Recently, there are many works on discriminant analysis, which promote the robustness of models against outliers by using L₁- or L2,1-norm as the distance metric. However, both of their robustness and discriminant power are limited. In this article, we present a new robust discriminant subspace (RDS) learning method for feature extraction, with an objective function formulated in a different form. To guarantee the subspace to be robust and discriminative, we measure the within-class distances based on L2,s-norm and use L2,p-norm to measure the between-class distances. This also makes our method include rotational invariance. Since the proposed model involves both L2,p-norm maximization and L2,s-norm minimization, it is very challenging to solve. To address this problem, we present an efficient nongreedy iterative algorithm. Besides, motivated by trace ratio criterion, a mechanism of automatically balancing the contributions of different terms in our objective is found. RDS is very flexible, as it can be extended to other existing feature extraction techniques. An in-depth theoretical analysis of the algorithm's convergence is presented in this article. Experiments are conducted on several typical databases for image classification, and the promising results indicate the effectiveness of RDS.

We describe the design, implementation and performance of a novel airborne system, which integrates commercial waveform LiDAR, CCD (Charge-Coupled Device) camera and hyperspectral sensors into a common platform system. CAF’s (The Chinese Academy of Forestry) LiCHy (LiDAR, CCD and Hyperspectral) Airborne Observation System is a unique system that permits simultaneous measurements of vegetation vertical structure, horizontal pattern, and foliar spectra from different view angles at very high spatial resolution (~1 m) on a wide range of airborne platforms. The horizontal geo-location accuracy of LiDAR and CCD is about 0.5 m, with LiDAR vertical resolution and accuracy 0.15 m and 0.3 m, respectively. The geo-location accuracy of hyperspectral image is within 2 pixels for nadir view observations and 5–7 pixels for large off-nadir observations of 55° with multi-angle modular when comparing to LiDAR product. The complementary nature of LiCHy’s sensors makes it an effective and comprehensive system for forest inventory, change detection, biodiversity monitoring, carbon accounting and ecosystem service evaluation. The LiCHy system has acquired more than 8000 km² of data over typical forests across China. These data are being used to investigate potential LiDAR and optical remote sensing applications in forest management, forest carbon accounting, biodiversity evaluation, and to aid in the development of similar satellite configurations. This paper describes the integration of the LiCHy system, the instrument performance and data processing workflow. We also demonstrate LiCHy’s data characteristics, current coverage, and potential vegetation applications.

Aboveground biomass (AGB) of shrub communities in the desert is a basic quantitative characteristic of the desert ecosystem and an important index to measure ecosystem productivity and monitor desertification. An accurate and efficient method of predicting the AGB of a shrub community is essential for studying the spatial patterns and ecological functions of the desert region. Even though there are several entries in the literature on the AGB prediction of desert shrub communities using remote sensing data, the applicability and accuracy of airborne LiDAR data and prediction methods have not been well studied. We first extracted the elevation, density and intensity variables based on the airborne LiDAR, and then sample plot-level AGB prediction models were constructed using the parametric regression (nonlinear regression) and nonparametric methods (Random Forest, Support Vector Machine, K-Nearest Neighbor, Gradient Boosting Machine, and Multivariate adaptive regression splines). We evaluated accuracies of all the AGB prediction models we developed based on the fit statistics. Results showed that: (1) the elevation, density and intensity variables obtained from LiDAR point cloud data effectively predicted the AGB of the desert shrub community at a sample plot level, (2) the kappa coefficient of nonlinear mixed-effects (NLME) model obtained was 0.6977 with an improvement by 13% due to the random effects included into the model, and (3) the nonparametric model, such as Support Vector Machine showed the best fit statistics (R² = 0.8992), which is 28% higher than the NLME-model, and effectively reduced the heteroscedasticity. The AGB prediction model presented in this paper, which is based on the airborne LiDAR data and machine learning algorithm, will provide a valuable tool to the managers and researchers for evaluating desert ecosystem productivity and monitoring desertification.

Research on the inversion of forest aboveground biomass based on airborne light detection and ranging (LiDAR) data focuses on finding the relationship between the two, such as established linear or nonlinear models. However, these models may have poorer estimation accuracy for tree-components biomass and cannot guarantee the additivity of each component. Therefore, we aimed to develop an error-in-variable biomass model system that ensures both the compatibility of the individual tree component biomass with the diameter at breast height and the additivity of component biomass. The system we developed used the airborne LiDAR data and field-measured data of principis-rupprechtii (Larix gmelinii var.) trees, collected from north China. Our model system not only ensured the additivity of nonlinear biomass models, it also accounted for the impact of measurement errors. We first selected the airborne LiDAR-derived variable with the highest contribution to the biomass of each component and then developed an inversion model system with that variable as an independent variable and with the biomass of each component as the dependent variable using allometric functions. Moreover, two model estimation methods, two-stage error (TSEM) and nonlinear seemingly unrelated regression (NSUR) with one-step, two-step, and summation methods, were also applied, and their performances were compared. The results showed that both NSUR-one-step and TSEM-one-step led to similar parameter estimates and performance for a system, and the fitting accuracy of a model system was not very attractive. The variance function included in a model system reduced the heteroscedasticity effectively and improved the model accuracy. Overall, this study successfully combined the error-in-variable modeling with the airborne LiDAR data, proposed methods that can be used for the extension of component biomass from an individual tree to a stand and that might improve the estimation accuracy of carbon storage. A compatible model system can be further improved if various sources of error in the variables are identified, and their impacts on the system are effectively accounted for.

Estimating individual tree diameters at breast height (DBH) from delineated crowns and tree heights on the basis of airborne light detection and ranging (LiDAR) data provides a good opportunity for large-scale forest inventory. Generally, ground-based measurements are more accurate, but LiDAR data and derived DBH values can be obtained over larger areas for a relatively smaller cost if a right procedure is developed. A nonlinear least squares (NLS) regression is not an appropriate approach to predict the aboveground biomass (AGB) of individual trees from the estimated DBH because both the response variable and the regressor are subject to measurement errors. In this study, a system of compatible individual tree DBH and AGB error-in-variable models was developed using error-in-variable regression techniques based on both airborne LiDAR and field-measured datasets of individual Picea crassifolia Kom. trees, collected in northwestern China. Two parameter estimation algorithms, i.e., the two-stage error-in-variable model (TSEM) and the nonlinear seemingly unrelated regression (NSUR), were proposed for estimating the parameters in the developed system of compatible individual tree DBH and AGB error-in-variable models. Moreover, two model structures were applied to estimate AGB for comparison purposes: NLS with AGB estimation depending on DBH (NLS&DD) and NLS with AGB estimation not depending on DBH (NLS&NDD). The results showed that both TSEM and NSUR led to almost the same parameter estimates for the developed system. Moreover, the developed system effectively accounted for the inherent correlation between DBH and AGB as well as for the effects of measurement errors in the DBH on the predictions of AGB, whereas NLS&DD and NLS&NDD did not. A leave-one-out cross-validation indicated that the prediction accuracy of the developed system of compatible individual tree DBH and AGB error-in-variable models with NSUR was the highest among those estimated by the four methods evaluated, but, statistically, the accuracy improvement was not significantly different from zero. The main reason might be that, except for the measurement errors, other source errors were ignored in the modeling. This study implies that, overall, the proposed method provides the potential to expand the estimations of both DBH and AGB from individual trees to stands by combining the error-in-variable modeling and LiDAR data and improve their estimation accuracies, but its application needs to be further validated by conducting a systematical uncertainty analysis of various source errors in a future study.

Forest health is an important variable that we need to monitor for forest management decision making. However, forest health is difficult to assess and monitor based merely on forest field surveys. In the present study, we first derived a comprehensive forest health indicator using 15 forest stand attributes extracted from forest inventory plots. Second, Pearson’s correlation analysis was performed to investigate the relationship between the forest health indicator and the spectral and textural measures extracted from SPOT-5 images. Third, all-subsets regression was performed to build the predictive model by including the statistically significant image-derived measures as independent variables. Finally, the developed model was evaluated using the coefficient of determination (R²) and the root mean square error (RMSE). Additionally, the produced model was further validated for its performance using the leave-one-out cross-validation approach. The results indicated that our produced model could provide reliable, fast and economic means to assess and monitor forest health. A thematic map of forest health was finally produced to support forest health management.