and minimum vertex degree （δ）. Using this result, we find lower and upper bounds on M2（G）. Also, we present lower and upper bounds on M2（G） ＋ M2（G） in terms of n, m, △, and δ, where denotes the complement of G. Moreover, we determine the bounds on first Zagreb coindex MI（G） and second Zagreb coindex M2（G）. Finally, we give a relation between the first Zagreb index and the second Zagreb index of graph G.