Building roof modeling from airborne laser scanning data based on level set approach

Determination of forest fuels characteristics in mortality-affected Pinus forests using integrated hyperspectral and ALS data

Biodiversity studies could strongly benefit from three-dimensional data on ecosystem structure derived from contemporary remote sensing technologies, such as Light Detection and Ranging (LiDAR). Despite the increasing availability of such data at regional and national scales, the average ecologist has been limited in accessing them due to high requirements on computing power and remote-sensing knowledge. We processed Denmark's publicly available national Airborne Laser Scanning (ALS) data set acquired in 2014/15 together with the accompanying elevation model to compute 70 rasterized descriptors of interest for ecological studies. With a grain size of 10 m, these data products provide a snapshot of high-resolution measures including vegetation height, structure and density, as well as topographic descriptors including elevation, aspect, slope and wetness across more than forty thousand square kilometres covering almost all of Denmark's terrestrial surface. The resulting data set is comparatively small (~ 87 GB, compressed 16.4 GB) and the raster data can be readily integrated into analytical workflows in software familiar to many ecologists (GIS software, R, Python). Source code and documentation for the processing workflow are openly available via a code repository, allowing for transfer to other ALS data sets, as well as modification or re-calculation of future instances of Denmark’s national ALS data set. We hope that our high-resolution ecological vegetation and terrain descriptors (EcoDes-DK15) will serve as an inspiration for the publication of further such data sets covering other countries and regions and that our rasterized data set will provide a baseline of the ecosystem structure for current and future studies of biodiversity, within Denmark and beyond.

Level-set approaches are a family of domain classification techniques that rely on defining a scalar level-set function (LSF), then carrying out the classification based on the value of the function relative to one or more thresholds. Most continuum topology optimization formulations are at heart, a classification problem of the design domain into structural materials and void. As such, level-set approaches are gaining acceptance and popularity in structural topology optimization. In conventional level set approaches, finding an optimum LSF involves solution of a Hamilton-Jacobi system of partial differential equations with a large number of degrees of freedom, which in turn, cannot be accomplished without gradients information of the objective being optimized. A new approach is proposed in this paper where design variables are defined as the values of the LSF at knot points, then a Kriging model is used sto interpolate the LSF values within the rest of the domain so that classification into material or void can be performed. Perceived advantages of the Kriging-interpolated level-set (KLS) approach include alleviating the need for gradients of objectives and constraints, while maintaining a reasonable number of design variables that is independent from the mesh size. A hybrid genetic algorithm (GA) is then used for solving the optimization problem(s). An example problem of a short cantilever is studied under various settings of the KLS parameters in order to infer the best practice recommendations for tuning the approach. Capabilities of the approach are then further demonstrated by exploring its performance on several test problems.

SummaryThe parametric level set approach is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, level set methods can be directly coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Moreover, the parametric level set scheme can not only inherit the primary advantages of the conventional level set methods, such as clear boundary representation and the flexibility in handling topological changes, but also alleviate some undesired features from the conventional level set methods, such as the need for reinitialization. However, in the existing radial basis function–based parametric level set method, it is difficult to identify the range of the design variables. Besides, the parametric level set evolution often struggles with large fluctuations during the optimization process. Those issues cause difficulties both in numerical stability and in material property mapping. In this paper, a cardinal basis function is constructed based on the radial basis function partition of unity collocation method to parameterize the level set function. The benefit of using cardinal basis function is that the range of the design variables can now be clearly specified as the value of the level set function. A distance regularization energy functional is also introduced, aiming to maintain the desired signed distance property during the level set evolution. With this desired feature, the level set evolution is stabilized against large fluctuations. In addition, the material properties mapped from the level set function to the finite element model can be more accurate.

Integrating airborne laser scanning data, space-borne radar data and digital aerial imagery to estimate aboveground carbon stock in Hyrcanian forests, Iran

A multi-phase level set framework for source reconstruction in bioluminescence tomography

Research regarding airborne laser scanning (ALS) point cloud semantic segmentation typically revolves around supervised machine learning, which requires time-consuming generation of training data. Therefore, the models are usually trained using one of the benchmarking datasets that cover a small area. Recently, many European countries published classified ALS data, which can be potentially used for training models. However, a review of the classification schemes of these datasets revealed that these schemes vary substantially, therefore limiting their applicability. Thus, our goal was three-fold. First, to develop a common classification scheme that can be applied for the semantic segmentation of various ALS datasets. Second, to unify the classification scheme of existing ALS datasets. Third, to employ them for the training of a classifier that will be able to classify data from different sources and will not require additional training. We propose a classification scheme of four classes: ground and water, vegetation, buildings and bridges, and ‘other’. The developed classifier is trained jointly using ALS data from Austria, Switzerland, and Poland. A test on unseen datasets demonstrates that the achieved intersection over union accuracy varies between 90.0–97.3% for ground and water, 68.0–95.9% for vegetation, 77.6–94.8% for buildings and bridges, and 13.5–52.7% for ‘other’. As a result, we conclude that the developed method generalizes well to previously unseen data.

This study focused on the derivation of basic stand characteristics from airborne laser scanning (ALS) data, aiming to elucidate which characteristics (mean height and diameter, dominant height and diameter) are best approximated by the variables obtained using ALS data. The height of trees of different species in four permanent plots located in the Slovak Republic was derived from the normalised digital surface model (nDSM) representing the canopy surface, using an automatic approach to identify local maxima (individual treetops). Tree identification was carried out using four different spatial resolutions of the nDSM (0.5 m, 1.0 m, 1.5 m, and 2.0 m) and the number of trees identified was compared with reference data obtained from field measurements. The highest percentage of tree detection (69-75%) was observed at the spatial resolutions of 1.0 and 1.5 m. Absolute differences of tree height between reference and ALS datasets ranged from 0 to 36% at all spatial resolutions. The smallest difference in mean height was obtained using the higher spatial resolution (0.5 m), while the smallest difference in the dominant height of the relative number of thickest trees (h10% and h20%) was observed using the lower spatial resolution (2 m). The same trends also apply to diameters. The average errors at resolution of 1.0 and 1.5 m was 8.7%, 5.9% and 9.7% for mean height, h20% and h10%, respectively. ALS-derived diameters (obtained using regression models from reference data and ALS-derived individual height as predictor) showed absolute errors in the range 0-48% at all spatial resolutions. The deviation in mean diameter at a resolution of 0.5 m ranged from -12.1% to 15.3%.

Level set methods have been widely used in image processing and computer vision. In conventional level set formulations, the level set function typically develops irregularities during its evolution, which may cause numerical errors and eventually destroy the stability of the evolution. Therefore, a numerical remedy, called reinitialization, is typically applied to periodically replace the degraded level set function with a signed distance function. However, the practice of reinitialization not only raises serious problems as when and how it should be performed, but also affects numerical accuracy in an undesirable way. This paper proposes a new variational level set formulation in which the regularity of the level set function is intrinsically maintained during the level set evolution. The level set evolution is derived as the gradient flow that minimizes an energy functional with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such that the derived level set evolution has a unique forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level set function, particularly a signed distance profile near the zero level set. This yields a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization effect eliminates the need for reinitialization and thereby avoids its induced numerical errors. In contrast to complicated implementations of conventional level set formulations, a simpler and more efficient finite difference scheme can be used to implement the DRLSE formulation. DRLSE also allows the use of more general and efficient initialization of the level set function. In its numerical implementation, relatively large time steps can be used in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation, and provide a simple narrowband implementation to greatly reduce computational cost.

A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

In conventional level set methods, the slope of the level set function needs to be well controlled to maintain the numerical stability during the topology optimization process. One common solution is to regularize the level set function to be a signed distance function, which is usually achieved by periodically implementing the so called re-initialization scheme to force the level set function to gain the desired signed distance property. However, the re-initialization scheme will bring some unwanted drawbacks to the optimization process, such as zero level set drifting, time consuming etc. In addition, re-initialization is usually implemented outside the optimization loop, which will cause convergence issues. In this paper, a distance regularization functional is introduced to the structural topology optimization objective functional to ensure the signed distance property of the level set function near the structure boundaries. This functional can also keep the level set function to be constant-value at positions far away from the structural boundaries. The radial basis function (RBF) based parameterization technique together with the mathematical programming are utilized to improve the potential capability of handling multiple constraints for the topology optimization. The combination of these two techniques makes the level set based topology optimization be capable of handling complicated multi-constrained problems with higher numerical efficiency, leaving no compromise to multiple drawbacks. To demonstrate the validity of the proposed scheme, benchmark examples on minimum compliance structural optimization are employed. This type of problem is computed by the conventional level set method with the introduced distance regularization functional, the RBF based parametric level set and at last, the distance regularized RBF based parametric level set separately to demonstrate their differences.

A volume-amending method is developed both to keep the level set function as an algebraic distance function and to preserve the bubble mass in a level set approach for incompressible two-phase flows with the significantly deformed free interface. After the traditional reinitialization procedure, a volume-amending method is added for correcting the position of the interface according to mass loss/gain error until the mass error falls in the allowable range designated in advance. The level set approach with this volume-amending method incorporated has been validated by three test cases: the motion of a single axisymmetrical bubble or drop in liquid, the motion of a two-dimensional water drop falling through the air into a water pool, and the interactional motion of two buoyancy-driven threedimensional deformable bubbles. The computational results with this volume-amending method incorporated are in good agreement with the reported experimental data and the mass is well preserved in all cases.

An improved variational level set method for MR image segmentation and bias field correction

Computation of moving interface by the level set method typically requires the reinitialization of level set function. An inaccurate estimation of level set function φ results in incorrect free-surface capturing and thus errors such as mass gain/loss. Therefore, an accurate and robust reinitialization process is essential to the simulation of free-surface flows. In the present paper, we pursue further development of the reinitialization process, which evaluates level set function directly using a normal vector on the interface without solving the re-distancing equation of hyperbolic type. The Taylor-Galerkin approximation and P1P1 splitting/SUPG (Streamline Upwind Petrov-Galerkin) FEM are adopted to discretize advection equation of the level set function and the incompressible Navier-Stokes equation, respectively. Advection equation and re-initialization process of free surface capturing are validated with benchmark problems, i.e., a broken dam flow and timereversed single vortex flow. The simulation results are in good agreement with the existing results.

ABSTRACTDespite the large number of studies conducted during the last three decades concerning 3D building modelling starting from Light detection and ranging (Lidar) data, two persistent problems still exist. The first one is the absence of some roof details, which will not only disappear in the building roof model due to their small areas regarding the point density but are also considered as undesirable noise among the modelling procedures. The second problem consists in that the involved segmentation algorithms do not perform well in the presence of noise in the building point cloud data. These two problems generate undesirable deformation in the final 3D building model. This paper proposes a new automatic approach for detecting and modelling the missing roof details in addition to improving the building roof segments. In this context, the error map matrix, which presents the deviations of points to their fitting planes, is considered. Moreover, this matrix is analysed in order to deduce the mask of missing roof details. At this stage, a new numeric factor is defined for estimating the roof segmentation accuracy in addition to the validity of the roof segmentation result. Then, the building point cloud is enhanced in order to decrease the negative noise influence and, consequently, to improve the building roof segments. Finally, the functionality and the accuracy of the proposed approach are tested and discussed.