Eigendecomposition of TDR waveforms: a novel method to determine water content and pore fluid concentration of sandy soils

In this study, an incident pulse signal of several harmonics (i.e., multiples of the fundamental frequency) was used as a source in the time domain reflectometry (TDR) probing technique. Reflected signals were captured by an oscilloscope and their characteristics were determined via eigendecomposition. Autoregressive modeling and singular value decomposition were used to calculate the eigenvalues and the most significant ones were identified based on power spectrum. A multivariate statistical analysis was performed for the two most dominant eigenvalues, which are dependent on water content and salt concentrations, and regression equations were obtained. To determine the water content and salt concentrations in terms of the first and second eigenvalues, a modified Powell hybrid algorithm was used to solve the obtained system of nonlinear equations. Actual and predicted results are in agreement indicating that the developed method is very successful in predicting water content and salt concentrations. Furthermore, on comparing the eigendecomposition method with Fourier spectral analysis, one can observe that the former is superior in predicting water content and salt concentrations.     

ALGEBRAIC COMPUTATION OF EIGENVECTORS, SIGNATURES, AND STABILITY OF INFINITESIMALLY SYMPLECTIC MATRICES

A procedure to compute the algebraic expression for eigenvectors using algebraic manipulators associated with numerical checks is presented. This method is applied to the computation of the eigenvectors of the matrices J·D²H for the general problems with two and three degrees of freedom. Furthermore, it is used to calculate the eigenvalues‘ signature and to analyze stability at some equilibrium points of a generalized Hénon-Heille's Hamiltonian by Krein theory. This revised version was published online in July 2006 with corrections to the Cover Date.     

Derivation of tree skeletons and error assessment using LiDAR point cloud data of varying quality

The architecture of trees is of particular interest for 3D model creation in forestry and ecolocical applications. Terrestrial (TLS) and mobile laser scanning (MLS) systems are used to acquire detailed geometrical data of trees. Since 3D point clouds from laser scanning consist of large data amounts representing uninterpreted topographical information including noise and data gaps, an extraction of salient tree structures is important for further applications. We present a fully automated modular workflow for topological reliable reconstruction of tree architecture. Object-based point cloud processing such as branch extraction is combined with tree skeletonization. Branch extraction is performed using a segmentation procedure followed by segment-based analysis of form indices derived from eigenvector metrics. Extracted branch primitives are simplified and connected to line features during skeletonization. The modular workflow allows comprehensive parameter tests and error assessments that are used for a calibration of the module parameters with respect to various characteristics of the input data (e.g noise, scanning resolution, and the number of scan positions). The estimated parameter settings are validated using an exemplary MLS data set. The quality of input point cloud data, strongly influencing the quality of the skeleton results, can be improved by the presented branch extraction procedure. The potential for data improvement increases with increasing point densities. For our object-based appoach, we can show that the presence of erroneous structures and filtering artifacts have the strongest influence onto the quality of the derived skeletons. In contrast to traditional skeletonization approaches, the existance of data gaps has less influence onto the results.