Fitting a smooth curve to 2D, a surface to 3D, and a manifold to 4D irregular point cloud data is becoming a common practice in many engineering and science applications. Piecewise-polynomial spline functions provide a powerful tool applicable to interpolation and approximation problems. This study presents the least squares B-spline approximation (LSBSA) theory, which is a generalized version of the spline interpolation and can be applied to any irregularly scattered point cloud data at knots specified by the user. The formulation allows to apply the well-established body of knowledge of least squares theory to the B-spline approximation. This for example has the benefit of embedding quality control measures such as hypothesis testing and proper error propagation to assess the quality of the approximation problem. The method is applicable to many 1D curve, 2D surface and 3D manifold fitting problems of which both simulated and real data are used to illustrate the efficacy of the proposed theory. In particular, its real-world applications to multi-beam echo-sounder bathymetric data, digital terrain modeling and Greenland ice sheet deformation monitoring will be highlighted. The performance of the method for linear, quadratic, cubic and quartic spline functions will be investigated. The primary application of LSBSA lies in its ability to perform 3D manifold fitting for deformation monitoring. This capability provides the possibility of monitoring changes in continuous spatial and temporal domains. The Python and Matlab source codes of LSBSA are freely accessible at https://github.com/tudelft4d/lsbsa.

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Open source Global Digital Elevation Models (GDEMs) serve as an important base for studies in geosciences. However, these models contain vertical errors due to various reasons. In this study, data from two Satellite LiDAR altimetry systems, GEDI and ICESat-2, were used to improve the vertical accuracy of GDEMs. Three different machine learning methods, namely an Artificial Neural Network (ANN), Extreme Gradient Boosting (XGBoost), and a Convolutional Neural Network (CNN), were employed to improve existing DEM data with satellite LiDAR data. The methodology was tested in five areas with varying characteristics. Ground control data were selected from high accuracy DEMs generated from Airborne LiDAR and GNSS data. The use of ANN method improved the vertical accuracy of SRTM data from 6.45 to 3.72 m in Test area-4. Similarly, the CNN method demonstrated an improvement in the vertical accuracy of bare ground SRTM data increasing from 3.4 to 0.6 m in Test area-4. In Test area-5, the ANN method improved the vertical accuracy of SRTM data with slopes between 30 and 60%, increasing from 3.8 to 0.5 m. Notably, the results underscore the successful improvement of GDEMs across all test areas.@en

Detailed 3D information on vulnerable archaeological sites can document cultural heritage and contribute to its preservation. The Late Bronze Age Mycenaean cemetery of Aidonia, Greece, is a representative case of a vulnerable site. Tomb looting has occurred sporadically since the 1970s, when the Greek government was made aware of the site. Anthropogenic activities and natural denudation may affect the loss of structural integrity of tombs. In this contribution, terrestrial laser scanning and geosciences are combined to document the vulnerable cemetery through the generation of a tomb catalogue. The emphasis is on techniques applied to point clouds to extract architectural elements. The catalogue consists of 208 architectural and geological measurements, 112 qualitative observations, maps, and point clouds images displaying the architecture of 16 tombs. The tombs are mainly orientated northeast-southwest and northwest-southeast, and their average total length is 13 m. The average volume of chambers with preserved roofs is 46 m3.

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The paper presents a new dry-dock method for assessing the deformation of submarine hulls using TLS point cloud data and the point cloud spatial expansion method (PCSE). The advantage of the proposed approach is the high-resolution deformation analysis that can be conducted in the case of both the availability and a lack of technical documentation on the submarine hull. The geometry assessment involves two-plane hull symmetry in longitudinal sections of a tested Kobben-class submarine located in Gdynia, Poland. The features of PCSE introduce additional geometrical parameters that are not available in the original point cloud method. The procedure for local fitting of a plane into the expansion eliminates the problem of varying densities of the hull point cloud. Accuracies of several millimetres are achieved and are applicable to multi-temporal monitoring of the deformations of submarine hulls. The assessment of similar deformations is not possible in the original point cloud method, due to the unknown parameters of the orientation and curvature of the convex cylindrical hull surface. The PCSE-based parameterisation presented here enables the creation of alternative quasi-planar point cloud projections to extract new spatial information on the object. The results of this study were verified using theoretical values derived from design data on the Kobben-class submarine, and demonstrated the effectiveness of our method in terms of detecting deformations even without design references. The proposed methodology is uniform, and can be adapted to other symmetrical structures.@en

Shoreward sand transport and dune development are increasingly influenced by the urbanization of beach-dune systems in the Netherlands. Three topographic datasets, on various spatio-temporal scales, are used to study the effect of standalone buildings on long term local dune development. On the smallest scale, terrestrial laser scans are used to study the geomorphological effects of two sea containers on the beach. On the intermediate scale, the geomorphological effects of a beach pavilion on the local dune development are studied with a 2-year topographic dataset of (bi) monthly permanent laser scans. Finally, 15 yearly airborne lidar scans of the beach-dune system in Noordwijk are used to evaluate the effect of multiple beach pavilions on dune growth variations. The small-scale experiment shows that horseshoe-shaped deposition patterns developed on the leeside of the containers. These depositions follow daily wind changes and leave deposits corresponding to the residual wind direction over the whole measuring period. Similar patterns are found around the larger beach pavilion, but anthropogenic activities like bulldozing and beach shaping make the determination of the effect on dune development harder to discern. Evaluation of the longer-term dataset reveals large variations in dune height and volume around beach pavilions. Dune height/volume increases vary between 1 and 8 m in height and 0–200 m3 in volume. A variability analysis shows that the length scale of alongshore variability in dune height/volume of urbanized dunes can be 10 times smaller than for natural dunes. For about half the beach pavilions, variations in dune height and volume are significantly correlated to the location of beach pavilions but correlation to particular beach pavilion properties is yet inconclusive.

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Sandy beach-dune systems make up a large part of coastal areas world wide. Their function as an eco-system as well as a protective barrier for human and natural habitat is under increased threat due to climate change. A thorough understanding of change processes at the sediment surface is essential to facilitate prediction of future development and management strategies to maintain their function. Especially slow and small scale processes happening over several days up to weeks at cm level, such as aeolian sand transport are difficult to identify and analyse. Permanent laser scanning (PLS) is a useful tool in the study and analysis of coastal processes as it captures a data representation of the evolution of the sediment surface over extended periods of time (up to several years) with high detail (at cm-dm level). The PLS data set considered for this study, consists of hourly acquired 3D point clouds representing the surface evolution of a section of the Dutch coast during three years. However, it is challenging to extract concrete information on specific change processes from the large and complex PLS data set. We use multiple hypothesis testing in order to reduce the PLS data set to a so-called inventory of trends, consisting of 12.8 million partial time series with associated rate of change and elevation. The inventory of trends proofs to be a suitable tool to identify natural processes such as storms and aeolian sand transport in our test area in the aeolian zone of a sandy beach-dune system on the Dutch coast. We identify these processes and provide a tool to derive summarising data from the complex PLS data set. We find that all partial time series identified as most likely representing aeolian sand transport, result in 1354 m³ of sand deposition in our study area over the course of three years. We also show a comparison with transects from JarKus data and find a correlation between anthropogenic activities and erosion in our test area with a correlation coefficient of 0.3.

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The TriMetrogon Aerial (TMA) archive is an archive of historical images of Antarctica taken by the US Navy between 1940 and 2000 with analogue cameras. The analysis of such historic data can give a view of Antarctica's glaciers predating modern satellite imagery and provide unique insights into the long-term impact of changing climate conditions with essential validation data for climate modelling. However, the lack of semantic information for these images presents a challenge for large-scale computer-driven analysis. Such information can be added to the data using semantic segmentation, but traditional algorithms fail on these scanned historical grayscale images, due to varying image quality, lack of colour information and artefacts in the images. To address this, we present a deep-learning-based U-net workflow. Our approach includes creating training data by pre-processing and labelling the raw images. Furthermore, different versions of the U-net are trained to optimize its hyperparameters and augmentation methods. With the optimal hyper-parameters and augmentation methods, a final model has been trained for a use-case to segment 118 images covering Adelaide Island. We tested our approach by segmenting challenging historical images using a U-net model with just 80 training images, achieving an accuracy of 73% for 20 validation images. While no test data is available for our use case, a visual examination of the segmented images shows that our method performs effectively. The comparison of the hyper-parameters and augmentation methods provides directions for training other U-net-based models so that the presented workflow can be used to segment other archives with historical imagery. Additionally, the labelled training data and the segmented images of the test are publicly available at https://github.com/fdahle/antarctic_segmentation.

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Inspired by the attractive features of least-squares theory in many practical applications, this contribution introduces least-squares-based deep learning (LSBDL). Least-squares theory connects explanatory variables to predicted variables, called observations, through a linear(ized) model in which the unknown parameters of this relation are estimated using the principle of least-squares. Conversely, deep learning (DL) methods establish nonlinear relationships for applications where predicted variables are unknown (nonlinear) functions of explanatory variables. This contribution presents the DL formulation based on least-squares theory in linear models. As a data-driven method, a network is trained to construct an appropriate design matrix of which its entries are estimated using two descent optimization methods: steepest descent and Gauss–Newton. In conjunction with interpretable and explainable artificial intelligence, LSBDL leverages the well-established least-squares theory for DL applications through the following three-fold objectives: (i) Quality control measures such as covariance matrix of predicted outcome can directly be determined. (ii) Available least-squares reliability theory and hypothesis testing can be established to identify mis-specification and outlying observations. (iii) Observations’ covariance matrix can be exploited to train a network with inconsistent, heterogeneous and statistically correlated data. Three examples are presented to demonstrate the theory. The first example uses LSBDL to train coordinate basis functions for a surface fitting problem. The second example applies LSBDL to time series forecasting. The third example showcases a real-world application of LSBDL to downscale groundwater storage anomaly data. LSBDL offers opportunities in many fields of geoscience, aviation, time series analysis, data assimilation and data fusion of multiple sensors.

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Coastal dunes provide an important role to society by fulfilling various ecosystem functions. These are however under pressure due to sea level rise, climate change and urbanization. Shoreward sand transport can partly mitigate sea level rise and climate effects by contributing to dune growth but increasing urbanization of beaches can block this transport and restoration of ecosystem functions. In this paper, we investigate the long-term effects of buildings and other anthropogenic influences on dune development up to a decadal temporal scale. A series of three topographic datasets is used to study the effect of anthropogenic actors on local dune development at an urban beach in Noordwijk, the Netherlands. Datasets range from a 100 to 3000-meter spatial scale and from a weekly to yearly temporal scale. On the smallest spatio-temporal scale topographic measurements of the effects of two containers placed on Noordwijk beach are studied. The intermediate dataset is obtained from the 2-year CoastScan project monitoring surface elevation around one beach pavilion at (bi) monthly intervals. Finally, 15 years of annual airborne lidar data along a 2.7-kilometer stretch of the beach/dune system in Noordwijk is used to evaluate the effect of 17 pavilions. The small-scale experiment shows that horseshoe-shaped deposition patterns developed on the leeside of the containers. These depositions follow daily wind changes and leave deposits corresponding to the residual wind direction over the whole measuring period. Similar patterns are found around the beach pavilion, but, due to anthropogenic influences like bulldozing and beach shaping, longer term patterns in the direct vicinity of the pavilion and the dunes are hard to discern. Evaluation of the longer term dataset reveals large variations in dune height and volume in the neighborhood of beach pavilions. Dune height/volume increases vary between 1-8 m in dune height and vary between 0-200 m3 in dune volume after 15 years along 2.7 km of coast. An autocorrelation analysis shows that the alongshore variability length scale in dune volume of urbanized dunes can be 10 times smaller than for natural dunes. For about half the beach pavilions, variations in dune height and volume are significantly correlated to the location of the beach pavilion. Here the growth behind the buildings is lower than in the surrounding area which might have consequences for long-term resilience against future climate changes.@en

The utility of historical image repositories is often limited due to the lack of geo-referencing. A good example is the TriMetrogon Aerial (TMA) archive, a collection of historical aerial images of Antarctica between 1940 and 2000. These images are difficult to use, as their geolocation is only approximately, with location errors in the order of tens of km. This study addresses this challenge by developing an automated geo-referencing workflow that leverages recent advancements in machine-learning-based tie-point matching. We use the algorithm LightGlue, to establish tie-points between geo-referenced Sentinel-2 satellite imagery and historical non-geo-referenced aerial images. To aid the process, we use already known approximate positions of the historical images. Due to the sub-optimal and inhomogeneous quality of the aerial images, only a portion of the images can be geo-referenced directly by matching. For the remaining images, we employed alternative means of geo-referencing, again based on tie-point matching. Out of a subset of 4,459 images located inside the research area, 3,393 images could be geo-referenced, a percentage of 76%. Reasons for the geo-referencing failing are insufficient contrast or an approximate position too far away from the real position. The workflow can easily be applied to historical images from other archives, to enhance the usability of historical image repositories for scientific research.

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Sandy beaches are subject to changes due to multiple factors, that are both natural (e.g. storms) and anthropogenic. Great efforts are being made to monitor these ecosystems and understand their dynamics in order to assure their conservation. The identification of anthropogenic changes and its differentiation from natural ones is an important task for coastal monitoring. In this study, we present a methodology for the detection of anthropogenic changes in a coastal ecosystem by automatically detecting active bulldozers in continuous beach video data. PCA is used to highlight changes in consecutive images due to moving objects. Next, the YOLO object detection algorithm is used to identify the bulldozers in the change images. YOLO was specifically trained for the task, obtaining a precision of 0.94 and a recall of 0.81. An automatic tool was developed, and the process was carried out on two months of video data, consisting of approximately 19 000 images. The resulting information was compared with changes derived from 3D data obtained from a permanent laser scanner. The correlation among the results of the two methodologies was computed. For a validation area and daily time frame a correlation of 0.88 was obtained between the number of detected bulldozers and the area affected by changes in height larger than 0.3 m.

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In the view of climate change, understanding and managing effects on coastal areas and adjacent cities is essential. Permanent Laser Scanning (PLS) is a successful technique to not only observe notably sandy coasts incidentally or once every year, but (nearly) continuously over extended periods of time. The collected point cloud observations form a 4D point cloud data set representing the evolution of the coast provide the opportunity to assess change processes at high level of detail. For an exemplary location in Noordwijk, The Netherlands, three years of hourly point clouds were acquired on a 1 km long section of a typical Dutch urban sandy beach. Often, the so-called level of detection is used to assess point cloud differences from two epochs. To explicitly incorporate the temporal dimension of the height estimates from the point cloud data set, we revisit statistical testing theory. We apply multiple hypothesis testing on elevation time series in order to identify different coastal processes, like aeolian sand transport or bulldozer works. We then estimate the minimal detectable bias for different alternative hypotheses, to quantify the minimal elevation change that can be estimated from the PLS observations over a certain period of time. Additionally, we analyse potential error sources and influences on the elevation estimations and provide orders of magnitudes and possible ways to deal with them. Finally we conclude that elevation time series from a long term PLS data set are a suitable input to identify aeolian sand transport with the help of multiple hypothesis testing. In our example case, slopes of 0.032 m/day and sudden changes of 0.031 m can be identified with statistical power of 80% and with 95% significance in 24-h time series on the upper beach. In the intertidal area the presented method allows to classify daily elevation time series over one month according to the dominating model (sudden change or linear trend) in either eroding or accreting behaviour.

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Church towers are key cultural heritage. In theory, towers are vertical, while facade elements are symmetrically positioned around the tower axis. However, during service of a structure, building and lifetime conditions cause deviations, with associated risks. Laser scanning point clouds can be used to assess the structural state but a universal approach was missing. The proposed algorithm first estimates the tower inclination, and tests which multi-axis representation best represents the course of the tower. Next, point cloud spatial expansion recovers relative distances and deviations of facade elements. The resulting procedure was applied to assess two Dutch medieval towers including the Old Church in Delft and the St. Bavo Church in Haarlem, respectively. As results of analysis, significant asymmetry was found with a 1.4° deviation of the multi-modal axis of the St. Bavo Church tower together with variations of 0.1%–1.5% for facade slopes, while 0.1°–3.1° radial deviations were found in the position of the turrets of the Old Church tower.

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Landslides are one of the major weather-related geohazards. To assess their potential impact and design mitigation solutions, a detailed understanding of the slope processes is required. Landslide modelling is typically based on data-rich geomechanical models. Recently, machine learning has shown promising results in modelling a variety of processes. Furthermore, slope conditions are now also monitored from space, in wide-area repeat surveys from satellites. In the present study we tested if use of machine learning, combined with readily available remote sensing data, allows us to build a deformation nowcasting model. A successful landslide deformation nowcast, based on remote sensing data and machine learning, would demonstrate effective understanding of the slope processes, even in the absence of physical modelling. We tested our methodology on the Vögelsberg, a deep-seated landslide near Innsbruck, Austria. Our results show that the formulation of such a machine learning system is not as straightforward as often hoped for. The primary issue is the freedom of the model compared to the number of acceleration events in the time series available for training, as well as inherent limitations of the standard quality metrics such as the mean squared error. Satellite remote sensing has the potential to provide longer time series, over wide areas. However, although longer time series of deformation and slope conditions are clearly beneficial for machine-learning-based analyses, the present study shows the importance of the training data quality but also that this technique is mostly applicable to the well-monitored, more dynamic deforming landslides.@en

The evolution and spreading of data capturing methods ranging from simple GPS devices like smart-phones to large scale imaging equipment – including very high resolution and hyperspectral cameras and LiDAR – resulted in an exponential growth in the amount of spatial data maintained by companies and organizations. At the same time methods for extracting information from such data are often behind in efficiency. In this paper we analyse the possibilities for nation-wide change detection of massive airborne laser altimetry point clouds, based on digital elevation models generated from them. The proposed workflow distinguishes modifications in the built-up area from other changes and noise. Our methodology combines different area processing spatial algorithms: object detection, noise filtering, morphological operations and clustering. Our proposed method is designed to scale dynamically on extensive datasets by processing a spatially partitioned input dataset in an easily parallelized manner. Favourable visualizations and aggregated representations of the results are examined, followed by a discussion of feasible validation methods. As a demonstration we showcase the implemented distributed evaluation of our workflow on the full Dutch altimetry archive – a dataset exceeding several terabytes of storage space – using a high-performance computing environment. While the average execution time was 47 h on a desktop computer, our solution only took less than 2.4 h to complete. The output was validated against the building layer of the TOP10NL topographic dataset, proving a 70% accuracy nation-wide and over 90% for urban areas. As a result our analysis shows that The Netherlands experienced an aggregated building volume change of 912.33 km³ between the acquisition of AHN-2 and AHN-3.

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Global Ecosystem Dynamics Investigate (GEDI) is a spaceborne laser altimeter system used for earth observation in many areas such as forest canopy, water level and terrain height estimation. GEDI data is affected by atmospheric effects due to the sensor used while observing. In this study, we propose a 7-step, multi-variable strategy for determining the elevation of the terrain with GEDI. These steps involve both different geoid models, GEDI ancillary data, and topographic features. We evaluated the effect of each step using high quality DEM data obtained by Airborne LiDAR over the central part of Puerto Rico, where building areas and forests are dominant, while the terrain has an average slope of 24%. The GEDI data of the test area consists of 3 different orbits (O06225, O07933, O08061) with different solar elevation and cloudiness rates. While the raw data of orbit O06225, obtained during a solar elevation of 8.4 and cloudy conditions, has a Root Mean Square Error (RMSE) of 418.67 m., the RMSE is reduced to 4.59 m. after applying all seven filtering steps. The raw data of orbit O07933, obtained with a solar elevation of 50.5 during cloud free conditions, has a RMSE of 10.04 m., and is reduced to a similar value of 4.8 m. as a result of the filtering steps. On the other hand, orbit O08061 was obtained with little clouds during a near-dawn solar elevation of -0.7. Its raw RMSE of 50,34 m could only be reduced to 12.41 m. by the proposed filtering procedure. It is concluded that although there are many outliers in data acquired during cloudy conditions, the accuracy of the data remaining after applying our filtering strategy can be as high as the accuracy obtained during cloud free conditions. Better results than 5 m were obtained according to the RMSE in areas with low solar elevation. In addition, it is observed that accuracy decreases strongly when the solar elevation is close to 0. Overall, it is concluded that appropriate filtering is required when determining terrain height with GEDI data.

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In construction projects, inspection of structural components mostly relies on classical measurements obtained by measuring tapes, levelling, or total stations. With those methods, only a few points on the structure can be measured, and the resulting inspection may not fully reflect the actual, detailed condition of the complete object. Laser scanning is an emerging remote sensing technology to accurately and quickly capture surfaces of structures in high details. However, because of the complex, massive point cloud data acquired at a construction project, in practice, data processing is still manual work with computer aided programs. To improve upon current workflows, this paper proposes a method to automatically extract point clouds of individual surfaces of structural components of a concrete building, which subsequently can be used to inspect construction quality based on geometric information of the surfaces. The proposed method explores both spatial point cloud information and contextual knowledge of structures (e.g., orientation or shape) derived from building design specifications and practice. For extracting point clouds of surfaces of each structural component, the proposed method consists of 4 consecutive steps for extracting: (1) floors, ceiling slabs, and walls, (2) columns, and (3) primary and (4) secondary beams. Each step consists of two ingredients: (i) rough extracting the candidate points of the component and (ii) fine filtering of the surface points of the components via cell-based and voxel-based region growing segmentation (CRG and VRG) incorporating contextual knowledge of the structural members. Experimental tests on two different types of concrete buildings showed that the proposed method successfully extracts the structural elements, in which the completeness, correctness, and quality from the point-based evaluation are larger than 96.0%, 96.9%, and 92.0%, respectively. Moreover, the evaluation based on a shape similarity showed that the extracted floor, ceiling slab and wall overlap to the ground truth more than 92.5%.

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Landslides are a major geohazard in hilly and mountainous environments. In-situ inspection of downslope motion is costly, sometimes dangerous and, requires prior knowledge of the existence of a landslide. Remote sensing from space is a way to detect and characterize landslides systematically at large scale. Interferometric Synthetic Aperture Radar (InSAR) has shown to be a valuable resource of deformation information, but it requires expert knowledge and considerable computational efforts. Moreover, the successful application of InSAR for landslides requires a favorable acquisition geometry relative to the landslide deformation pattern. Consequently, there is a need for a widely applicable tool to assess the potential of InSAR at a particular location a priori. Here we present a novel, generic approach to assess the potential of InSAR-based deformation tracking, providing a standardised and automated method applicable on any slope. We define the detection potential as the sensitivity of InSAR to detect downslope displacement combined with the presence of coherently scattering surfaces. We show that deformation can be detected on at least 91% of the global landslide-prone slopes, and provide an open source Google Earth Engine tool for the quick assessment of the availability of potential coherent scatterers. This tool enables any person interested in applying InSAR to routinely assess the potential for monitoring landslide deformation in their region of interest.@en

Precise and accurate delineation of flooding areas with synthetic aperture radar (SAR) and multi-spectral (MS) data is challenging because flooded areas are inherently heterogeneous as emergent vegetation (EV) and turbid water (TW) are common. We addressed these challenges by developing and applying a new stepwise sequence of unsupervised and supervised classification methods using both SAR and MS data. The MS and SAR signatures of land and water targets in the study area were evaluated prior to the classification to identify the land and water classes that could be delineated. The delineation based on a simple thresholding method provided a satisfactory estimate of the total flooded area but did not perform well on heterogeneous surface water. To deal with the heterogeneity and fragmentation of water patches, a new unsupervised classification approach based on a combination of thresholding and segmentation (CThS) was developed. Since sandy areas and emergent vegetation could not be classified by the SAR-based unsupervised methods, supervised random forest (RF) classification was applied to a time series of SAR and co-event MS data, both combined and separated. The new stepwise approach was tested for determining the flood extent of two events in Italy. The results showed that all the classification methods applied to MS data outperformed the ones applied to SAR data. Although the supervised RF classification may lead to better accuracies, the CThS (unsupervised) method achieved precision and accuracy comparable to the RF, making it more appropriate for rapid flood mapping due to its ease of implementation.@en

Most deep learning (DL) methods that are not end-to-end use several multi-scale and multi-type hand-crafted features that make the network challenging, more computationally intensive and vulnerable to overfitting. Furthermore, reliance on empirically-based feature dimensionality reduction may lead to misclassification. In contrast, efficient feature management can reduce storage and computational complexities, builds better classifiers, and improves overall performance. Principal Component Analysis (PCA) is a well-known dimension reduction technique that has been used for feature extraction. This paper presents a two-step PCA based feature extraction algorithm that employs a variant of feature-based PointNet (Qi et al., 2017a) for point cloud classification. This paper extends the PointNet framework for use on large-scale aerial LiDAR data, and contributes by (i) developing a new feature extraction algorithm, (ii) exploring the impact of dimensionality reduction in feature extraction, and (iii) introducing a non-end-to-end PointNet variant for per point classification in point clouds. This is demonstrated on aerial laser scanning (ALS) point clouds. The algorithm successfully reduces the dimension of the feature space without sacrificing performance, as benchmarked against the original PointNet algorithm. When tested on the well-known Vaihingen data set, the proposed algorithm achieves an Overall Accuracy (OA) of 74.64% by using 9 input vectors and 14 shape features, whereas with the same 9 input vectors and only 5PCs (principal components built by the 14 shape features) it actually achieves a higher OA of 75.36% which demonstrates the effect of efficient dimensionality reduction.

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