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The goal of this review is to present leading examples of current methodologies for extracting forest characteristics from full-waveform LiDAR data. Four key questions are addressed: (i) does full-waveform LiDAR provide advantages over discrete-return laser sensors; (ii) will full-waveform LiDAR provide valid results in support of forest inventory operations and allow for a decrease in ground sampling efforts; (iii) is the use of full-waveform LiDAR data cost effective; and (iv) what is the scope of the applied methods (

One long-standing objective of forest ecosystem remote sensing has been to provide methods for extracting metrics of interest with equal or better accuracy than ground-based forest inventory methods. The use of remote sensing technologies is expanding due to an increasing need to collect data to model complex environmental dynamics (see

The objective of this review is to provide an outline of current methods that have been used successfully for extracting key forest information from FW LiDAR data. This paper is divided into the following sections: an overview of FW characteristics, a description of common pre-processing steps, a discussion of tree-scale and plot-scale methods and a final tabular summary of highlights (

Unlike discrete-return laser systems, full-waveform LiDAR samples and records the entire back-scattered signal intensity (

Depending on the sampling frequency, the vertical resolution of a waveform can vary. For example, many systems sample once every 1 ns (a frequency of 1GHz), which corresponds to a vertical resolution of 15 cm according to the following equation (

where

Signal pre-processing is used to normalize LiDAR information and to decrease or eliminate any element that can be a source of error in further processing steps (

After pre-processing, a waveform can be parametrized to extract peak data by recording the corresponding peak amplitude, width and range index of the peak maximum. Waveform peaks correspond to surface elements that were intercepted by the laser pulse. A common method for peak detection is Gaussian decomposition (

Further details on full-waveform analysis can be found in the existing literature. The work of

The processing steps mentioned above are often implemented within proprietary software that is provided by LiDAR sensor engineering companies. Pre-processing is not a task that is required by end-users unless there are specific research needs.

The accuracy of applications for extracting tree-scale information from FW LiDAR data, such as the estimation of dendrometric characteristics and species classification, has been assessed. The accuracy of results at the single-tree scale is limited by the point density; FW increases the point density by a factor of two relative to conventional discrete-return LiDAR (

Small-footprint, high-resolution LiDAR data (25 points m^{-2}) were used by _{g}, inner tree geometry S_{i} and intensity-related tree structure S_{I}. S_{g} consists of two metrics, S_{g} ^{1} and S_{g} ^{2}; both metrics select crown points from among all tree points by detecting the crown base by dividing points in a tree segment into 0.5-m vertical layers and finding the layer that contains more than 1% of the total tree points. S_{g} ^{1} contains two parameters {a,b} of a parabolic surface fitted to points found by fitting a convex hull to all points belonging to the crown. S_{g} ^{2} is the mean radius (mean distance of all points from the stem position, which in turn is estimated to be at the coordinate of the highest crown point) for each vertical layer (_{i} metrics are divided into two sub-groups, S_{i} ^{h} and S_{i} ^{d} _{,} which are both inspired by the tree characterization metrics developed by _{i} ^{h} is the percentile of the point height distribution in a tree segment (_{i} ^{d} is the percentage of total tree points in each layer (_{I} metric relates to two aspects of the peak intensities detected in the waveform: S_{I} ^{1} is the mean intensity in each vertical layer, and S_{I} ^{2} is the overall mean intensity of all the tree points.

The estimation of tree positions can also be improved by stem detection using a cluster algorithm followed by stem reconstruction using a RANSAC-based adjustment (^{-2} had little effect on the accuracy of voxel-based classifications (

To my knowledge, the methods described above are the only tree-scale FW processing methods present in the current literature. Extensive experimentation using discrete-return LiDAR data has been performed, and therefore it is likely that future research will also produce experimental results based on FW LiDAR. Due to high point-density requirements, large acquisition costs and dataset sizes are likely to lead to longer processing times and higher overall costs, which may limit the applicability of FW LiDAR tree-scale approaches.

Small-footprint (<1 m) LiDAR systems use a different sampling scale than large-footprint systems; therefore, approaches to data processing differ. When using small-footprint LiDAR with a consistent point density, vegetation geometry can be modeled with greater detail because each laser pulse samples different parts of the tree; in contrast, large footprints, with a size comparable to crown diameters, sample the entire tree. Consequently, more flight time is required to cover equivalent areas when using a small footprint approach (

^{-2} and integrated different multispectral images (aerial and SPOT satellite sensors) to obtain an efficient forest inventory. The method of Rossmann et al. used decision tree classification criteria based on digital image analysis results for vegetation detected using a LiDAR-derived canopy height model (CHM). Tree stands with a similar stock were automatically identified and merged (when contiguous) on the map through a region-merging process. For each merged area, stand attributes were extracted using the CHM to find the dominant tree height and density, and the yield class was then derived using water balance information for the area.

The location (range index) within the waveform. This metric is the point where the signal increased above a mean noise level threshold (

The location within the waveform of the centre of the last Gaussian pulse (

The difference between metrics 1 and 2. This value was used to extract the canopy height.

Height of the median energy. This metric is the location of of median energy height relative to the ground location and was used to derive the vertical arrangement of canopy elements, canopy openness and tree density.

Median/height ratio. This metric is defined as the value derived from point 4 divided by the canopy height at point 1 and was used to estimate the median position relative to the canopy surface. Ground return ratio. This metric is the sum of all values in the last return peak divided by all other values (only values above noise level are considered) and was used to infer the degree of canopy closure.

smooth the signal (sum six consecutive bins) to decrease the background noise;

find the background noise level by calculating the signal mean and variance beyond the last return;

differentiate the ground and canopy returns. The last ground return is the last return that is a multiple of the background noise variance, and the peak of the ground return is the first inflection before the last ground return;

adjust the amplitude to account for differences in reflectance;

compute the height distribution of the canopy closure;

apply an occlusion transformation to yield a normalized height distribution of the plant area.

This method has proven to be reproducible and significantly (P < 0.0001) correlated to ground-measured and LiDAR-estimated CHP for young (R^{2 }= 0.75), intermediate (R^{2 }= 0.52), mature (R^{2 }= 0.33) and old-growth (R^{2}=0.43) stands.

Lefsky et al. (^{2 }= 0.84) using a unified equation (AGBM = 0.378 · MCH^{2}) when estimating AGBMs of temperate deciduous broadleaf, temperate coniferous needleleaf and boreal coniferous needleleaf biomes. The second study tested the ability to estimate LAI information based on SLICER data for five different temperate coniferous needleleaf biome sites containing one or more of the following species: open-canopy

SLICER sensor data were also used to assess vertical canopy material distributions and canopy cover. Vertical canopy distributions are essential to estimating other parameters, such as AGBM, state of the forest and age of a plantation (

Full-waveform LiDAR processing is a promising technique for various forestry applications. There are important factors to consider when processing return signals. One is pulse geolocation, which must have an acceptable accuracy relative to the target spatial scale and is especially important for single-tree metrics. Another parameter that differentiates FW LiDAR surveys from other methods is the footprint size. Large footprints sample large areas; therefore, elements inside an area are mixed within the resulting return pulse shape. Because of the laser beam size, FW LiDAR has a high degree of probability of finding openings in the canopy, reaching the ground and providing a ground return signal (

It is apparent from the literature that there are numerous methods for processing FW LiDAR data for the estimation of forest parameters. Certain models are applicable at either the plot or regional level, and some methods are influenced by leaf-off/leaf-off conditions. The application context is therefore important and must be assessed before planning a LiDAR survey. It is crucial to delineate the scope of suitability for each methodology; when estimating key characteristics, such as tree height distribution, crown diameter and relative structural tree parameters, metrics derived from FW signals are not always significantly correlated. For some forest types, the correlation is very high (

Currently, the main drawback of performing LiDAR-based estimations is the high cost of data acquisition, especially for high-density and small-footprint surveys. Robust and dedicated software for signal processing is limited to a few proprietary products, and it is expected that future research will result in the development of dedicated open-source tools. It is reasonable to expect that FW LiDAR data processing will be used in forestry research with the same regularity as digital image analysis.

The author wishes to thank Josef Reitberger (Munich University of Applied Science) for his help on commenting part of the text. This work is part of a project financially supported by the University of Padova (Progetto di Ricerca di Ateneo 2009 - CPDA097420).

The following abbreviations have been used in this paper:

FW: full waveform;

AGBM: above-ground biomass;

CHM: canopy height model;

CHP: canopy height profile;

MCH: mean canopy height;

ABA: average basal area;

DBH: breast height diameter;

LAI: leaf area index.

Correlation values are expressed throughout the paper as the coefficient of determination, R^{2}.

(A) Schema of a full-waveform return signal from forested cover; (B) plot of digitizer counts as a function of time; (C) modeled waveform where each peak is characterized by a range, width and amplitude.

Tree layers for tree structuremetrics (from

(A): Voxel-based segmentation of dense FW LiDAR points; and (B): resulting single trees (from

Generic waveform plot with various metrics: start of the canopy surface, canopy and ground return with the derived canopy height.

Sampling geometry of a large-footprint LiDAR survey; circles represent laser footprints, and black dots represent a regular sampling grid (from

Highlights of experimental results from full-waveform LiDAR applications in forestry. (*): single tree scale; (§): small footprint, plot-scale; (#): large footprint, plot-scale.

Scale | Authors | Key-line of method | Main results |
---|---|---|---|

* | Reitberger et al. (2007) | Improve tree position detection by modelling stem | 61% and 41% detection rate respectively for coniferous and deciduous. |

* | Reitberger et al. (2008) | Tree features computed from the 3-dimensional coordinates of the reflections, the intensity and the pulse width are used to detect coniferous and deciduous trees by an unsupervised classification | 85% and 96% accuracy respectively for leaf-on and leaf-off conditions in distinguishing coniferous from deciduous. |

* | Reitberger et al. (2009a) | Use Normalized cut segmentation - based on voxel space - plus unsupervised classification to detect trees. | Improved classification by 12% compared to common watershed algorithm. |

* | Reitberger et al. (2009b) | Use Normalized cut segmentation and unsupervised classification based on waveform metrics to detect single trees also in lower layer. | Best classification 93% of trees, also in lower layer, point density very little impact. |

§ | Wagner et al. (2008) | Decision tree classification using number of return peaks, width and amplitude information. | Kappa coefficient of concordance = 0.8 in stand segmentation. |

§ | Rossmann et al. (2009) | Integrate FW LiDAR with SPOT - aerial image analysis for stand segmentation and characterization using decision tree, object-oriented classification. | 2.8% error on overall volume estimation. |

§ | Chauve et al. (2008) | Additional point detection from weak echoes -using advanced peak detection and modelling - improves height estimation and increases the amount of information on lower storey. | 5 cm improvement of bias and standard deviation in CHM compared to discrete-return LiDAR. |

# | Drake et al. (2002) | Several metrics describing vertical distribution of forest structure are derived from the waveform of return pulse to infer key parameters. | Quadratic mean BHD, ABA and AGBM had significant correlation values of 0.93, 0.72 and 0.93 respectively. |

# | Anderson et al. (2008) | AGBM information estimated from LiDAR integrated with digital image analysis to extract quadratic mean BHD, ABA and AGBM. | 8-9% improvement in correlation and a decrease of 5-8% in error |

# | Harding et al. (2001) | Canopy height profiling by processing the waveform to extract height distribution of canopy closure from waveform. | ground-measured and LiDAR -estimated CHP correlation of: young (0.75), intermediate (0.52) mature (0.33) and old-growth (0.43). |

# | Lefsky et al. (2002), Lefsky et al. (2005) | Three different biomes (2002) and five different contexts in same biome (2005) tested for quality of estimation of LAI and AGBM. | AGBM correlation value of 0.84 over biomes with general equation. Best LAI and AGBM 0.81 and 0.92 respectively. Regional scale validity. |

# | Means et al. (1999) | Interactive graphical and regression techniques used for modelling forest characteristics with FW LiDAR metrics over coniferous forest. | Height, basal area, total biomass and leaf biomass R2 of 0.95, 0.96, 0.96, and 0.84, respectively. |