Segmentation of vessel structures from photoacoustic images with reliability assessment

Photoacoustic imaging enables the imaging of soft biological tissue with combined optical contrast and ultrasound resolution. One of the targets of interest is tissue vasculature. However, the photoacoustic images may not directly provide the information on, for example, vasculature structure. Therefore, the images are improved by reducing noise and artefacts, and processed for better visualisation of the target of interest. In this work, we present a new segmentation method of photoacoustic images that also straightforwardly produces assessments of its reliability. The segmentation depends on parameters which have a natural tendency to increase the reliability as the parameter values monotonically change. The reliability is assessed by counting classifications of image voxels with different parameter values. The resulting segmentation with reliability offers new ways and tools to analyse photoacoustic images and new possibilities for utilising them as anatomical priors in further computations. Our MATLAB implementation of the method is available as an open-source software package [P. Raumonen, Matlab, 2018]

Non-intersecting leaf insertion algorithm for tree structure models

We present an algorithm and an implementation to insert broadleaves or needleleaves to 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 the work is to offer a tool for making more realistic simulations with tree models with leaves, particularly for tree models developed from terrestrial laser scan (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 doing 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 minutes. Various leaf area density distributions were defined, and the resulting leaf covers were compared to 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 3D structure and radiative transfer simulation applications, including remote sensing, ecology and forestry, among others

Improving TLS-based stem volume estimates by field measurements

The prediction of tree stem volumes has conventionally been based on simple field measurements and applicable allometric functions, but terrestrial laser scanning (TLS) has enabled new opportunities for extracting stem volumes of single trees. TLS-based tree dimensions are commonly estimated by automatized cylinder- or circle-based fitting approaches which, given that the stem cross-sections are relatively round and the whole stem is sufficiently covered by TLS points, enable an accurate prediction of the stem volume. The results are, however, often deteriorated by co-registration errors and occlusions, i.e., incompletely visible parts of the stem, which easily lead to poorly fitted features and problems in locating the actual treetop. As these defects are difficult to be controlled or totally avoided when collecting data at a plot level, taking advantage of additional field measurements is proposed to improve the fitting process and mitigate gross errors in the prediction of stem volumes. In this paper, this is demonstrated by modelling the stems first as cylinders by only using TLS data, after which the results are refined with the assistance of field data. The applied data consists of various field-measured stem dimensions which are used to define the acceptable diameter estimation limits and set the correct vertical extents for the analyzed tree. This approach is tested using two data sets, differing in the scanning setup, location, and the measured field variables. Adding field data improves the results and, at best, enables almost unbiased volumetric predictions with an RMSE of less than 5%. According to these results, combining TLS point clouds and simple field measurements has the potential to produce stem volume information at a considerably higher accuracy than TLS data alone

Finite element analysis of trees in the wind based on terrestrial laser scanning data

Wind damage is an important driver of forest structure and dynamics, but it is poorly understood in natural broadleaf forests. This paper presents a new approach in the study of wind damage: combining terrestrial laser scanning (TLS) data and finite element analysis. Recent advances in tree reconstruction from TLS data allowed us to accurately represent the 3D geometry of a tree in a mechanical simulation, without the need for arduous manual mapping or simplifying assumptions about tree shape. We used this simulation to predict the mechanical strains produced on the trunks of 21 trees in Wytham Woods, UK, and validated it using strain data measured on these same trees. For a subset of five trees near the anemometer, the model predicted a five-minute time-series of strain with a mean cross-correlation coefficient of 0.71, when forced by the locally measured wind speed data. Additionally, the maximum strain associated with a 5 ms−1 or 15 ms-1 wind speed was well predicted by the model (N = 17, R2 = 0.81 and R2 = 0.79, respectively). We also predicted the critical wind speed at which the trees will break from both the field data and models and find a good overall agreement (N = 17, R2 = 0.40). Finally, the model predicted the correct trend in the fundamental frequencies of the trees (N = 20, R2 = 0.38) although there was a systematic underprediction, possibly due to the simplified treatment of material properties in the model. The current approach relies on local wind data, so must be combined with wind flow modelling to be applicable at the landscape-scale or over complex terrain. This approach is applicable at the plot level and could also be applied to open-grown trees, such as in cities or parks

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

Estimating above ground biomass from terrestrial laser scanning in Australian Eucalypt open forest

Terrestrial laser scanning (TLS) produces 3D data with high detail and accuracy. In this paper we explore the potential of TLS data in combination with a method for reconstruction tree structure to estimate above ground biomass (AGB) in Australian eucalypt forest. Single trees are isolated from the registered TLS point cloud and are used as input for the reconstruction method. We explore the impact of different input parameters on the reconstruction and compare inferred AGB estimates from volume reconstruction and basic density with destructively sampled reference values. Based on a limited number of samples, regression analysis demonstrated R2 of 0.98 to 0.99, with an intercept of 110 kg for unfiltered TLS point clouds and 19.8 kg for filtered point clouds. These initial results demonstrate the potential of tree reconstruction from TLS for rapid, repeatable and robust AGB estimation

Terrestrial laser scanning for plot-scale forest measurement

Plot-scale measurements have been the foundation for forest surveys and reporting for over 200 years. Through recent integration with airborne and satellite remote sensing, manual measurements of vegetation structure at the plot scale are now the basis for landscape, continental and international mapping of our forest resources. The use of terrestrial laser scanning (TLS) for plot-scale measurement was first demonstrated over a decade ago, with the intimation that these instruments could replace manual measurement methods. This has not yet been the case, despite the unparalleled structural information that TLS can capture. For TLS to reach its full potential, these instruments cannot be viewed as a logical progression of existing plot-based measurement. TLS must be viewed as a disruptive technology that requires a rethink of vegetation surveys and their application across a wide range of disciplines. We review the development of TLS as a plotscale measurement tool, including the evolution of both instrument hardware and key data processing methodologies. We highlight two broad data modelling approaches of gap probability and geometrical modelling and the basic theory that underpins these. Finally, we discuss the future prospects for increasing the utilisation of TLS for plot-scale forest assessment and forest monitoring

The Laegeren site: an augmented forest laboratory combining 3-D reconstruction and radiative transfer models for trait-based assessment of functional diversity

Given the increased pressure on forests and their diversity in the context of global change, new ways of monitoring diversity are needed. Remote sensing has the potential to inform essential biodiversity variables on the global scale, but validation of data and products, particularly in remote areas, is difficult. We show how radiative transfer (RT) models, parameterized with a detailed 3-D forest reconstruction based on laser scanning, can be used to upscale leaf-level information to canopy scale. The simulation approach is compared with actual remote sensing data, showing very good agreement in both the spectral and spatial domains. In addition, we compute a set of physiological and morphological traits from airborne imaging spectroscopy and laser scanning data and show how these traits can be used to estimate the functional richness of a forest at regional scale. The presented RT modeling framework has the potential to prototype and validate future spaceborne observation concepts aimed at informing variables of biodiversity, while the trait-based mapping of diversity could augment in situ networks of diversity, providing effective spatiotemporal gap filling for a comprehensive assessment of changes to diversity

Mathematical structures for dimensional reduction and equivalence classification of electromagnetic boundary value problems

Boundary value problems (BVPs) are fundamental in electromagnetic engineering. The aim of this thesis is to introduce mathematical structures that can be exploited in a new way to formulate electromagnetic BVPs. The tools employed come from differential geometry and the theory of manifolds. The structures offer a way to model electromagnetism in a coordinate-free manner, which is independent of the chosen metric. Differentiable manifolds and differential forms are used as models for space and electromagnetic fields, respectively. Together with the pullback, exterior derivative, and wedge product, they can be employed to introduce a formulation of electromagnetism that is invariant under diffeomorphisms. Differential geometry enables us to formulate general electromagnetic BVPs, including static, initial value, and Cauchy problems, in a unified setting. Furthermore, under diffeomorphisms, equivalence of BVPs arises naturally and provides a unified theoretical setting for many traditional, seemingly different methods and approaches. Because of the diffeomorphism-invariance, in formulations of electromagnetic BVPs the metric of space is needed only to make the first connection between the model and the observations. The thesis introduces also (3 + 1)-decompositions of Maxwell’s equations based on coordinate- and metric-free observer fields. A major results of this thesis is this unified aspect to BVPs and its applications to solution methods. The structures used are also generic to all dimensions, which makes them natural tools to formulate electromagnetic BVPs of any dimension. In particular, another main result of this thesis is a symmetry-based theory of dimensional reduction of electromagnetic BVPs. It includes a dimensional reduction theorem that gives sufficient conditions for a BVP to be solved as a lower-dimensional BVP and also formulates the lower-dimensional BVP. Because the theory is completely independent of coordinates, metric, and dimension, differential geometric structures are virtually custom-made for it. The thesis presents several applications and numerical examples, in which the structures offer new insight and benefits. These applications and examples include mesh generation problems, speeding up parametric models that include shape optimization and movement, open-boundary problems, invisibility cloaking, and dimensional reduction of helicoidal geometries

Mathematical structures for dimensional reduction and equivalence classification of electromagnetic boundary value problems

Boundary value problems (BVPs) are fundamental in electromagnetic engineering. The aim of this thesis is to introduce mathematical structures that can be exploited in a new way to formulate electromagnetic BVPs. The tools employed come from differential geometry and the theory of manifolds. The structures offer a way to model electromagnetism in a coordinate-free manner, which is independent of the chosen metric. Differentiable manifolds and differential forms are used as models for space and electromagnetic fields, respectively. Together with the pullback, exterior derivative, and wedge product, they can be employed to introduce a formulation of electromagnetism that is invariant under diffeomorphisms. Differential geometry enables us to formulate general electromagnetic BVPs, including static, initial value, and Cauchy problems, in a unified setting. Furthermore, under diffeomorphisms, equivalence of BVPs arises naturally and provides a unified theoretical setting for many traditional, seemingly different methods and approaches. Because of the diffeomorphism-invariance, in formulations of electromagnetic BVPs the metric of space is needed only to make the first connection between the model and the observations. The thesis introduces also (3 + 1)-decompositions of Maxwell’s equations based on coordinate- and metric-free observer fields. A major results of this thesis is this unified aspect to BVPs and its applications to solution methods. The structures used are also generic to all dimensions, which makes them natural tools to formulate electromagnetic BVPs of any dimension. In particular, another main result of this thesis is a symmetry-based theory of dimensional reduction of electromagnetic BVPs. It includes a dimensional reduction theorem that gives sufficient conditions for a BVP to be solved as a lower-dimensional BVP and also formulates the lower-dimensional BVP. Because the theory is completely independent of coordinates, metric, and dimension, differential geometric structures are virtually custom-made for it. The thesis presents several applications and numerical examples, in which the structures offer new insight and benefits. These applications and examples include mesh generation problems, speeding up parametric models that include shape optimization and movement, open-boundary problems, invisibility cloaking, and dimensional reduction of helicoidal geometries