Markku Åkerblom

Analysis of Geometric Primitives in Quantitative Structure Models of Tree Stems

One way to model a tree is to use a collection of geometric primitives to represent the surface and topology of the stem and branches of a tree. The circular cylinder is often used as the geometric primitive, but it is not the only possible choice. We investigate various geometric primitives and modelling schemes, discuss their properties and give practical estimates for expected modelling errors associated with the primitives. We find that the circular cylinder is the most robust primitive in the sense of a well-bounded volumetric modelling error, even with noise and gaps in the data. Its use does not cause errors significantly larger than those with more complex primitives, while the latter are much more sensitive to data quality. However, in some cases, a hybrid approach with more complex primitives for the stem is useful.

Non-intersecting leaf insertion algorithm for tree structure models

We present an algorithm and an implementation to insert broadleaves or needleleaves into a quantitative structure model according to an arbitrary distribution, and a data structure to store the required information efficiently. A structure model contains the geometry and branching structure of a tree. The purpose of this work is to offer a tool for making more realistic simulations of tree models with leaves, particularly for tree models developed from terrestrial laser scanning (TLS) measurements. We demonstrate leaf insertion using cylinder-based structure models, but the associated software implementation is written in a way that enables the easy use of other types of structure models. Distributions controlling leaf location, size and angles as well as the shape of individual leaves are user definable, allowing any type of distribution. The leaf generation process consist of two stages, the first of which generates individual leaf geometry following the input distributions, while in the other stage intersections are prevented by carrying out transformations when required. Initial testing was carried out on English oak trees to demonstrate the approach and to assess the required computational resources. Depending on the size and complexity of the tree, leaf generation takes between 6 and 18 min. Various leaf area density distributions were defined, and the resulting leaf covers were compared with manual leaf harvesting measurements. The results are not conclusive, but they show great potential for the method. In the future, if our method is demonstrated to work well for TLS data from multiple tree types, the approach is likely to be very useful for three-dimensional structure and radiative transfer simulation applications, including remote sensing, ecology and forestry, among others.

Comprehensive quantitative tree models from TLS data

We present comprehensive and quantitative tree models reconstructed from terrestrial laser scanning data. The tree models consist of large number of cylinders whose location, size, and orientation locally approximate the geometry of the tree. The parent-child relations of the cylinders also record the topological branching structure of the tree. The modeling process is automatic and scale-independent. When the tree model is computed once, it can be used to compute tree attributes, such as branch size distributions and taper functions, without the need to revisit the original dataset. The model is also compact, achieving a hundred- to thousandfold data size compression compared to the original dataset. We present also a validation of the model using generated tree models and examples of models from measurements of actual trees.

Uncertainty in multispectral lidar signals caused by incidence angle effects

Multispectral terrestrial laser scanning (TLS) is an emerging technology. Several manufacturers already offer commercial dual or three wavelength airborne laser scanners, while multispectral TLS is still carried out mainly with research instruments. Many of these research efforts have focused on the study of vegetation. The aim of this paper is to study the uncertainty of the measurement of spectral indices of vegetation with multispectral lidar. Using two spectral indices as examples, we find that the uncertainty is due to systematic errors caused by the wavelength dependency of laser incidence angle effects. This finding is empirical, and the error cannot be removed by modelling or instrument modification. The discovery and study of these effects has been enabled by hyperspectral and multispectral TLS, and it has become a subject of active research within the past few years. We summarize the most recent studies on multi-wavelength incidence angle effects and present new results on the effect of specular reflection from the leaf surface, and the surface structure, which have been suggested to play a key role. We also discuss the consequences to the measurement of spectral indices with multispectral TLS, and a possible correction scheme using a synthetic laser footprint.

Realistic Forest Stand Reconstruction from Terrestrial LiDAR for Radiative Transfer Modelling

Forest biophysical variables derived from remote sensing observations are vital for climate research. The combination of structurally and radiometrically accurate 3D “virtual” forests with radiative transfer (RT) models creates a powerful tool to facilitate the calibration and validation of remote sensing data and derived biophysical products by helping us understand the assumptions made in data processing algorithms. We present a workflow that uses highly detailed 3D terrestrial laser scanning (TLS) data to generate virtual forests for RT model simulations. Our approach to forest stand reconstruction from a co-registered point cloud is unique as it models each tree individually. Our approach follows three steps: (1) tree segmentation; (2) tree structure modelling and (3) leaf addition. To demonstrate this approach, we present the measurement and construction of a one hectare model of the deciduous forest in Wytham Woods (Oxford, UK). The model contains 559 individual trees. We matched the TLS data with traditional census data to determine the species of each individual tree and allocate species-specific radiometric properties. Our modelling framework is generic, highly transferable and adjustable to data collected with other TLS instruments and different ecosystems. The Wytham Woods virtual forest is made publicly available through an online repository.

A generator of morphological clones for plant species

Detailed and realistic tree form generators have numerous applications in ecology and forestry. Here, we present an algorithm for generating morphological tree “clones” based on the detailed reconstruction of the laser scanning data, statistical measure of similarity, and a plant growth algorithm with simple stochastic rules. The algorithm is designed to produce tree forms, i.e. morphological clones, similar as a whole (coarse-grain scale), but varying in minute details of organization (fine-grain scale). We present a general procedure for obtaining these morphological clones. Although we opted for certain choices in our algorithm, its various parts may vary depending on the application. Namely, we have shown that specific multi-purpose procedural stochastic growth model can be algorithmically adjusted to produce the morphological clones replicated from the target experimentally measured tree. For this, we have developed a statistical measure of similarity (structural distance) between any given pair of trees, which allows for the comprehensive comparing of the tree morphologies in question by means of empirical distributions describing geometrical and topological features of a tree. Our algorithm can be used in variety of applications and contexts for exploration of the morphological potential of the growth models, arising in all sectors of plant science research. Summary Statement We present an algorithmic framework, based on the Bayesian inference, for generating morphological tree clones using a combination of stochastic growth models and experimentally derived tree structures.

Bayes Forest: a data-intensive generator of morphological tree clones

Abstract Detailed and realistic tree form generators have numerous applications in ecology and forestry. For example, the varying morphology of trees contributes differently to formation of landscapes, natural habitats of species, and eco-physiological characteristics of the biosphere. Here, we present an algorithm for generating morphological tree “clones” based on the detailed reconstruction of the laser scanning data, statistical measure of similarity, and a plant growth model with simple stochastic rules. The algorithm is designed to produce tree forms, i.e., morphological clones, similar (and not identical) in respect to tree-level structure, but varying in fine-scale structural detail. Although we opted for certain choices in our algorithm, individual parts may vary depending on the application, making it a general adaptable pipeline. Namely, we showed that a specific multipurpose procedural stochastic growth model can be algorithmically adjusted to produce the morphological clones replicated from the target experimentally measured tree. For this, we developed a statistical measure of similarity (structural distance) between any given pair of trees, which allows for the comprehensive comparing of the tree morphologies by means of empirical distributions describing the geometrical and topological features of a tree. Finally, we developed a programmable interface to manipulate data required by the algorithm. Our algorithm can be used in a variety of applications for exploration of the morphological potential of the growth models (both theoretical and experimental), arising in all sectors of plant science research.

A Simulator for Infinite-Dimensional Systems with a Self-Tuning Controller

Abstract A simple and easy to use simulator, for linear time invariant exponentially stable infinite-dimensional systems with a self-tuning controller, is presented. The simulator is written in Matlab and allows one to to examine the robust regulation problem with a self-tuning controller described by the authors in an earlier paper.